Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

Optimized phase gradient measurements and phase-amplitude interplay in optical coherence elastography

NASA Astrophysics Data System (ADS)

Zaitsev, Vladimir Y.; Matveyev, Alexander L.; Matveev, Lev A.; Gelikonov, Grigory V.; Sovetsky, Aleksandr A.; Vitkin, Alex

2016-11-01

In compressional optical coherence elastography, phase-variation gradients are used for estimating quasistatic strains created in tissue. Using reference and deformed optical coherence tomography (OCT) scans, one typically compares phases from pixels with the same coordinates in both scans. Usually, this limits the allowable strains to fairly small values < to 10-3, with the caveat that such weak phase gradients may become corrupted by stronger measurement noises. Here, we extend the OCT phase-resolved elastographic methodology by (1) showing that an order of magnitude greater strains can significantly increase the accuracy of derived phase-gradient differences, while also avoiding error-phone phase-unwrapping procedures and minimizing the influence of decorrelation noise caused by suprapixel displacements, (2) discussing the appearance of artifactual stiff inclusions in resultant OCT elastograms in the vicinity of bright scatterers due to the amplitude-phase interplay in phase-variation measurements, and (3) deriving/evaluating methods of phase-gradient estimation that can outperform conventionally used least-square gradient fitting. We present analytical arguments, numerical simulations, and experimental examples to demonstrate the advantages of the proposed optimized phase-variation methodology.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

NASA Astrophysics Data System (ADS)

Featherstone, W. E.; McCubbine, J. C.; Brown, N. J.; Claessens, S. J.; Filmer, M. S.; Kirby, J. F.

2018-02-01

We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, land and altimeter-derived gravity anomalies and terrain corrections. The model has been extended to include Australia's offshore territories and maritime boundaries using newer datasets comprising an additional {˜ }280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at 1^' ' }× 1^' ' } resolution. The error propagation uses a remove-restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50-60 mm across most of the Australian landmass, increasing to {˜ }100 mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates.

Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints.

PubMed

Kuldeep, B; Singh, V K; Kumar, A; Singh, G K

2015-01-01

In this article, a novel approach for 2-channel linear phase quadrature mirror filter (QMF) bank design based on a hybrid of gradient based optimization and optimization of fractional derivative constraints is introduced. For the purpose of this work, recently proposed nature inspired optimization techniques such as cuckoo search (CS), modified cuckoo search (MCS) and wind driven optimization (WDO) are explored for the design of QMF bank. 2-Channel QMF is also designed with particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization techniques. The design problem is formulated in frequency domain as sum of L2 norm of error in passband, stopband and transition band at quadrature frequency. The contribution of this work is the novel hybrid combination of gradient based optimization (Lagrange multiplier method) and nature inspired optimization (CS, MCS, WDO, PSO and ABC) and its usage for optimizing the design problem. Performance of the proposed method is evaluated by passband error (ϕp), stopband error (ϕs), transition band error (ϕt), peak reconstruction error (PRE), stopband attenuation (As) and computational time. The design examples illustrate the ingenuity of the proposed method. Results are also compared with the other existing algorithms, and it was found that the proposed method gives best result in terms of peak reconstruction error and transition band error while it is comparable in terms of passband and stopband error. Results show that the proposed method is successful for both lower and higher order 2-channel QMF bank design. A comparative study of various nature inspired optimization techniques is also presented, and the study singles out CS as a best QMF optimization technique. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

Objective sea level pressure analysis for sparse data areas

NASA Technical Reports Server (NTRS)

Druyan, L. M.

1972-01-01

A computer procedure was used to analyze the pressure distribution over the North Pacific Ocean for eleven synoptic times in February, 1967. Independent knowledge of the central pressures of lows is shown to reduce the analysis errors for very sparse data coverage. The application of planned remote sensing of sea-level wind speeds is shown to make a significant contribution to the quality of the analysis especially in the high gradient mid-latitudes and for sparse coverage of conventional observations (such as over Southern Hemisphere oceans). Uniform distribution of the available observations of sea-level pressure and wind velocity yields results far superior to those derived from a random distribution. A generalization of the results indicates that the average lower limit for analysis errors is between 2 and 2.5 mb based on the perfect specification of the magnitude of the sea-level pressure gradient from a known verification analysis. A less than perfect specification will derive from wind-pressure relationships applied to satellite observed wind speeds.

b matrix errors in echo planar diffusion tensor imaging

PubMed Central

Boujraf, Saïd; Luypaert, Robert; Osteaux, Michel

2001-01-01

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) is a recognized tool for early detection of infarction of the human brain. DW‐MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion‐weighted images with different values of b matrix are acquired during one individual investigation, it is possible to calculate apparent diffusion coefficient maps that are the elements of the diffusion tensor. The diffusion tensor elements represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relation between signal intensity in the diffusion‐weighted images, diffusion tensor, and b matrix is derived from the Bloch equations. Our goal is to establish the magnitude of the error made in the calculation of the elements of the diffusion tensor when the imaging gradients are ignored. PACS number(s): 87.57. –s, 87.61.–c PMID:11602015

Image Motion Detection And Estimation: The Modified Spatio-Temporal Gradient Scheme

NASA Astrophysics Data System (ADS)

Hsin, Cheng-Ho; Inigo, Rafael M.

1990-03-01

The detection and estimation of motion are generally involved in computing a velocity field of time-varying images. A completely new modified spatio-temporal gradient scheme to determine motion is proposed. This is derived by using gradient methods and properties of biological vision. A set of general constraints is proposed to derive motion constraint equations. The constraints are that the second directional derivatives of image intensity at an edge point in the smoothed image will be constant at times t and t+L . This scheme basically has two stages: spatio-temporal filtering, and velocity estimation. Initially, image sequences are processed by a set of oriented spatio-temporal filters which are designed using a Gaussian derivative model. The velocity is then estimated for these filtered image sequences based on the gradient approach. From a computational stand point, this scheme offers at least three advantages over current methods. The greatest advantage of the modified spatio-temporal gradient scheme over the traditional ones is that an infinite number of motion constraint equations are derived instead of only one. Therefore, it solves the aperture problem without requiring any additional assumptions and is simply a local process. The second advantage is that because of the spatio-temporal filtering, the direct computation of image gradients (discrete derivatives) is avoided. Therefore the error in gradients measurement is reduced significantly. The third advantage is that during the processing of motion detection and estimation algorithm, image features (edges) are produced concurrently with motion information. The reliable range of detected velocity is determined by parameters of the oriented spatio-temporal filters. Knowing the velocity sensitivity of a single motion detection channel, a multiple-channel mechanism for estimating image velocity, seldom addressed by other motion schemes in machine vision, can be constructed by appropriately choosing and combining different sets of parameters. By applying this mechanism, a great range of velocity can be detected. The scheme has been tested for both synthetic and real images. The results of simulations are very satisfactory.

Approximate error conjugation gradient minimization methods

DOEpatents

Kallman, Jeffrey S

2013-05-21

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

[Accurate 3D free-form registration between fan-beam CT and cone-beam CT].

PubMed

Liang, Yueqiang; Xu, Hongbing; Li, Baosheng; Li, Hongsheng; Yang, Fujun

2012-06-01

Because the X-ray scatters, the CT numbers in cone-beam CT cannot exactly correspond to the electron densities. This, therefore, results in registration error when the intensity-based registration algorithm is used to register planning fan-beam CT and cone-beam CT. In order to reduce the registration error, we have developed an accurate gradient-based registration algorithm. The gradient-based deformable registration problem is described as a minimization of energy functional. Through the calculus of variations and Gauss-Seidel finite difference method, we derived the iterative formula of the deformable registration. The algorithm was implemented by GPU through OpenCL framework, with which the registration time was greatly reduced. Our experimental results showed that the proposed gradient-based registration algorithm could register more accurately the clinical cone-beam CT and fan-beam CT images compared with the intensity-based algorithm. The GPU-accelerated algorithm meets the real-time requirement in the online adaptive radiotherapy.

Do We Really Need Sinusoidal Surface Temperatures to Apply Heat Tracing Techniques to Estimate Streambed Fluid Fluxes?

NASA Astrophysics Data System (ADS)

Luce, C. H.; Tonina, D.; Applebee, R.; DeWeese, T.

2017-12-01

Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes, thermal conductivity, or bed surface elevation from temperature time series in streambeds are that the solution assumes that 1) the surface boundary condition is a sine wave or nearly so, and 2) there is no gradient in mean temperature with depth. Concerns on these subjects are phrased in various ways, including non-stationarity in frequency, amplitude, or phase. Although the mathematical posing of the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we re-derive the inverse solution of the 1-D advection-diffusion equation starting with an arbitrary surface boundary condition for temperature. In doing so, we demonstrate the frequency-independence of the solution, meaning any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes, gradients in the mean temperature with depth, or `non-stationary' amplitude and frequency (or phase) do not actually represent violations of assumptions, and they should not cause errors in estimates when using one of the suite of existing solution methods derived based on a single frequency. Misattribution of errors to these issues constrains progress on solving real sources of error. Numerical and physical experiments are used to verify this conclusion and consider the utility of information at `non-standard' frequencies and multiple frequencies to augment the information derived from time series of temperature.

Density interface topography recovered by inversion of satellite gravity gradiometry observations

NASA Astrophysics Data System (ADS)

Ramillien, G. L.

2017-08-01

A radial integration of spherical mass elements (i.e. tesseroids) is presented for evaluating the six components of the second-order gravity gradient (i.e. second derivatives of the Newtonian mass integral for the gravitational potential) created by an uneven spherical topography consisting of juxtaposed vertical prisms. The method uses Legendre polynomial series and takes elastic compensation of the topography by the Earth's surface into account. The speed of computation of the polynomial series increases logically with the observing altitude from the source of anomaly. Such a forward modelling can be easily applied for reduction of observed gravity gradient anomalies by the effects of any spherical interface of density. An iterative least-squares inversion of measured gravity gradient coefficients is also proposed to estimate a regional set of juxtaposed topographic heights. Several tests of recovery have been made by considering simulated gradients created by idealistic conical and irregular Great Meteor seamount topographies, and for varying satellite altitudes and testing different levels of uncertainty. In the case of gravity gradients measured at a GOCE-type altitude of ˜ 300 km, the search converges down to a stable but smooth topography after 10-15 iterations, while the final root-mean-square error is ˜ 100 m that represents only 2 % of the seamount amplitude. This recovery error decreases with the altitude of the gravity gradient observations by revealing more topographic details in the region of survey.

3D joint inversion of gravity-gradient and borehole gravity data

NASA Astrophysics Data System (ADS)

Geng, Meixia; Yang, Qingjie; Huang, Danian

2017-12-01

Borehole gravity is increasingly used in mineral exploration due to the advent of slim-hole gravimeters. Given the full-tensor gradiometry data available nowadays, joint inversion of surface and borehole data is a logical next step. Here, we base our inversions on cokriging, which is a geostatistical method of estimation where the error variance is minimised by applying cross-correlation between several variables. In this study, the density estimates are derived using gravity-gradient data, borehole gravity and known densities along the borehole as a secondary variable and the density as the primary variable. Cokriging is non-iterative and therefore is computationally efficient. In addition, cokriging inversion provides estimates of the error variance for each model, which allows direct assessment of the inverse model. Examples are shown involving data from a single borehole, from multiple boreholes, and combinations of borehole gravity and gravity-gradient data. The results clearly show that the depth resolution of gravity-gradient inversion can be improved significantly by including borehole data in addition to gravity-gradient data. However, the resolution of borehole data falls off rapidly as the distance between the borehole and the feature of interest increases. In the case where the borehole is far away from the target of interest, the inverted result can be improved by incorporating gravity-gradient data, especially all five independent components for inversion.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

PubMed

Xu, Dongpo; Xia, Yili; Mandic, Danilo P

2016-02-01

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.

Analysis of the numerical differentiation formulas of functions with large gradients

NASA Astrophysics Data System (ADS)

Tikhovskaya, S. V.

2017-10-01

The solution of a singularly perturbed problem corresponds to a function with large gradients. Therefore the question of interpolation and numerical differentiation of such functions is relevant. The interpolation based on Lagrange polynomials on uniform mesh is widely applied. However, it is known that the use of such interpolation for the function with large gradients leads to estimates that are not uniform with respect to the perturbation parameter and therefore leads to errors of order O(1). To obtain the estimates that are uniform with respect to the perturbation parameter, we can use the polynomial interpolation on a fitted mesh like the piecewise-uniform Shishkin mesh or we can construct on uniform mesh the interpolation formula that is exact on the boundary layer components. In this paper the numerical differentiation formulas for functions with large gradients based on the interpolation formulas on the uniform mesh, which were proposed by A.I. Zadorin, are investigated. The formulas for the first and the second derivatives of the function with two or three interpolation nodes are considered. Error estimates that are uniform with respect to the perturbation parameter are obtained in the particular cases. The numerical results validating the theoretical estimates are discussed.

Test of Shi et al. Method to Infer the Magnetic Reconnection Geometry from Spacecraft Data: MHD Simulation with Guide Field and Antiparallel Kinetic Simulation

NASA Technical Reports Server (NTRS)

Denton, R.; Sonnerup, B. U. O.; Swisdak, M.; Birn, J.; Drake, J. F.; Heese, M.

2012-01-01

When analyzing data from an array of spacecraft (such as Cluster or MMS) crossing a site of magnetic reconnection, it is desirable to be able to accurately determine the orientation of the reconnection site. If the reconnection is quasi-two dimensional, there are three key directions, the direction of maximum inhomogeneity (the direction across the reconnection site), the direction of the reconnecting component of the magnetic field, and the direction of rough invariance (the "out of plane" direction). Using simulated spacecraft observations of magnetic reconnection in the geomagnetic tail, we extend our previous tests of the direction-finding method developed by Shi et al. (2005) and the method to determine the structure velocity relative to the spacecraft Vstr. These methods require data from four proximate spacecraft. We add artificial noise and calibration errors to the simulation fields, and then use the perturbed gradient of the magnetic field B and perturbed time derivative dB/dt, as described by Denton et al. (2010). Three new simulations are examined: a weakly three-dimensional, i.e., quasi-two-dimensional, MHD simulation without a guide field, a quasi-two-dimensional MHD simulation with a guide field, and a two-dimensional full dynamics kinetic simulation with inherent noise so that the apparent minimum gradient was not exactly zero, even without added artificial errors. We also examined variations of the spacecraft trajectory for the kinetic simulation. The accuracy of the directions found varied depending on the simulation and spacecraft trajectory, but all the directions could be found within about 10 for all cases. Various aspects of the method were examined, including how to choose averaging intervals and the best intervals for determining the directions and velocity. For the kinetic simulation, we also investigated in detail how the errors in the inferred gradient directions from the unmodified Shi et al. method (using the unperturbed gradient) depended on the amplitude of the calibration errors. For an accuracy of 3 for the maximum gradient direction, the calibration errors could be as large as 3% of reconnection magnetic field, while for the same accuracy for the minimum gradient direction, the calibration errors could only be as large as 0.03% of the reconnection magnetic field. These results suggest that the maximum gradient direction can normally be determined by the unmodified Shi et al. method, while the modified method or some other method must be used to accurately determine the minimum gradient direction. The structure velocity was found with magnitude accurate to 2% and direction accurate to within 5%.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Tests of general relativity in earth orbit using a superconducting gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1989-01-01

Interesting new tests of general relativity could be performed in earth orbit using a sensitive superconducting gravity gradiometer under development. Two such experiments are discussed here: a null test of the tracelessness of the Riemann tensor and detection of the Lense-Thirring term in the earth's gravity field. The gravity gradient signals in various spacecraft orientations are derived, and dominant error sources in each experimental setting are discussed. The instrument, spacecraft, and orbit requirements imposed by the experiments are derived.

Derivative based sensitivity analysis of gamma index

PubMed Central

Sarkar, Biplab; Pradhan, Anirudh; Ganesh, T.

2015-01-01

Originally developed as a tool for patient-specific quality assurance in advanced treatment delivery methods to compare between measured and calculated dose distributions, the gamma index (γ) concept was later extended to compare between any two dose distributions. It takes into effect both the dose difference (DD) and distance-to-agreement (DTA) measurements in the comparison. Its strength lies in its capability to give a quantitative value for the analysis, unlike other methods. For every point on the reference curve, if there is at least one point in the evaluated curve that satisfies the pass criteria (e.g., δDD = 1%, δDTA = 1 mm), the point is included in the quantitative score as “pass.” Gamma analysis does not account for the gradient of the evaluated curve - it looks at only the minimum gamma value, and if it is <1, then the point passes, no matter what the gradient of evaluated curve is. In this work, an attempt has been made to present a derivative-based method for the identification of dose gradient. A mathematically derived reference profile (RP) representing the penumbral region of 6 MV 10 cm × 10 cm field was generated from an error function. A general test profile (GTP) was created from this RP by introducing 1 mm distance error and 1% dose error at each point. This was considered as the first of the two evaluated curves. By its nature, this curve is a smooth curve and would satisfy the pass criteria for all points in it. The second evaluated profile was generated as a sawtooth test profile (STTP) which again would satisfy the pass criteria for every point on the RP. However, being a sawtooth curve, it is not a smooth one and would be obviously poor when compared with the smooth profile. Considering the smooth GTP as an acceptable profile when it passed the gamma pass criteria (1% DD and 1 mm DTA) against the RP, the first and second order derivatives of the DDs (δD’, δD”) between these two curves were derived and used as the boundary values for evaluating the STTP against the RP. Even though the STTP passed the simple gamma pass criteria, it was found failing at many locations when the derivatives were used as the boundary values. The proposed derivative-based method can identify a noisy curve and can prove to be a useful tool for improving the sensitivity of the gamma index. PMID:26865761

Impact of gradient timing error on the tissue sodium concentration bioscale measured using flexible twisted projection imaging

NASA Astrophysics Data System (ADS)

Lu, Aiming; Atkinson, Ian C.; Vaughn, J. Thomas; Thulborn, Keith R.

2011-12-01

The rapid biexponential transverse relaxation of the sodium MR signal from brain tissue requires efficient k-space sampling for quantitative imaging in a time that is acceptable for human subjects. The flexible twisted projection imaging (flexTPI) sequence has been shown to be suitable for quantitative sodium imaging with an ultra-short echo time to minimize signal loss. The fidelity of the k-space center location is affected by the readout gradient timing errors on the three physical axes, which is known to cause image distortion for projection-based acquisitions. This study investigated the impact of these timing errors on the voxel-wise accuracy of the tissue sodium concentration (TSC) bioscale measured with the flexTPI sequence. Our simulations show greater than 20% spatially varying quantification errors when the gradient timing errors are larger than 10 μs on all three axes. The quantification is more tolerant of gradient timing errors on the Z-axis. An existing method was used to measure the gradient timing errors with <1 μs error. The gradient timing error measurement is shown to be RF coil dependent, and timing error differences of up to ˜16 μs have been observed between different RF coils used on the same scanner. The measured timing errors can be corrected prospectively or retrospectively to obtain accurate TSC values.

Linear shoaling of free-surface waves in multi-layer non-hydrostatic models

NASA Astrophysics Data System (ADS)

Bai, Yefei; Cheung, Kwok Fai

2018-01-01

The capability to describe shoaling over sloping bottom is fundamental to modeling of coastal wave transformation. The linear shoaling gradient provides a metric to measure this property in non-hydrostatic models with layer-integrated formulations. The governing equations in Boussinesq form facilitate derivation of the linear shoaling gradient, which is in the form of a [ 2 P + 2 , 2 P ] expansion of the water depth parameter kd with P equal to 1 for a one-layer model and (4 N - 4) for an N-layer model. The expansion reproduces the analytical solution from Airy wave theory at the shallow water limit and maintains a reasonable approximation up to kd = 1.2 and 2 for the one and two-layer models. Additional layers provide rapid and monotonic convergence of the shoaling gradient into deep water. Numerical experiments of wave propagation over a plane slope illustrate manifestation of the shoaling errors through the transformation processes from deep to shallow water. Even though outside the zone of active wave transformation, shoaling errors from deep to intermediate water are cumulative to produce appreciable impact to the wave amplitude in shallow water.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Coupling temporal and spatial gradient information in high-density unstructured Lagrangian measurements

NASA Astrophysics Data System (ADS)

Wong, Jaime G.; Rosi, Giuseppe A.; Rouhi, Amirreza; Rival, David E.

2017-10-01

Particle tracking velocimetry (PTV) produces high-quality temporal information that is often neglected when computing spatial gradients. A method is presented here to utilize this temporal information in order to improve the estimation of spatial gradients for spatially unstructured Lagrangian data sets. Starting with an initial guess, this method penalizes any gradient estimate where the substantial derivative of vorticity along a pathline is not equal to the local vortex stretching/tilting. Furthermore, given an initial guess, this method can proceed on an individual pathline without any further reference to neighbouring pathlines. The equivalence of the substantial derivative and vortex stretching/tilting is based on the vorticity transport equation, where viscous diffusion is neglected. By minimizing the residual of the vorticity-transport equation, the proposed method is first tested to reduce error and noise on a synthetic Taylor-Green vortex field dissipating in time. Furthermore, when the proposed method is applied to high-density experimental data collected with `Shake-the-Box' PTV, noise within the spatial gradients is significantly reduced. In the particular test case investigated here of an accelerating circular plate captured during a single run, the method acts to delineate the shear layer and vortex core, as well as resolve the Kelvin-Helmholtz instabilities, which were previously unidentifiable without the use of ensemble averaging. The proposed method shows promise for improving PTV measurements that require robust spatial gradients while retaining the unstructured Lagrangian perspective.

Evaluation of Latent Heat Flux Fields from Satellites and Models during SEMAPHORE.

NASA Astrophysics Data System (ADS)

Bourras, Denis; Liu, W. Timothy; Eymard, Laurence; Tang, Wenqing

2003-02-01

Latent heat fluxes were derived from satellite observations in the region of Structure des Echanges Mer-Atmosphère, Propriétés des Hétérogénéités Océaniques: Recherche Expérimentale (SEMAPHORE), which was conducted near the Azores islands in the North Atlantic Ocean in autumn of 1993. The satellite fluxes were compared with output fields of two atmospheric circulation models and in situ measurements. The rms error of the instantaneous satellite fluxes is between 35 and 40 W m-2 and the bias is 60-85 W m-2. The large bias is mainly attributed to a bias in satellite-derived atmospheric humidity and is related to the particular shape of the vertical humidity profiles during SEMAPHORE. The bias in humidity implies that the range of estimated fluxes is smaller than the range of ship fluxes, by 34%-38%. The rms errors for fluxes from models are 30-35 W m-2, and the biases are smaller than the biases in satellite fluxes (14-18 W m-2). Two case studies suggest that the satellites detect horizontal gradients of wind speed and specific humidity if the magnitude of the gradients exceeds a detection threshold, which is 1.27 g kg-1 (100 km)-1 for specific humidity and between 0.35 and 0.82 m s-1 (30 km)-1 for wind speed. In contrast, the accuracy of the spatial gradients of bulk variables from models always varies as a function of the location and number of assimilated observations. A comparison between monthly fluxes from satellites and models reveals that satellite-derived flux anomaly fields are consistent with reanalyzed fields, whereas operational model products lack part of the mesoscale structures present in the satellite fields.

SDSS-IV MaNGA: the impact of diffuse ionized gas on emission-line ratios, interpretation of diagnostic diagrams and gas metallicity measurements

NASA Astrophysics Data System (ADS)

Zhang, Kai; Yan, Renbin; Bundy, Kevin; Bershady, Matthew; Haffner, L. Matthew; Walterbos, René; Maiolino, Roberto; Tremonti, Christy; Thomas, Daniel; Drory, Niv; Jones, Amy; Belfiore, Francesco; Sánchez, Sebastian F.; Diamond-Stanic, Aleksandar M.; Bizyaev, Dmitry; Nitschelm, Christian; Andrews, Brett; Brinkmann, Jon; Brownstein, Joel R.; Cheung, Edmond; Li, Cheng; Law, David R.; Roman Lopes, Alexandre; Oravetz, Daniel; Pan, Kaike; Storchi Bergmann, Thaisa; Simmons, Audrey

2017-04-01

Diffuse ionized gas (DIG) is prevalent in star-forming galaxies. Using a sample of 365 nearly face-on star-forming galaxies observed by Mapping Nearby Galaxies at APO, we demonstrate how DIG in star-forming galaxies impacts the measurements of emission-line ratios, hence the interpretation of diagnostic diagrams and gas-phase metallicity measurements. At fixed metallicity, DIG-dominated low ΣHα regions display enhanced [S II]/Hα, [N II]/Hα, [O II]/Hβ and [O I]/Hα. The gradients in these line ratios are determined by metallicity gradients and ΣHα. In line ratio diagnostic diagrams, contamination by DIG moves H II regions towards composite or low-ionization nuclear emission-line region (LI(N)ER)-like regions. A harder ionizing spectrum is needed to explain DIG line ratios. Leaky H II region models can only shift line ratios slightly relative to H II region models, and thus fail to explain the composite/LI(N)ER line ratios displayed by DIG. Our result favours ionization by evolved stars as a major ionization source for DIG with LI(N)ER-like emission. DIG can significantly bias the measurement of gas metallicity and metallicity gradients derived using strong-line methods. Metallicities derived using N2O2 are optimal because they exhibit the smallest bias and error. Using O3N2, R23, N2 = [N II]/Hα and N2S2Hα to derive metallicities introduces bias in the derived metallicity gradients as large as the gradient itself. The strong-line method of Blanc et al. (IZI hereafter) cannot be applied to DIG to get an accurate metallicity because it currently contains only H II region models that fail to describe the DIG.

Recursive least-squares learning algorithms for neural networks

NASA Astrophysics Data System (ADS)

Lewis, Paul S.; Hwang, Jenq N.

1990-11-01

This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is 0(N2) where N is the number of network parameters. This is due to the estimation of the N x N inverse Hessian matrix. Less computationally intensive approximations of the ilLS algorithms can be easily derived by using only block diagonal elements of this matrix thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6 1 BACKGROUND Artificial neural networks (ANNs) offer an interesting and potentially useful paradigm for signal processing and pattern recognition. The majority of ANN applications employ the feed-forward multilayer perceptron (MLP) network architecture in which network parameters are " trained" by a supervised learning algorithm employing the generalized delta rule (GDIt) [1 2]. The GDR algorithm approximates a fixed step steepest descent algorithm using derivatives computed by error backpropagatiori. The GDII algorithm is sometimes referred to as the backpropagation algorithm. However in this paper we will use the term backpropagation to refer only to the process of computing error derivatives. While multilayer perceptrons provide a very powerful nonlinear modeling capability GDR training can be very slow and inefficient. In linear adaptive filtering the analog of the GDR algorithm is the leastmean- squares (LMS) algorithm. Steepest descent-based algorithms such as GDR or LMS are first order because they use only first derivative or gradient information about the training error to be minimized. To speed up the training process second order algorithms may be employed that take advantage of second derivative or Hessian matrix information. Second order information can be incorporated into MLP training in different ways. In many applications especially in the area of pattern recognition the training set is finite. In these cases block learning can be applied using standard nonlinear optimization techniques [3 4 5].

Wave Gradiometry for the Central U.S

NASA Astrophysics Data System (ADS)

liu, Y.; Holt, W. E.

2013-12-01

Wave gradiometry is a new technique utilizing the shape of seismic wave fields captured by USArray transportable stations to determine fundamental wave propagation characteristics. The horizontal and vertical wave displacements, spatial gradients and time derivatives of displacement are linearly linked by two coefficients which can be used to infer wave slowness, back azimuth, radiation pattern and geometrical spreading. The reducing velocity method from Langston [2007] is applied to pre-process our data. Spatial gradients of the shifted displacement fields are estimated using bi-cubic splines [Beavan and Haines, 2001]. Using singular value decomposition, the spatial gradients are then inverted to iteratively solve for wave parameters mentioned above. Numerical experiments with synthetic data sets provided by Princeton University's Neal Real Time Global Seismicity Portal are conducted to test the algorithm stability and evaluate errors. Our results based on real records in the central U.S. show that, the average Rayleigh wave phase velocity ranges from 3.8 to 4.2 km/s for periods from 60-125s, and 3.6 to 4.0 km/s for periods from 25-60s, which is consistent with earth model. Geometrical spreading and radiation pattern show similar features between different frequency bands. Azimuth variations are partially correlated with phase velocity change. Finally, we calculated waveform amplitude and spatial gradient uncertainties to determine formal errors in the estimated wave parameters. Further effort will be put into calculating shear wave velocity structure with respect to depth in the studied area. The wave gradiometry method is now being employed across the USArray using real observations and results obtained to date are for stations in eastern portion of the U.S. Rayleigh wave phase velocity derived from Aug, 20th, 2011 Vanuatu earthquake for periods from 100 - 125 s.

Statistical Mechanics of Node-perturbation Learning with Noisy Baseline

NASA Astrophysics Data System (ADS)

Hara, Kazuyuki; Katahira, Kentaro; Okada, Masato

2017-02-01

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

Equilibrium Propagation: Bridging the Gap between Energy-Based Models and Backpropagation

PubMed Central

Scellier, Benjamin; Bengio, Yoshua

2017-01-01

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal “back-propagated” during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task. PMID:28522969

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

NASA Astrophysics Data System (ADS)

Lu, Biao; Luo, Zhicai; Zhong, Bo; Zhou, Hao; Flechtner, Frank; Förste, Christoph; Barthelmes, Franz; Zhou, Rui

2017-11-01

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components V_{xy} and V_{yz} of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7° . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of V_{xy} and V_{yz} are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1's accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

NASA Astrophysics Data System (ADS)

Zheng, Wei; Hsu, Hou-Tse; Zhong, Min; Yun, Mei-Juan

2012-10-01

The accuracy of the Earth's gravitational field measured from the gravity field and steady-state ocean circulation explorer (GOCE), up to 250 degrees, influenced by the radial gravity gradient Vzz and three-dimensional gravity gradient Vij from the satellite gravity gradiometry (SGG) are contrastively demonstrated based on the analytical error model and numerical simulation, respectively. Firstly, the new analytical error model of the cumulative geoid height, influenced by the radial gravity gradient Vzz and three-dimensional gravity gradient Vij are established, respectively. In 250 degrees, the GOCE cumulative geoid height error measured by the radial gravity gradient Vzz is about 2½ times higher than that measured by the three-dimensional gravity gradient Vij. Secondly, the Earth's gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient Vzz and three-dimensional gravity gradient Vij by numerical simulation, respectively. The study results show that when the measurement error of the gravity gradient is 3 × 10-12/s2, the cumulative geoid height errors using the radial gravity gradient Vzz and three-dimensional gravity gradient Vij are 12.319 cm and 9.295 cm at 250 degrees, respectively. The accuracy of the cumulative geoid height using the three-dimensional gravity gradient Vij is improved by 30%-40% on average compared with that using the radial gravity gradient Vzz in 250 degrees. Finally, by mutual verification of the analytical error model and numerical simulation, the orders of magnitude from the accuracies of the Earth's gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients, respectively. Therefore, it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10-13/s2-10-15/s2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

Synthetic temperature profiles derived from Geosat altimetry: Comparison with air-dropped expendable bathythermograph profiles

NASA Astrophysics Data System (ADS)

Carnes, Michael R.; Mitchell, Jim L.; de Witt, P. Webb

1990-10-01

Synthetic temperature profiles are computed from altimeter-derived sea surface heights in the Gulf Stream region. The required relationships between surface height (dynamic height at the surface relative to 1000 dbar) and subsurface temperature are provided from regression relationships between dynamic height and amplitudes of empirical orthogonal functions (EOFs) of the vertical structure of temperature derived by de Witt (1987). Relationships were derived for each month of the year from historical temperature and salinity profiles from the region surrounding the Gulf Stream northeast of Cape Hatteras. Sea surface heights are derived using two different geoid estimates, the feature-modeled geoid and the air-dropped expendable bathythermograph (AXBT) geoid, both described by Carnes et al. (1990). The accuracy of the synthetic profiles is assessed by comparison to 21 AXBT profile sections which were taken during three surveys along 12 Geosat ERM ground tracks nearly contemporaneously with Geosat overflights. The primary error statistic considered is the root-mean-square (rms) difference between AXBT and synthetic isotherm depths. The two sources of error are the EOF relationship and the altimeter-derived surface heights. EOF-related and surface height-related errors in synthetic temperature isotherm depth are of comparable magnitude; each translates into about a 60-m rms isotherm depth error, or a combined 80 m to 90 m error for isotherms in the permanent thermocline. EOF-related errors are responsible for the absence of the near-surface warm core of the Gulf Stream and for the reduced volume of Eighteen Degree Water in the upper few hundred meters of (apparently older) cold-core rings in the synthetic profiles. The overall rms difference between surface heights derived from the altimeter and those computed from AXBT profiles is 0.15 dyn m when the feature-modeled geoid is used and 0.19 dyn m when the AXBT geoid is used; the portion attributable to altimeter-derived surface height errors alone is 0.03 dyn m less for each. In most cases, the deeper structure of the Gulf Stream and eddies is reproduced well by vertical sections of synthetic temperature, with largest errors typically in regions of high horizontal gradient such as across rings and the Gulf Stream front.

3-D direct current resistivity anisotropic modelling by goal-oriented adaptive finite element methods

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Qiu, Lewen; Tang, Jingtian; Wu, Xiaoping; Xiao, Xiao; Zhou, Zilong

2018-01-01

Although accurate numerical solvers for 3-D direct current (DC) isotropic resistivity models are current available even for complicated models with topography, reliable numerical solvers for the anisotropic case are still an open question. This study aims to develop a novel and optimal numerical solver for accurately calculating the DC potentials for complicated models with arbitrary anisotropic conductivity structures in the Earth. First, a secondary potential boundary value problem is derived by considering the topography and the anisotropic conductivity. Then, two a posteriori error estimators with one using the gradient-recovery technique and one measuring the discontinuity of the normal component of current density are developed for the anisotropic cases. Combing the goal-oriented and non-goal-oriented mesh refinements and these two error estimators, four different solving strategies are developed for complicated DC anisotropic forward modelling problems. A synthetic anisotropic two-layer model with analytic solutions verified the accuracy of our algorithms. A half-space model with a buried anisotropic cube and a mountain-valley model are adopted to test the convergence rates of these four solving strategies. We found that the error estimator based on the discontinuity of current density shows better performance than the gradient-recovery based a posteriori error estimator for anisotropic models with conductivity contrasts. Both error estimators working together with goal-oriented concepts can offer optimal mesh density distributions and highly accurate solutions.

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2017-09-01

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63-84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10-30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.

Gradient Pre-Emphasis to Counteract First-Order Concomitant Fields on Asymmetric MRI Gradient Systems

PubMed Central

Tao, Shengzhen; Weavers, Paul T.; Trzasko, Joshua D.; Shu, Yunhong; Huston, John; Lee, Seung-Kyun; Frigo, Louis M.; Bernstein, Matt A.

2016-01-01

PURPOSE To develop a gradient pre-emphasis scheme that prospectively counteracts the effects of the first-order concomitant fields for any arbitrary gradient waveform played on asymmetric gradient systems, and to demonstrate the effectiveness of this approach using a real-time implementation on a compact gradient system. METHODS After reviewing the first-order concomitant fields that are present on asymmetric gradients, a generalized gradient pre-emphasis model assuming arbitrary gradient waveforms is developed to counteract their effects. A numerically straightforward, simple to implement approximate solution to this pre-emphasis problem is derived, which is compatible with the current hardware infrastructure used on conventional MRI scanners for eddy current compensation. The proposed method was implemented on the gradient driver sub-system, and its real-time use was tested using a series of phantom and in vivo data acquired from 2D Cartesian phase-difference, echo-planar imaging (EPI) and spiral acquisitions. RESULTS The phantom and in vivo results demonstrate that unless accounted for, first-order concomitant fields introduce considerable phase estimation error into the measured data and result in images exhibiting spatially dependent blurring/distortion. The resulting artifacts are effectively prevented using the proposed gradient pre-emphasis. CONCLUSION An efficient and effective gradient pre-emphasis framework is developed to counteract the effects of first-order concomitant fields of asymmetric gradient systems. PMID:27373901

Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

NASA Astrophysics Data System (ADS)

Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy

2017-11-01

Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.

Convergence of fractional adaptive systems using gradient approach.

PubMed

Gallegos, Javier A; Duarte-Mermoud, Manuel A

2017-07-01

Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the concept of sufficiently exciting signals is introduced, characterized and related to the concept of persistently exciting signals used in the integer order case. An application is designed in adaptive indirect control of integer order systems using fractional equations to adjust parameters. This application is illustrated for a pole placement adaptive problem. Advantages of using fractional adjustment in control adaptive schemes are experimentally obtained. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

NASA Astrophysics Data System (ADS)

Khani, Sina; Porté-Agel, Fernando

2017-12-01

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin-Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.

Skin Friction at Very High Reynolds Numbers in the National Transonic Facility

NASA Technical Reports Server (NTRS)

Watson, Ralph D.; Anders, John B.; Hall, Robert M.

2006-01-01

Skin friction coefficients were derived from measurements using standard measurement technologies on an axisymmetric cylinder in the NASA Langley National Transonic Facility (NTF) at Mach numbers from 0.2 to 0.85. The pressure gradient was nominally zero, the wall temperature was nominally adiabatic, and the ratio of boundary layer thickness to model diameter within the measurement region was 0.10 to 0.14, varying with distance along the model. Reynolds numbers based on momentum thicknesses ranged from 37,000 to 605,000. The measurements approximately doubled the range of available data for flat plate skin friction coefficients. Three different techniques were used to measure surface shear. The maximum error of Preston tube measurements was estimated to be 2.5 percent, while that of Clauser derived measurements was estimated to be approximately 5 percent. Direct measurements by skin friction balance proved to be subject to large errors and were not considered reliable.

Gradient pre-emphasis to counteract first-order concomitant fields on asymmetric MRI gradient systems.

PubMed

Tao, Shengzhen; Weavers, Paul T; Trzasko, Joshua D; Shu, Yunhong; Huston, John; Lee, Seung-Kyun; Frigo, Louis M; Bernstein, Matt A

2017-06-01

To develop a gradient pre-emphasis scheme that prospectively counteracts the effects of the first-order concomitant fields for any arbitrary gradient waveform played on asymmetric gradient systems, and to demonstrate the effectiveness of this approach using a real-time implementation on a compact gradient system. After reviewing the first-order concomitant fields that are present on asymmetric gradients, we developed a generalized gradient pre-emphasis model assuming arbitrary gradient waveforms to counteract their effects. A numerically straightforward, easily implemented approximate solution to this pre-emphasis problem was derived that was compatible with the current hardware infrastructure of conventional MRI scanners for eddy current compensation. The proposed method was implemented on the gradient driver subsystem, and its real-time use was tested using a series of phantom and in vivo data acquired from two-dimensional Cartesian phase-difference, echo-planar imaging, and spiral acquisitions. The phantom and in vivo results demonstrated that unless accounted for, first-order concomitant fields introduce considerable phase estimation error into the measured data and result in images with spatially dependent blurring/distortion. The resulting artifacts were effectively prevented using the proposed gradient pre-emphasis. We have developed an efficient and effective gradient pre-emphasis framework to counteract the effects of first-order concomitant fields of asymmetric gradient systems. Magn Reson Med 77:2250-2262, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Spatially Resolved Isotopic Source Signatures of Wetland Methane Emissions

NASA Astrophysics Data System (ADS)

Ganesan, A. L.; Stell, A. C.; Gedney, N.; Comyn-Platt, E.; Hayman, G.; Rigby, M.; Poulter, B.; Hornibrook, E. R. C.

2018-04-01

We present the first spatially resolved wetland δ13C(CH4) source signature map based on data characterizing wetland ecosystems and demonstrate good agreement with wetland signatures derived from atmospheric observations. The source signature map resolves a latitudinal difference of 10‰ between northern high-latitude (mean -67.8‰) and tropical (mean -56.7‰) wetlands and shows significant regional variations on top of the latitudinal gradient. We assess the errors in inverse modeling studies aiming to separate CH4 sources and sinks by comparing atmospheric δ13C(CH4) derived using our spatially resolved map against the common assumption of globally uniform wetland δ13C(CH4) signature. We find a larger interhemispheric gradient, a larger high-latitude seasonal cycle, and smaller trend over the period 2000-2012. The implication is that erroneous CH4 fluxes would be derived to compensate for the biases imposed by not utilizing spatially resolved signatures for the largest source of CH4 emissions. These biases are significant when compared to the size of observed signals.

Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

NASA Astrophysics Data System (ADS)

Loseille, A.; Dervieux, A.; Alauzet, F.

2010-04-01

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps. First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation. 3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

PubMed

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

A general theory of multimetric indices and their properties

USGS Publications Warehouse

Schoolmaster, Donald R.; Grace, James B.; Schweiger, E. William

2012-01-01

1. Stewardship of biological and ecological resources requires the ability to make integrative assessments of ecological integrity. One of the emerging methods for making such integrative assessments is multimetric indices (MMIs). These indices synthesize data, often from multiple levels of biological organization, with the goal of deriving a single index that reflects the overall effects of human disturbance. Despite the widespread use of MMIs, there is uncertainty about why this approach can be effective. An understanding of MMIs requires a quantitative theory that illustrates how the properties of candidate metrics relates to MMIs generated from those metrics. 2. We present the initial basis for such a theory by deriving the general mathematical characteristics of MMIs assembled from metrics. We then use the theory to derive quantitative answers to the following questions: Is there an optimal number of metrics to comprise an index? How does covariance among metrics affect the performance of the index derived from those metrics? And what are the criteria to decide whether a given metric will improve the performance of an index? 3. We find that the optimal number of metrics to be included in an index depends on the theoretical distribution of signal of the disturbance gradient contained in each metric. For example, if the rank-ordered parameters of a metric-disturbance regression can be described by a monotonically decreasing function, then an optimum number of metrics exists and can often be derived analytically. We derive the conditions by which adding a given metric can be expected to improve an index. 4. We find that the criterion defining such conditions depends nonlinearly of the signal of the disturbance gradient, the noise (error) of the metric and the correlation of the metric errors. Importantly, we find that correlation among metric errors increases the signal required for the metric to improve the index. 5. The theoretical framework presented in this study provides the basis for understanding the properties of MMIs. It can also be useful throughout the index construction process. Specifically, it can be used to aid understanding of the benefits and limitations of combining metrics into indices; it can inform selection/collection of candidate metrics; and it can be used directly as a decision aid in effective index construction.

Stochastic estimates of gradient from laser measurements for an autonomous Martian roving vehicle

NASA Technical Reports Server (NTRS)

Burger, P. A.

1973-01-01

The general problem of estimating the state vector x from the state equation h = Ax where h, A, and x are all stochastic, is presented. Specifically, the problem is for an autonomous Martian roving vehicle to utilize laser measurements in estimating the gradient of the terrain. Error exists due to two factors - surface roughness and instrumental measurements. The errors in slope depend on the standard deviations of these noise factors. Numerically, the error in gradient is expressed as a function of instrumental inaccuracies. Certain guidelines for the accuracy of permissable gradient must be set. It is found that present technology can meet these guidelines.

Global grids of gravity anomalies and vertical gravity gradients at 10 km altitude from GOCE gradient data 2009-2011 and polar gravity.

NASA Astrophysics Data System (ADS)

Tscherning, Carl Christian; Arabelos, Dimitrios; Reguzzoni, Mirko

2013-04-01

The GOCE satellite measures gravity gradients which are filtered and transformed to gradients into an Earth-referenced frame by the GOCE High Level processing Facility. More than 80000000 data with 6 components are available from the period 2009-2011. IAG Arctic gravity was used north of 83 deg., while data at the Antarctic was not used due to bureaucratic restrictions by the data-holders. Subsets of the data have been used to produce gridded values at 10 km altitude of gravity anomalies and vertical gravity gradients in 20 deg. x 20 deg. blocks with 10' spacing. Various combinations and densities of data were used to obtain values in areas with known gravity anomalies. The (marginally) best choice was vertical gravity gradients selected with an approximately 0.125 deg spacing. Using Least-Squares Collocation, error-estimates were computed and compared to the difference between the GOCE-grids and grids derived from EGM2008 to deg. 512. In general a good agreement was found, however with some inconsistencies in certain areas. The computation time on a usual server with 24 processors was typically 100 minutes for a block with generally 40000 GOCE vertical gradients as input. The computations will be updated with new Wiener-filtered data in the near future.

Analysis of Correlation between Ionospheric Spatial Gradients and Space Weather Intensity under Nominal Conditions for Ground-Based Augmentation Systems

NASA Astrophysics Data System (ADS)

Lee, J.

2013-12-01

Ground-Based Augmentation Systems (GBAS) support aircraft precision approach and landing by providing differential GPS corrections to aviation users. For GBAS applications, most of ionospheric errors are removed by applying the differential corrections. However, ionospheric correction errors may exist due to ionosphere spatial decorrelation between GBAS ground facility and users. Thus, the standard deviation of ionosphere spatial decorrelation (σvig) is estimated and included in the computation of error bounds on user position solution. The σvig of 4mm/km, derived for the Conterminous United States (CONUS), bounds one-sigma ionospheric spatial gradients under nominal conditions (including active, but not stormy condition) with an adequate safety margin [1]. The conservatism residing in the current σvig by fixing it to a constant value for all non-stormy conditions could be mitigated by subdividing ionospheric conditions into several classes and using different σvig for each class. This new concept, real-time σvig adaptation, will be possible if the level of ionospheric activity can be well classified based on space weather intensity. This paper studies correlation between the statistics of nominal ionospheric spatial gradients and space weather indices. The analysis was carried out using two sets of data collected from Continuous Operating Reference Station (CORS) Network; 9 consecutive (nominal and ionospherically active) days in 2004 and 19 consecutive (relatively 'quiet') days in 2010. Precise ionospheric delay estimates are obtained using the simplified truth processing method and vertical ionospheric gradients are computed using the well-known 'station pair method' [2]. The remaining biases which include carrier-phase leveling errors and Inter-frequency Bias (IFB) calibration errors are reduced by applying linear slip detection thresholds. The σvig was inflated to overbound the distribution of vertical ionospheric gradients with the required confidence level. Using the daily maximum values of σvig, day-to-day variations of spatial gradients are compared to those of two space weather indices; Disturbance, Storm Time (Dst) index and Interplanetary Magnetic Field Bz (IMF Bz). The day-to-day variations of both space weather indices showed a good agreement with those of daily maximum σvig. The results demonstrate that ionospheric gradient statistics are highly correlated with space weather indices on nominal and off-nominal days. Further investigation on this relationship would facilitate prediction of upcoming ionospheric behavior based on space weather information and adjusting σvig in real time. Consequently it will improve GBAS availability by adding external information to operation. [1] Lee, J., S. Pullen, S. Datta-Barua, and P. Enge (2007), Assessment of ionosphere spatial decorrelation for GPS-based aircraft landing systems, J. Aircraft, 44(5), 1662-1669, doi:10.2514/1.28199. [2] Jung, S., and J. Lee (2012), Long-term ionospheric anomaly monitoring for ground based augmentation systems, Radio Sci., 47, RS4006, doi:10.1029/2012RS005016.

Dip and anisotropy effects on flow using a vertically skewed model grid.

PubMed

Hoaglund, John R; Pollard, David

2003-01-01

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

Estimations of ABL fluxes and other turbulence parameters from Doppler lidar data

NASA Technical Reports Server (NTRS)

Gal-Chen, Tzvi; Xu, Mei; Eberhard, Wynn

1989-01-01

Techniques for extraction boundary layer parameters from measurements of a short-pulse CO2 Doppler lidar are described. The measurements are those collected during the First International Satellites Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE). By continuously operating the lidar for about an hour, stable statistics of the radial velocities can be extracted. Assuming that the turbulence is horizontally homogeneous, the mean wind, its standard deviations, and the momentum fluxes were estimated. Spectral analysis of the radial velocities is also performed from which, by examining the amplitude of the power spectrum at the inertial range, the kinetic energy dissipation was deduced. Finally, using the statistical form of the Navier-Stokes equations, the surface heat flux is derived as the residual balance between the vertical gradient of the third moment of the vertical velocity and the kinetic energy dissipation. Combining many measurements would normally reduce the error provided that, it is unbiased and uncorrelated. The nature of some of the algorithms however, is such that, biased and correlated errors may be generated even though the raw measurements are not. Data processing procedures were developed that eliminate bias and minimize error correlation. Once bias and error correlations are accounted for, the large sample size is shown to reduce the errors substantially. The principal features of the derived turbulence statistics for two case studied are presented.

A spiral, bi-planar gradient coil design for open magnetic resonance imaging.

PubMed

Zhang, Peng; Shi, Yikai; Wang, Wendong; Wang, Yaohui

2018-01-01

To design planar gradient coil for MRI applications without discretization of continuous current density and loop-loop connection errors. In the new design method, the coil current is represented using a spiral curve function described by just a few control parameters. Using a proper parametric equation set, an ensemble of spiral contours is reshaped to satisfy the coil design requirements, such as gradient linearity, inductance and shielding. In the given case study, by using the spiral coil design, the magnetic field errors in the imaging area were reduced from 5.19% (non-spiral design) to 4.47% (spiral design) for the transverse gradient coils, and for the longitudinal gradient coil design, the magnetic field errors were reduced to 5.02% (spiral design). The numerical evaluation shows that when compared with conventional wire loop, the inductance and resistance of spiral coil was reduced by 11.55% and 8.12% for x gradient coil, respectively. A novel spiral gradient coil design for biplanar MRI systems, the new design offers better magnetic field gradients, smooth contours than the conventional connected counterpart, which improves manufacturability.

Stochastic estimates of gradient from laser measurements for an autonomous Martian Roving Vehicle

NASA Technical Reports Server (NTRS)

Shen, C. N.; Burger, P.

1973-01-01

The general problem presented in this paper is one of estimating the state vector x from the state equation h = Ax, where h, A, and x are all stochastic. Specifically, the problem is for an autonomous Martian Roving Vehicle to utilize laser measurements in estimating the gradient of the terrain. Error exists due to two factors - surface roughness and instrumental measurements. The errors in slope depend on the standard deviations of these noise factors. Numerically, the error in gradient is expressed as a function of instrumental inaccuracies. Certain guidelines for the accuracy of permissable gradient must be set. It is found that present technology can meet these guidelines.-

Cell-to-cell variation sets a tissue-rheology–dependent bound on collective gradient sensing

PubMed Central

Camley, Brian A.; Rappel, Wouter-Jan

2017-01-01

When a single cell senses a chemical gradient and chemotaxes, stochastic receptor–ligand binding can be a fundamental limit to the cell’s accuracy. For clusters of cells responding to gradients, however, there is a critical difference: Even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate, the resulting bias can be much larger than the effects of ligand–receptor binding. Specifically, when a strongly responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: We derive a link between cluster accuracy, cell-to-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity. PMID:29114053

Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory.

PubMed

Maradzike, Elvis; Gidofalvi, Gergely; Turney, Justin M; Schaefer, Henry F; DePrince, A Eugene

2017-09-12

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix (2-RDM)-driven complete active space self-consistent field (CASSCF) method. The active-space 2-RDM is determined using a semidefinite programing (SDP) algorithm built upon an augmented Lagrangian formalism. Expressions for analytic gradients are simplified by the fact that the Lagrangian is stationary with respect to variations in both the primal and the dual solutions to the SDP problem. Orbital response contributions to the gradient are identical to those that arise in conventional CASSCF methods in which the electronic structure of the active space is described by a full configuration interaction (CI) wave function. We explore the relative performance of variational 2-RDM (v2RDM)- and CI-driven CASSCF for the equilibrium geometries of 20 small molecules. When enforcing two-particle N-representability conditions, full-valence v2RDM-CASSCF-optimized bond lengths display a mean unsigned error of 0.0060 Å and a maximum unsigned error of 0.0265 Å, relative to those obtained from full-valence CI-CASSCF. When enforcing partial three-particle N-representability conditions, the mean and maximum unsigned errors are reduced to only 0.0006 and 0.0054 Å, respectively. For these same molecules, full-valence v2RDM-CASSCF bond lengths computed in the cc-pVQZ basis set deviate from experimentally determined ones on average by 0.017 and 0.011 Å when enforcing two- and three-particle conditions, respectively, whereas CI-CASSCF displays an average deviation of 0.010 Å. The v2RDM-CASSCF approach with two-particle conditions is also applied to the equilibrium geometry of pentacene; optimized bond lengths deviate from those derived from experiment, on average, by 0.015 Å when using a cc-pVDZ basis set and a (22e,22o) active space.

An evaluation of satellite-derived humidity and its relationship to convective development

NASA Technical Reports Server (NTRS)

Fuelberg, Henry E.

1993-01-01

An aircraft prototype of the High-Resolution Interferometer Sounder (HIS) was flown over Tennessee and northern Alabama during summer 1986. The HIS temperature and dewpoint soundings were examined on two flight days to determine their error characteristics and utility in mesoscale analyses. Random errors were calculated from structure functions while total errors were obtained by pairing the HIS soundings with radiosonde-derived profiles. Random temperature errors were found to be less than 1 C at most levels, but random dewpoint errors ranged from 1 to 5 C. Total errors of both parameters were considerably greater, with dewpoint errors especially large on the day having a pronounced subsidence inversion. Cumulus cloud cover on 15 June limited HIS mesoscale analyses on that day. Previously undetected clouds were found in many HIS fields of view, and these probably produced the low-level horizontal temperature and dewpoint variations observed in the retrievals. HIS dewpoints at 300 mb indicated a strong moisture gradient that was confirmed by GOES 6.7-micron imagery. HIS mesoscale analyses on 19 June revealed a tongue of humid air stretching across the study area. The moist region was confirmed by radiosonde data and imagery from the Multispectral Atmospheric Mapping Sensor (MAMS). Convective temperatures derived from HIS retrievals helped explain the cloud formation that occurred after the HIS overflights. Crude estimates of Bowen ratio were obtained from HIS data using a mixing-line approach. Values indicated that areas of large sensible heat flux were the areas of first cloud development. These locations were also suggested by GOES visible and infrared imagery. The HIS retrievals indicated that areas of thunderstorm formation were regions of greatest instability. Local landscape variability and atmospheric temperature and humidity fluctuations were found to be important factors in producing the cumulus clouds on 19 June. HIS soundings were capable of detecting some of this variability. The authors were impressed by HIS's performance on the two study days.

Estimating IMU heading error from SAR images.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doerry, Armin Walter

Angular orientation errors of the real antenna for Synthetic Aperture Radar (SAR) will manifest as undesired illumination gradients in SAR images. These gradients can be measured, and the pointing error can be calculated. This can be done for single images, but done more robustly using multi-image methods. Several methods are provided in this report. The pointing error can then be fed back to the navigation Kalman filter to correct for problematic heading (yaw) error drift. This can mitigate the need for uncomfortable and undesired IMU alignment maneuvers such as S-turns.

Ray tracing evaluation of a technique for correcting the refraction errors in satellite tracking data

NASA Technical Reports Server (NTRS)

Gardner, C. S.; Rowlett, J. R.; Hendrickson, B. E.

1978-01-01

Errors may be introduced in satellite laser ranging data by atmospheric refractivity. Ray tracing data have indicated that horizontal refractivity gradients may introduce nearly 3-cm rms error when satellites are near 10-degree elevation. A correction formula to compensate for the horizontal gradients has been developed. Its accuracy is evaluated by comparing it to refractivity profiles. It is found that if both spherical and gradient correction formulas are employed in conjunction with meteorological measurements, a range resolution of one cm or less is feasible for satellite elevation angles above 10 degrees.

Accurate prediction of retention in hydrophilic interaction chromatography by back calculation of high pressure liquid chromatography gradient profiles.

PubMed

Wang, Nu; Boswell, Paul G

2017-10-20

Gradient retention times are difficult to project from the underlying retention factor (k) vs. solvent composition (φ) relationships. A major reason for this difficulty is that gradients produced by HPLC pumps are imperfect - gradient delay, gradient dispersion, and solvent mis-proportioning are all difficult to account for in calculations. However, we recently showed that a gradient "back-calculation" methodology can measure these imperfections and take them into account. In RPLC, when the back-calculation methodology was used, error in projected gradient retention times is as low as could be expected based on repeatability in the k vs. φ relationships. HILIC, however, presents a new challenge: the selectivity of HILIC columns drift strongly over time. Retention is repeatable in short time, but selectivity frequently drifts over the course of weeks. In this study, we set out to understand if the issue of selectivity drift can be avoid by doing our experiments quickly, and if there any other factors that make it difficult to predict gradient retention times from isocratic k vs. φ relationships when gradient imperfections are taken into account with the back-calculation methodology. While in past reports, the accuracy of retention projections was >5%, the back-calculation methodology brought our error down to ∼1%. This result was 6-43 times more accurate than projections made using ideal gradients and 3-5 times more accurate than the same retention projections made using offset gradients (i.e., gradients that only took gradient delay into account). Still, the error remained higher in our HILIC projections than in RPLC. Based on the shape of the back-calculated gradients, we suspect the higher error is a result of prominent gradient distortion caused by strong, preferential water uptake from the mobile phase into the stationary phase during the gradient - a factor our model did not properly take into account. It appears that, at least with the stationary phase we used, column distortion is an important factor to take into account in retention projection in HILIC that is not usually important in RPLC. Copyright © 2017 Elsevier B.V. All rights reserved.

Application of retention modelling to the simulation of separation of organic anions in suppressed ion chromatography.

PubMed

Zakaria, Philip; Dicinoski, Greg W; Ng, Boon Khing; Shellie, Robert A; Hanna-Brown, Melissa; Haddad, Paul R

2009-09-18

The ion-exchange separation of organic anions of varying molecular mass has been demonstrated using ion chromatography with isocratic, gradient and multi-step eluent profiles on commercially available columns with UV detection. A retention model derived previously for inorganic ions and based solely on electrostatic interactions between the analytes and the stationary phase was applied. This model was found to accurately describe the observed elution of all the anions under isocratic, gradient and multi-step eluent conditions. Hydrophobic interactions, although likely to be present to varying degrees, did not limit the applicability of the ion-exchange retention model. Various instrumental configurations were investigated to overcome problems associated with the use of organic modifiers in the eluent which caused compatibility issues with the electrolytically derived, and subsequently suppressed, eluent. The preferred configuration allowed the organic modifier stream to bypass the eluent generator, followed by subsequent mixing before entering the injection valve and column. Accurate elution prediction was achieved even when using 5-step eluent profiles with errors in retention time generally being less than 1% relative standard deviation (RSD) and all being less than 5% RSD. Peak widths for linear gradient separations were also modelled and showed good agreement with experimentally determined values.

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Demonstration of Nonlinearity Bias in the Measurement of the Apparent Diffusion Coefficient in Multicenter Trials

PubMed Central

Malyarenko, Dariya; Newitt, David; Wilmes, Lisa; Tudorica, Alina; Helmer, Karl G.; Arlinghaus, Lori R.; Jacobs, Michael A.; Jajamovich, Guido; Taouli, Bachir; Yankeelov, Thomas E.; Huang, Wei; Chenevert, Thomas L.

2015-01-01

Purpose Characterize system-specific bias across common magnetic resonance imaging (MRI) platforms for quantitative diffusion measurements in multicenter trials. Methods Diffusion weighted imaging (DWI) was performed on an ice-water phantom along the superior-inferior (SI) and right-left (RL) orientations spanning ±150 mm. The same scanning protocol was implemented on 14 MRI systems at seven imaging centers. The bias was estimated as a deviation of measured from known apparent diffusion coefficient (ADC) along individual DWI directions. The relative contributions of gradient nonlinearity, shim errors, imaging gradients and eddy currents were assessed independently. The observed bias errors were compared to numerical models. Results The measured systematic ADC errors scaled quadratically with offset from isocenter, and ranged between −55% (SI) and 25% (RL). Nonlinearity bias was dependent on system design and diffusion gradient direction. Consistent with numerical models, minor ADC errors (±5%) due to shim, imaging and eddy currents were mitigated by double echo DWI and image co-registration of individual gradient directions. Conclusion The analysis confirms gradient nonlinearity as a major source of spatial DW bias and variability in off-center ADC measurements across MRI platforms, with minor contributions from shim, imaging gradients and eddy currents. The developed protocol enables empiric description of systematic bias in multicenter quantitative DWI studies. PMID:25940607

Demonstration of nonlinearity bias in the measurement of the apparent diffusion coefficient in multicenter trials.

PubMed

Malyarenko, Dariya I; Newitt, David; J Wilmes, Lisa; Tudorica, Alina; Helmer, Karl G; Arlinghaus, Lori R; Jacobs, Michael A; Jajamovich, Guido; Taouli, Bachir; Yankeelov, Thomas E; Huang, Wei; Chenevert, Thomas L

2016-03-01

Characterize system-specific bias across common magnetic resonance imaging (MRI) platforms for quantitative diffusion measurements in multicenter trials. Diffusion weighted imaging (DWI) was performed on an ice-water phantom along the superior-inferior (SI) and right-left (RL) orientations spanning ± 150 mm. The same scanning protocol was implemented on 14 MRI systems at seven imaging centers. The bias was estimated as a deviation of measured from known apparent diffusion coefficient (ADC) along individual DWI directions. The relative contributions of gradient nonlinearity, shim errors, imaging gradients, and eddy currents were assessed independently. The observed bias errors were compared with numerical models. The measured systematic ADC errors scaled quadratically with offset from isocenter, and ranged between -55% (SI) and 25% (RL). Nonlinearity bias was dependent on system design and diffusion gradient direction. Consistent with numerical models, minor ADC errors (± 5%) due to shim, imaging and eddy currents were mitigated by double echo DWI and image coregistration of individual gradient directions. The analysis confirms gradient nonlinearity as a major source of spatial DW bias and variability in off-center ADC measurements across MRI platforms, with minor contributions from shim, imaging gradients and eddy currents. The developed protocol enables empiric description of systematic bias in multicenter quantitative DWI studies. © 2015 Wiley Periodicals, Inc.

Covariance analyses of satellite-derived mesoscale wind fields

NASA Technical Reports Server (NTRS)

Maddox, R. A.; Vonder Haar, T. H.

1979-01-01

Statistical structure functions have been computed independently for nine satellite-derived mesoscale wind fields that were obtained on two different days. Small cumulus clouds were tracked at 5 min intervals, but since these clouds occurred primarily in the warm sectors of midlatitude cyclones the results cannot be considered representative of the circulations within cyclones in general. The field structure varied considerably with time and was especially affected if mesoscale features were observed. The wind fields on the 2 days studied were highly anisotropic with large gradients in structure occurring approximately normal to the mean flow. Structure function calculations for the combined set of satellite winds were used to estimate random error present in the fields. It is concluded for these data that the random error in vector winds derived from cumulus cloud tracking using high-frequency satellite data is less than 1.75 m/s. Spatial correlation functions were also computed for the nine data sets. Normalized correlation functions were considerably different for u and v components and decreased rapidly as data point separation increased for both components. The correlation functions for transverse and longitudinal components decreased less rapidly as data point separation increased.

Registration of 2D to 3D joint images using phase-based mutual information

NASA Astrophysics Data System (ADS)

Dalvi, Rupin; Abugharbieh, Rafeef; Pickering, Mark; Scarvell, Jennie; Smith, Paul

2007-03-01

Registration of two dimensional to three dimensional orthopaedic medical image data has important applications particularly in the area of image guided surgery and sports medicine. Fluoroscopy to computer tomography (CT) registration is an important case, wherein digitally reconstructed radiographs derived from the CT data are registered to the fluoroscopy data. Traditional registration metrics such as intensity-based mutual information (MI) typically work well but often suffer from gross misregistration errors when the image to be registered contains a partial view of the anatomy visible in the target image. Phase-based MI provides a robust alternative similarity measure which, in addition to possessing the general robustness and noise immunity that MI provides, also employs local phase information in the registration process which makes it less susceptible to the aforementioned errors. In this paper, we propose using the complex wavelet transform for computing image phase information and incorporating that into a phase-based MI measure for image registration. Tests on a CT volume and 6 fluoroscopy images of the knee are presented. The femur and the tibia in the CT volume were individually registered to the fluoroscopy images using intensity-based MI, gradient-based MI and phase-based MI. Errors in the coordinates of fiducials present in the bone structures were used to assess the accuracy of the different registration schemes. Quantitative results demonstrate that the performance of intensity-based MI was the worst. Gradient-based MI performed slightly better, while phase-based MI results were the best consistently producing the lowest errors.

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

NASA Technical Reports Server (NTRS)

Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.

2014-01-01

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

IR GRIN optics: design and fabrication

NASA Astrophysics Data System (ADS)

Gibson, Daniel; Bayya, Shyam; Nguyen, Vinh; Sanghera, Jas; Kotov, Mikhail; McClain, Collin; Deegan, John; Lindberg, George; Unger, Blair; Vizgaitis, Jay

2017-06-01

Infrared (IR) transmitting gradient index (GRIN) materials have been developed for broad-band IR imaging. This material is derived from the diffusion of homogeneous chalcogenide glasses has good transmission for all IR wavebands. The optical properties of the IR-GRIN materials are presented and the fabrication and design methodologies are discussed. Modeling and optimization of the diffusion process is exploited to minimize the deviation of the index profile from the design profile. Fully diffused IR-GRIN blanks with Δn of 0.2 are demonstrated with deviation errors of +/-0.01 refractive index units.

Determination of the mean solid-liquid interface energy of pivalic acid

NASA Technical Reports Server (NTRS)

Singh, N. B.; Gliksman, M. E.

1989-01-01

A high-confidence solid-liquid interfacial energy is determined for an anisotropic material. A coaxial composite having a cylindrical specimen chamber geometry provides a thermal gradient with an axial heating wire. The surface energy is derived from measurements of grain boundary groove shapes. Applying this method to pivalic acid, a surface energy of 2.84 erg/sq cm was determined with a total systematic and random error less than 10 percent. The value of interfacial energy corresponds to 24 percent of the latent heat of fusion per molecule.

FORTRAN program for analyzing ground-based radar data: Usage and derivations, version 6.2

NASA Technical Reports Server (NTRS)

Haering, Edward A., Jr.; Whitmore, Stephen A.

1995-01-01

A postflight FORTRAN program called 'radar' reads and analyzes ground-based radar data. The output includes position, velocity, and acceleration parameters. Air data parameters are also provided if atmospheric characteristics are input. This program can read data from any radar in three formats. Geocentric Cartesian position can also be used as input, which may be from an inertial navigation or Global Positioning System. Options include spike removal, data filtering, and atmospheric refraction corrections. Atmospheric refraction can be corrected using the quick White Sands method or the gradient refraction method, which allows accurate analysis of very low elevation angle and long-range data. Refraction properties are extrapolated from surface conditions, or a measured profile may be input. Velocity is determined by differentiating position. Accelerations are determined by differentiating velocity. This paper describes the algorithms used, gives the operational details, and discusses the limitations and errors of the program. Appendices A through E contain the derivations for these algorithms. These derivations include an improvement in speed to the exact solution for geodetic altitude, an improved algorithm over earlier versions for determining scale height, a truncation algorithm for speeding up the gradient refraction method, and a refinement of the coefficients used in the White Sands method for Edwards AFB, California. Appendix G contains the nomenclature.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Tolerance assignment in optical design

NASA Astrophysics Data System (ADS)

Youngworth, Richard Neil

2002-09-01

Tolerance assignment is necessary in any engineering endeavor because fabricated systems---due to the stochastic nature of manufacturing and assembly processes---necessarily deviate from the nominal design. This thesis addresses the problem of optical tolerancing. The work can logically be split into three different components that all play an essential role. The first part addresses the modeling of manufacturing errors in contemporary fabrication and assembly methods. The second component is derived from the design aspect---the development of a cost-based tolerancing procedure. The third part addresses the modeling of image quality in an efficient manner that is conducive to the tolerance assignment process. The purpose of the first component, modeling manufacturing errors, is twofold---to determine the most critical tolerancing parameters and to understand better the effects of fabrication errors. Specifically, mid-spatial-frequency errors, typically introduced in sub-aperture grinding and polishing fabrication processes, are modeled. The implication is that improving process control and understanding better the effects of the errors makes the task of tolerance assignment more manageable. Conventional tolerancing methods do not directly incorporate cost. Consequently, tolerancing approaches tend to focus more on image quality. The goal of the second part of the thesis is to develop cost-based tolerancing procedures that facilitate optimum system fabrication by generating the loosest acceptable tolerances. This work has the potential to impact a wide range of optical designs. The third element, efficient modeling of image quality, is directly related to the cost-based optical tolerancing method. Cost-based tolerancing requires efficient and accurate modeling of the effects of errors on the performance of optical systems. Thus it is important to be able to compute the gradient and the Hessian, with respect to the parameters that need to be toleranced, of the figure of merit that measures the image quality of a system. An algebraic method for computing the gradient and the Hessian is developed using perturbation theory.

A general strategy for performing temperature-programming in high performance liquid chromatography--prediction of segmented temperature gradients.

PubMed

Wiese, Steffen; Teutenberg, Thorsten; Schmidt, Torsten C

2011-09-28

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed to predict retention times for segmented-temperature gradients based on temperature-gradient input data in liquid chromatography (LC) with high accuracy. The LES model assumes that retention times for isothermal separations can be predicted based on two temperature gradients and is employed to calculate the retention factor of an analyte when changing the start temperature of the temperature gradient. In this study it was investigated whether this approach can also be employed in LC. It was shown that this approximation cannot be transferred to temperature-programmed LC where a temperature range from 60°C up to 180°C is investigated. Major relative errors up to 169.6% were observed for isothermal retention factor predictions. In order to predict retention times for temperature gradients with different start temperatures in LC, another relationship is required to describe the influence of temperature on retention. Therefore, retention times for isothermal separations based on isothermal input runs were predicted using a plot of the natural logarithm of the retention factor vs. the inverse temperature and a plot of the natural logarithm of the retention factor vs. temperature. It could be shown that a plot of lnk vs. T yields more reliable isothermal/isocratic retention time predictions than a plot of lnk vs. 1/T which is usually employed. Hence, in order to predict retention times for temperature-gradients with different start temperatures in LC, two temperature gradient and two isothermal measurements have been employed. In this case, retention times can be predicted with a maximal relative error of 5.5% (average relative error: 2.9%). In comparison, if the start temperature of the simulated temperature gradient is equal to the start temperature of the input data, only two temperature-gradient measurements are required. Under these conditions, retention times can be predicted with a maximal relative error of 4.3% (average relative error: 2.2%). As an example, the systematic method development for an isothermal as well as a temperature gradient separation of selected sulfonamides by means of the adapted LES model is demonstrated using a pure water mobile phase. Both methods are compared and it is shown that the temperature-gradient separation provides some advantages over the isothermal separation in terms of limits of detection and analysis time. Copyright © 2011 Elsevier B.V. All rights reserved.

Analysis of deformable image registration accuracy using computational modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong Hualiang; Kim, Jinkoo; Chetty, Indrin J.

2010-03-15

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration (DIR) were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results showmore » that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution (SR) and multiresolution (MR) registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image (and 0.7 mm mean error averaged in the lung only). For the low gradient prostate phantom, these algorithms (both SR and MR) required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance (mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively) on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy (1.4 mm for SR and 1.5 mm for MR). The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous (low intensity gradient) regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.« less

An Optimal Control Modification to Model-Reference Adaptive Control for Fast Adaptation

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Krishnakumar, Kalmanje; Boskovic, Jovan

2008-01-01

This paper presents a method that can achieve fast adaptation for a class of model-reference adaptive control. It is well-known that standard model-reference adaptive control exhibits high-gain control behaviors when a large adaptive gain is used to achieve fast adaptation in order to reduce tracking error rapidly. High gain control creates high-frequency oscillations that can excite unmodeled dynamics and can lead to instability. The fast adaptation approach is based on the minimization of the squares of the tracking error, which is formulated as an optimal control problem. The necessary condition of optimality is used to derive an adaptive law using the gradient method. This adaptive law is shown to result in uniform boundedness of the tracking error by means of the Lyapunov s direct method. Furthermore, this adaptive law allows a large adaptive gain to be used without causing undesired high-gain control effects. The method is shown to be more robust than standard model-reference adaptive control. Simulations demonstrate the effectiveness of the proposed method.

Analysis of phase error effects in multishot diffusion-prepared turbo spin echo imaging

PubMed Central

Cervantes, Barbara; Kooijman, Hendrik; Karampinos, Dimitrios C.

2017-01-01

Background To characterize the effect of phase errors on the magnitude and the phase of the diffusion-weighted (DW) signal acquired with diffusion-prepared turbo spin echo (dprep-TSE) sequences. Methods Motion and eddy currents were identified as the main sources of phase errors. An analytical expression for the effect of phase errors on the acquired signal was derived and verified using Bloch simulations, phantom, and in vivo experiments. Results Simulations and experiments showed that phase errors during the diffusion preparation cause both magnitude and phase modulation on the acquired data. When motion-induced phase error (MiPe) is accounted for (e.g., with motion-compensated diffusion encoding), the signal magnitude modulation due to the leftover eddy-current-induced phase error cannot be eliminated by the conventional phase cycling and sum-of-squares (SOS) method. By employing magnitude stabilizers, the phase-error-induced magnitude modulation, regardless of its cause, was removed but the phase modulation remained. The in vivo comparison between pulsed gradient and flow-compensated diffusion preparations showed that MiPe needed to be addressed in multi-shot dprep-TSE acquisitions employing magnitude stabilizers. Conclusions A comprehensive analysis of phase errors in dprep-TSE sequences showed that magnitude stabilizers are mandatory in removing the phase error induced magnitude modulation. Additionally, when multi-shot dprep-TSE is employed the inconsistent signal phase modulation across shots has to be resolved before shot-combination is performed. PMID:28516049

Assessment of the Derivative-Moment Transformation method for unsteady-load estimation

NASA Astrophysics Data System (ADS)

Mohebbian, Ali; Rival, David

2011-11-01

It is often difficult, if not impossible, to measure the aerodynamic or hydrodynamic forces on a moving body. For this reason, a classical control-volume technique is typically applied to extract the unsteady forces instead. However, measuring the acceleration term within the volume of interest using PIV can be limited by optical access, reflections as well as shadows. Therefore in this study an alternative approach, termed the Derivative-Moment Transformation (DMT) method, is introduced and tested on a synthetic data set produced using numerical simulations. The test case involves the unsteady loading of a flat plate in a two-dimensional, laminar periodic gust. The results suggest that the DMT method can accurately predict the acceleration term so long as appropriate spatial and temporal resolutions are maintained. The major deficiency was found to be the determination of pressure in the wake. The effect of control-volume size was investigated suggesting that smaller domains work best by minimizing the associated error with the pressure field. When increasing the control-volume size, the number of calculations necessary for the pressure-gradient integration increases, in turn substantially increasing the error propagation.

Improved Saturated Hydraulic Conductivity Pedotransfer Functions Using Machine Learning Methods

NASA Astrophysics Data System (ADS)

Araya, S. N.; Ghezzehei, T. A.

2017-12-01

Saturated hydraulic conductivity (Ks) is one of the fundamental hydraulic properties of soils. Its measurement, however, is cumbersome and instead pedotransfer functions (PTFs) are often used to estimate it. Despite a lot of progress over the years, generic PTFs that estimate hydraulic conductivity generally don't have a good performance. We develop significantly improved PTFs by applying state of the art machine learning techniques coupled with high-performance computing on a large database of over 20,000 soils—USKSAT and the Florida Soil Characterization databases. We compared the performance of four machine learning algorithms (k-nearest neighbors, gradient boosted model, support vector machine, and relevance vector machine) and evaluated the relative importance of several soil properties in explaining Ks. An attempt is also made to better account for soil structural properties; we evaluated the importance of variables derived from transformations of soil water retention characteristics and other soil properties. The gradient boosted models gave the best performance with root mean square errors less than 0.7 and mean errors in the order of 0.01 on a log scale of Ks [cm/h]. The effective particle size, D10, was found to be the single most important predictor. Other important predictors included percent clay, bulk density, organic carbon percent, coefficient of uniformity and values derived from water retention characteristics. Model performances were consistently better for Ks values greater than 10 cm/h. This study maximizes the extraction of information from a large database to develop generic machine learning based PTFs to estimate Ks. The study also evaluates the importance of various soil properties and their transformations in explaining Ks.

Quantification of susceptibility change at high-concentrated SPIO-labeled target by characteristic phase gradient recognition.

PubMed

Zhu, Haitao; Nie, Binbin; Liu, Hua; Guo, Hua; Demachi, Kazuyuki; Sekino, Masaki; Shan, Baoci

2016-05-01

Phase map cross-correlation detection and quantification may produce highlighted signal at superparamagnetic iron oxide nanoparticles, and distinguish them from other hypointensities. The method may quantify susceptibility change by performing least squares analysis between a theoretically generated magnetic field template and an experimentally scanned phase image. Because characteristic phase recognition requires the removal of phase wrap and phase background, additional steps of phase unwrapping and filtering may increase the chance of computing error and enlarge the inconsistence among algorithms. To solve problem, phase gradient cross-correlation and quantification method is developed by recognizing characteristic phase gradient pattern instead of phase image because phase gradient operation inherently includes unwrapping and filtering functions. However, few studies have mentioned the detectable limit of currently used phase gradient calculation algorithms. The limit may lead to an underestimation of large magnetic susceptibility change caused by high-concentrated iron accumulation. In this study, mathematical derivation points out the value of maximum detectable phase gradient calculated by differential chain algorithm in both spatial and Fourier domain. To break through the limit, a modified quantification method is proposed by using unwrapped forward differentiation for phase gradient generation. The method enlarges the detectable range of phase gradient measurement and avoids the underestimation of magnetic susceptibility. Simulation and phantom experiments were used to quantitatively compare different methods. In vivo application performs MRI scanning on nude mice implanted by iron-labeled human cancer cells. Results validate the limit of detectable phase gradient and the consequent susceptibility underestimation. Results also demonstrate the advantage of unwrapped forward differentiation compared with differential chain algorithms for susceptibility quantification at high-concentrated iron accumulation. Copyright © 2015 Elsevier Inc. All rights reserved.

Parameter estimation for terrain modeling from gradient data. [navigation system for Martian rover

NASA Technical Reports Server (NTRS)

Dangelo, K. R.

1974-01-01

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

Error field penetration and locking to the backward propagating wave

DOE PAGES

Finn, John M.; Cole, Andrew J.; Brennan, Dylan P.

2015-12-30

In this letter we investigate error field penetration, or locking, behavior in plasmas having stable tearing modes with finite real frequencies w r in the plasma frame. In particular, we address the fact that locking can drive a significant equilibrium flow. We show that this occurs at a velocity slightly above v = w r/k, corresponding to the interaction with a backward propagating tearing mode in the plasma frame. Results are discussed for a few typical tearing mode regimes, including a new derivation showing that the existence of real frequencies occurs for viscoresistive tearing modes, in an analysis including themore » effects of pressure gradient, curvature and parallel dynamics. The general result of locking to a finite velocity flow is applicable to a wide range of tearing mode regimes, indeed any regime where real frequencies occur.« less

Measuring attitude with a gradiometer

NASA Technical Reports Server (NTRS)

Sonnabend, David; Gardner, Thomas G.

1994-01-01

This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.

Effects of horizontal refractivity gradients on the accuracy of laser ranging to satellites

NASA Technical Reports Server (NTRS)

Gardner, C. S.

1976-01-01

Numerous formulas have been developed to partially correct laser ranging data for the effects of atmospheric refraction. All the formulas assume the atmospheric refractivity profile is spherically symmetric. The effects of horizontal refractivity gradients are investigated by ray tracing through spherically symmetric and three-dimensional refractivity profiles. The profiles are constructed from radiosonde data. The results indicate that the horizontal gradients introduce an rms error of approximately 3 cm when the satellite is near 10 deg elevation. The error decreases to a few millimeters near zenith.

Supplemental optical specifications for imaging systems: parameters of phase gradient

NASA Astrophysics Data System (ADS)

Xuan, Bin; Li, Jun-Feng; Wang, Peng; Chen, Xiao-Ping; Song, Shu-Mei; Xie, Jing-Jiang

2009-12-01

Specifications of phase error, peak to valley (PV), and root mean square (rms) are not able to represent the properties of a wavefront reasonably because of their irresponsibility for spatial frequencies. Power spectral density is a parameter that is especially effective to indicate the frequency regime. However, it seems not convenient for opticians to implement. Parameters of phase gradient, PV gradient, and rms gradient are most correlated with a point-spread function of an imaging system, and they can provide clear instruction of manufacture. The algorithms of gradient parameters have been modified in order to represent the image quality better. In order to demonstrate the analyses, an experimental spherical mirror has been worked out. It is clear that imaging performances can be maintained while manufacture difficulties are decreased when a reasonable trade-off between specifications of phase error and phase gradient is made.

A refined model of sedimentary rock cover in the southeastern part of the Congo basin from GOCE gravity and vertical gravity gradient observations

NASA Astrophysics Data System (ADS)

Martinec, Zdeněk; Fullea, Javier

2015-03-01

We aim to interpret the vertical gravity and vertical gravity gradient of the GOCE-GRACE combined gravity model over the southeastern part of the Congo basin to refine the published model of sedimentary rock cover. We use the GOCO03S gravity model and evaluate its spherical harmonic representation at or near the Earth's surface. In this case, the gradiometry signals are enhanced as compared to the original measured GOCE gradients at satellite height and better emphasize the spatial pattern of sedimentary geology. To avoid aliasing, the omission error of the modelled gravity induced by the sedimentary rocks is adjusted to that of the GOCO03S gravity model. The mass-density Green's functions derived for the a priori structure of the sediments show a slightly greater sensitivity to the GOCO03S vertical gravity gradient than to the vertical gravity. Hence, the refinement of the sedimentary model is carried out for the vertical gravity gradient over the basin, such that a few anomalous values of the GOCO03S-derived vertical gravity gradient are adjusted by refining the model. We apply the 5-parameter Helmert's transformation, defined by 2 translations, 1 rotation and 2 scale parameters that are searched for by the steepest descent method. The refined sedimentary model is only slightly changed with respect to the original map, but it significantly improves the fit of the vertical gravity and vertical gravity gradient over the basin. However, there are still spatial features in the gravity and gradiometric data that remain unfitted by the refined model. These may be due to lateral density variation that is not contained in the model, a density contrast at the Moho discontinuity, lithospheric density stratifications or mantle convection. In a second step, the refined sedimentary model is used to find the vertical density stratification of sedimentary rocks. Although the gravity data can be interpreted by a constant sedimentary density, such a model does not correspond to the gravitational compaction of sedimentary rocks. Therefore, the density model is extended by including a linear increase in density with depth. Subsequent L2 and L∞ norm minimization procedures are applied to find the density parameters by adjusting both the vertical gravity and the vertical gravity gradient. We found that including the vertical gravity gradient in the interpretation of the GOCO03S-derived data reduces the non-uniqueness of the inverse gradiometric problem for density determination. The density structure of the sedimentary formations that provide the optimum predictions of the GOCO03S-derived gravity and vertical gradient of gravity consists of a surface density contrast with respect to surrounding rocks of 0.24-0.28 g/cm3 and its decrease with depth of 0.05-0.25 g/cm3 per 10 km. Moreover, the case where the sedimentary rocks are gravitationally completely compacted in the deepest parts of the basin is supported by L∞ norm minimization. However, this minimization also allows a remaining density contrast at the deepest parts of the sedimentary basin of about 0.1 g/cm3.

Velocity encoding with the slice select refocusing gradient for faster imaging and reduced chemical shift-induced phase errors.

PubMed

Middione, Matthew J; Thompson, Richard B; Ennis, Daniel B

2014-06-01

To investigate a novel phase-contrast MRI velocity-encoding technique for faster imaging and reduced chemical shift-induced phase errors. Velocity encoding with the slice select refocusing gradient achieves the target gradient moment by time shifting the refocusing gradient, which enables the use of the minimum in-phase echo time (TE) for faster imaging and reduced chemical shift-induced phase errors. Net forward flow was compared in 10 healthy subjects (N = 10) within the ascending aorta (aAo), main pulmonary artery (PA), and right/left pulmonary arteries (RPA/LPA) using conventional flow compensated and flow encoded (401 Hz/px and TE = 3.08 ms) and slice select refocused gradient velocity encoding (814 Hz/px and TE = 2.46 ms) at 3 T. Improved net forward flow agreement was measured across all vessels for slice select refocused gradient compared to flow compensated and flow encoded: aAo vs. PA (1.7% ± 1.9% vs. 5.8% ± 2.8%, P = 0.002), aAo vs. RPA + LPA (2.1% ± 1.7% vs. 6.0% ± 4.3%, P = 0.03), and PA vs. RPA + LPA (2.9% ± 2.1% vs. 6.1% ± 6.3%, P = 0.04), while increasing temporal resolution (35%) and signal-to-noise ratio (33%). Slice select refocused gradient phase-contrast MRI with a high receiver bandwidth and minimum in-phase TE provides more accurate and less variable flow measurements through the reduction of chemical shift-induced phase errors and a reduced TE/repetition time, which can be used to increase the temporal/spatial resolution and/or reduce breath hold durations. Copyright © 2013 Wiley Periodicals, Inc.

Sapwood temperature gradients between lower stems and the crown do not influence estimates of stand-level stem CO(2) efflux.

PubMed

Bowman, William P; Turnbull, Matthew H; Tissue, David T; Whitehead, David; Griffin, Kevin L

2008-10-01

Temperature plays a critical role in the regulation of respiration rates and is often used to scale measurements of respiration to the stand-level and calculate annual respiratory fluxes. Previous studies have indicated that failure to consider temperature gradients between sun-exposed stems and branches in the crown and shaded lower stems may result in errors when deriving stand-level estimates of stem CO(2) efflux. We measured vertical gradients in sapwood temperature in a mature lowland podocarp rain forest in New Zealand to: (1) estimate the effects of within-stem temperature variation on the vertical distribution of stem CO(2) efflux; and (2) use these findings to estimate stand-level stem CO(2) efflux for this forest. Large within-stem gradients in sapwood temperature (1.6 +/- 0.1 to 6.0 +/- 0.5 degrees C) were observed. However, these gradients did not significantly influence the stand-level estimate of stem CO(2) efflux in this forest (536 +/- 42 mol CO(2) ha(-1) day(-1)) or the vertical distribution of stem CO(2) efflux, because of the opposing effects of daytime warming and nighttime cooling on CO(2) efflux in the canopy, and the small fraction of the woody biomass in the crowns of forest trees. Our findings suggest that detailed measurements of within-stand temperature gradients are unlikely to greatly improve the accuracy of tree- or stand-level estimates of stem CO(2) efflux.

Phase correction system for automatic focusing of synthetic aperture radar

DOEpatents

Eichel, Paul H.; Ghiglia, Dennis C.; Jakowatz, Jr., Charles V.

1990-01-01

A phase gradient autofocus system for use in synthetic aperture imaging accurately compensates for arbitrary phase errors in each imaged frame by locating highlighted areas and determining the phase disturbance or image spread associated with each of these highlight areas. An estimate of the image spread for each highlighted area in a line in the case of one dimensional processing or in a sector, in the case of two-dimensional processing, is determined. The phase error is determined using phase gradient processing. The phase error is then removed from the uncorrected image and the process is iteratively performed to substantially eliminate phase errors which can degrade the image.

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Analysis and forecast experiments incorporating satellite soundings and cloud and water vapor drift wind information

NASA Technical Reports Server (NTRS)

Goodman, Brian M.; Diak, George R.; Mills, Graham A.

1986-01-01

A system for assimilating conventional meteorological data and satellite-derived data in order to produce four-dimensional gridded data sets of the primary atmospheric variables used for updating limited area forecast models is described. The basic principles of a data assimilation scheme as proposed by Lorenc (1984) are discussed. The design of the system and its incremental assimilation cycles are schematically presented. The assimilation system was tested using radiosonde, buoy, VAS temperature, dew point, gradient wind data, cloud drift, and water vapor motion data. The rms vector errors for the data are analyzed.

Importance of Ionospheric Gradients for error Correction

NASA Astrophysics Data System (ADS)

Ravula, Ramprasad

Importance of Ionospheric Gradients for error Correction R. Ram Prasad1, P.Nagasekhar2 1Sai Spurthi Institute of Technology-JNTU Hyderabad,2Sai Spurthi Institute of Technology-JNTU Hyderabad Email ID:rams.ravula@gmail.com In India, Indian Space Research Organization (ISRO) has established with an objective to develop space technology and its application to various national tasks. To cater to the needs of civil aviation applications, GPS Aided Geo Augmented Navigation (GAGAN) system is being jointly implemented along with Airports Authority of India (AAI) over the Indian region. The most predominant parameter affecting the navigation accuracy of GAGAN is ionospheric delay which is a function of total number of electrons present in one square meter cylindrical cross sectional area in the line of site direction between the satellite and the user on the earth i.e. Total Electron Content (TEC).The irregular distribution of electron densities i.e. rate of TEC variation, causes Ionospheric gradients such as spatial gradients (Expressed in TECu/km) and temporal gradients (Expressed in TECu /minute). Among the satellite signals arriving to the earth in multiple directions, the signals which suffer from severe ionospheric gradients can be estimated i.e. Rate of TEC Index (ROTI) and Rate of TEC (ROT). These aspects which contribute to errors can be treated for improving GAGAN positional accuracy.

Analysis of Measurement Error and Estimator Shape in Three-Point Hydraulic Gradient Estimators

NASA Astrophysics Data System (ADS)

McKenna, S. A.; Wahi, A. K.

2003-12-01

Three spatially separated measurements of head provide a means of estimating the magnitude and orientation of the hydraulic gradient. Previous work with three-point estimators has focused on the effect of the size (area) of the three-point estimator and measurement error on the final estimates of the gradient magnitude and orientation in laboratory and field studies (Mizell, 1980; Silliman and Frost, 1995; Silliman and Mantz, 2000; Ruskauff and Rumbaugh, 1996). However, a systematic analysis of the combined effects of measurement error, estimator shape and estimator orientation relative to the gradient orientation has not previously been conducted. Monte Carlo simulation with an underlying assumption of a homogeneous transmissivity field is used to examine the effects of uncorrelated measurement error on a series of eleven different three-point estimators having the same size but different shapes as a function of the orientation of the true gradient. Results show that the variance in the estimate of both the magnitude and the orientation increase linearly with the increase in measurement error in agreement with the results of stochastic theory for estimators that are small relative to the correlation length of transmissivity (Mizell, 1980). Three-point estimator shapes with base to height ratios between 0.5 and 5.0 provide accurate estimates of magnitude and orientation across all orientations of the true gradient. As an example, these results are applied to data collected from a monitoring network of 25 wells at the WIPP site during two different time periods. The simulation results are used to reduce the set of all possible combinations of three wells to those combinations with acceptable measurement errors relative to the amount of head drop across the estimator and base to height ratios between 0.5 and 5.0. These limitations reduce the set of all possible well combinations by 98 percent and show that size alone as defined by triangle area is not a valid discriminator of whether or not the estimator provides accurate estimates of the gradient magnitude and orientation. This research was funded by WIPP programs administered by the U.S Department of Energy. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Temporal and spatial deviation in F2 peak parameters derived from FORMOSAT-3/COSMIC

NASA Astrophysics Data System (ADS)

Kumar, Sanjay; Singh, R. P.; Tan, Eng Leong; Singh, A. K.; Ghodpage, R. N.; Siingh, Devendraa

2016-06-01

The plasma frequency profiles derived from the Constellation of Observing System for Meteorology, Ionosphere and Climate (COSMIC) radio occultation measurements are compared with ground-based ionosonde data during the year 2013. Equatorial and midlatitude five stations located in the Northern and Southern Hemisphere are considered: Jicamarca, Jeju, Darwin, Learmonth, and Juliusruh. The aim is to validate the COSMIC-derived data with ground-based measurements and to estimate the difference in plasma frequency (which represents electron density) and height of F2 layer peak during the daytime/nighttime and during different seasons by comparing the two data sets. Analysis showed that the nighttime data are better correlated than the daytime, and the maximum difference occurs at the equatorial ionospheric anomaly (EIA) station as compared to lower and midlatitude stations during the equinox months. The difference between daytime and nighttime correlations becomes insignificant at midlatitude stations. The statistical analysis of computed errors in foF2 (hmF2) showed Gaussian nature with the most probable error range of ±15% (±10%) at the equatorial and EIA stations, ±9% (±7%) outside the EIA region which reduced to ±8% (±6%) at midlatitude stations. The reduction in error at midlatitudes is attributed to the decrease in latitudinal electron density gradients. Comparing the analyzed data during the three geomagnetic storms and quiet days of the same months, it is observed that the differences are significantly enhanced during storm periods and the magnitude of difference in foF2 increases with the intensity of geomagnetic storm.

Error measure comparison of currently employed dose-modulation schemes for e-beam proximity effect control

NASA Astrophysics Data System (ADS)

Peckerar, Martin C.; Marrian, Christie R.

1995-05-01

Standard matrix inversion methods of e-beam proximity correction are compared with a variety of pseudoinverse approaches based on gradient descent. It is shown that the gradient descent methods can be modified using 'regularizers' (terms added to the cost function minimized during gradient descent). This modification solves the 'negative dose' problem in a mathematically sound way. Different techniques are contrasted using a weighted error measure approach. It is shown that the regularization approach leads to the highest quality images. In some cases, ignoring negative doses yields results which are worse than employing an uncorrected dose file.

Multipolar Ewald methods, 1: theory, accuracy, and performance.

PubMed

Giese, Timothy J; Panteva, Maria T; Chen, Haoyuan; York, Darrin M

2015-02-10

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Differentiation from First Principles Using Spreadsheets

ERIC Educational Resources Information Center

Lim, Kieran F.

2008-01-01

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by…

Correction of phase errors in quantitative water-fat imaging using a monopolar time-interleaved multi-echo gradient echo sequence.

PubMed

Ruschke, Stefan; Eggers, Holger; Kooijman, Hendrik; Diefenbach, Maximilian N; Baum, Thomas; Haase, Axel; Rummeny, Ernst J; Hu, Houchun H; Karampinos, Dimitrios C

2017-09-01

To propose a phase error correction scheme for monopolar time-interleaved multi-echo gradient echo water-fat imaging that allows accurate and robust complex-based quantification of the proton density fat fraction (PDFF). A three-step phase correction scheme is proposed to address a) a phase term induced by echo misalignments that can be measured with a reference scan using reversed readout polarity, b) a phase term induced by the concomitant gradient field that can be predicted from the gradient waveforms, and c) a phase offset between time-interleaved echo trains. Simulations were carried out to characterize the concomitant gradient field-induced PDFF bias and the performance estimating the phase offset between time-interleaved echo trains. Phantom experiments and in vivo liver and thigh imaging were performed to study the relevance of each of the three phase correction steps on PDFF accuracy and robustness. The simulation, phantom, and in vivo results showed in agreement with the theory an echo time-dependent PDFF bias introduced by the three phase error sources. The proposed phase correction scheme was found to provide accurate PDFF estimation independent of the employed echo time combination. Complex-based time-interleaved water-fat imaging was found to give accurate and robust PDFF measurements after applying the proposed phase error correction scheme. Magn Reson Med 78:984-996, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

A comparison of methods for computing the sigma-coordinate pressure gradient force for flow over sloped terrain in a hybrid theta-sigma model

NASA Technical Reports Server (NTRS)

Johnson, D. R.; Uccellini, L. W.

1983-01-01

In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Derivative Free Gradient Projection Algorithms for Rotation

ERIC Educational Resources Information Center

Jennrich, Robert I.

2004-01-01

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients…

Simulation studies of wide and medium field of view earth radiation data analysis

NASA Technical Reports Server (NTRS)

Green, R. N.

1978-01-01

A parameter estimation technique is presented to estimate the radiative flux distribution over the earth from radiometer measurements at satellite altitude. The technique analyzes measurements from a wide field of view (WFOV), horizon to horizon, nadir pointing sensor with a mathematical technique to derive the radiative flux estimates at the top of the atmosphere for resolution elements smaller than the sensor field of view. A computer simulation of the data analysis technique is presented for both earth-emitted and reflected radiation. Zonal resolutions are considered as well as the global integration of plane flux. An estimate of the equator-to-pole gradient is obtained from the zonal estimates. Sensitivity studies of the derived flux distribution to directional model errors are also presented. In addition to the WFOV results, medium field of view results are presented.

Communication: Exact analytical derivatives for the domain-based local pair natural orbital MP2 method (DLPNO-MP2)

NASA Astrophysics Data System (ADS)

Pinski, Peter; Neese, Frank

2018-01-01

Electron correlation methods based on pair natural orbitals (PNOs) have gained an increasing degree of interest in recent years, as they permit energy calculations to be performed on systems containing up to many hundred atoms, while maintaining chemical accuracy for reaction energies. We present an approach for taking exact analytical first derivatives of the energy contributions in the simplest method of the family of Domain-based Local Pair Natural Orbital (DLPNO) methods, closed-shell DLPNO-MP2. The Lagrangian function contains constraints to account for the relaxation of PNOs. RI-MP2 reference geometries are reproduced accurately, as exemplified for four systems with a substantial degree of nonbonding interactions. By the example of electric field gradients, we demonstrate that omitting PNO-specific constraints can lead to dramatic errors for orbital-relaxed properties.

A single-gradient junction technique to replace multiple-junction shifts for craniospinal irradiation treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hadley, Austin; Ding, George X., E-mail: george.ding@vanderbilt.edu

2014-01-01

Craniospinal irradiation (CSI) requires abutting fields at the cervical spine. Junction shifts are conventionally used to prevent setup error–induced overdosage/underdosage from occurring at the same location. This study compared the dosimetric differences at the cranial-spinal junction between a single-gradient junction technique and conventional multiple-junction shifts and evaluated the effect of setup errors on the dose distributions between both techniques for a treatment course and single fraction. Conventionally, 2 lateral brain fields and a posterior spine field(s) are used for CSI with weekly 1-cm junction shifts. We retrospectively replanned 4 CSI patients using a single-gradient junction between the lateral brain fieldsmore » and the posterior spine field. The fields were extended to allow a minimum 3-cm field overlap. The dose gradient at the junction was achieved using dose painting and intensity-modulated radiation therapy planning. The effect of positioning setup errors on the dose distributions for both techniques was simulated by applying shifts of ± 3 and 5 mm. The resulting cervical spine doses across the field junction for both techniques were calculated and compared. Dose profiles were obtained for both a single fraction and entire treatment course to include the effects of the conventional weekly junction shifts. Compared with the conventional technique, the gradient-dose technique resulted in higher dose uniformity and conformity to the target volumes, lower organ at risk (OAR) mean and maximum doses, and diminished hot spots from systematic positioning errors over the course of treatment. Single-fraction hot and cold spots were improved for the gradient-dose technique. The single-gradient junction technique provides improved conformity, dose uniformity, diminished hot spots, lower OAR mean and maximum dose, and one plan for the entire treatment course, which reduces the potential human error associated with conventional 4-shifted plans.« less

What is the best way to contour lung tumors on PET scans? Multiobserver validation of a gradient-based method using a NSCLC digital PET phantom.

PubMed

Werner-Wasik, Maria; Nelson, Arden D; Choi, Walter; Arai, Yoshio; Faulhaber, Peter F; Kang, Patrick; Almeida, Fabio D; Xiao, Ying; Ohri, Nitin; Brockway, Kristin D; Piper, Jonathan W; Nelson, Aaron S

2012-03-01

To evaluate the accuracy and consistency of a gradient-based positron emission tomography (PET) segmentation method, GRADIENT, compared with manual (MANUAL) and constant threshold (THRESHOLD) methods. Contouring accuracy was evaluated with sphere phantoms and clinically realistic Monte Carlo PET phantoms of the thorax. The sphere phantoms were 10-37 mm in diameter and were acquired at five institutions emulating clinical conditions. One institution also acquired a sphere phantom with multiple source-to-background ratios of 2:1, 5:1, 10:1, 20:1, and 70:1. One observer segmented (contoured) each sphere with GRADIENT and THRESHOLD from 25% to 50% at 5% increments. Subsequently, seven physicians segmented 31 lesions (7-264 mL) from 25 digital thorax phantoms using GRADIENT, THRESHOLD, and MANUAL. For spheres <20 mm in diameter, GRADIENT was the most accurate with a mean absolute % error in diameter of 8.15% (10.2% SD) compared with 49.2% (51.1% SD) for 45% THRESHOLD (p < 0.005). For larger spheres, the methods were statistically equivalent. For varying source-to-background ratios, GRADIENT was the most accurate for spheres >20 mm (p < 0.065) and <20 mm (p < 0.015). For digital thorax phantoms, GRADIENT was the most accurate (p < 0.01), with a mean absolute % error in volume of 10.99% (11.9% SD), followed by 25% THRESHOLD at 17.5% (29.4% SD), and MANUAL at 19.5% (17.2% SD). GRADIENT had the least systematic bias, with a mean % error in volume of -0.05% (16.2% SD) compared with 25% THRESHOLD at -2.1% (34.2% SD) and MANUAL at -16.3% (20.2% SD; p value <0.01). Interobserver variability was reduced using GRADIENT compared with both 25% THRESHOLD and MANUAL (p value <0.01, Levene's test). GRADIENT was the most accurate and consistent technique for target volume contouring. GRADIENT was also the most robust for varying imaging conditions. GRADIENT has the potential to play an important role for tumor delineation in radiation therapy planning and response assessment. Copyright © 2012. Published by Elsevier Inc.

Ultrafast NMR diffusion measurements exploiting chirp spin echoes.

PubMed

Ahola, Susanna; Mankinen, Otto; Telkki, Ville-Veikko

2017-04-01

Standard diffusion NMR measurements require the repetition of the experiment multiple times with varying gradient strength or diffusion delay. This makes the experiment time-consuming and restricts the use of hyperpolarized substances to boost sensitivity. We propose a novel single-scan diffusion experiment, which is based on spatial encoding of two-dimensional data, employing the spin-echoes created by two successive adiabatic frequency-swept chirp π pulses. The experiment is called ultrafast pulsed-field-gradient spin-echo (UF-PGSE). We present a rigorous derivation of the echo amplitude in the UF-PGSE experiment, justifying the theoretical basis of the method. The theory reveals also that the standard analysis of experimental data leads to a diffusion coefficient value overestimated by a few per cent. Although the overestimation is of the order of experimental error and thus insignificant in many practical applications, we propose that it can be compensated by a bipolar gradient version of the experiment, UF-BP-PGSE, or by corresponding stimulated-echo experiment, UF-BP-pulsed-field-gradient stimulated-echo. The latter also removes the effect of uniform background gradients. The experiments offer significant prospects for monitoring fast processes in real time as well as for increasing the sensitivity of experiments by several orders of magnitude by nuclear spin hyperpolarization. Furthermore, they can be applied as basic blocks in various ultrafast multidimensional Laplace NMR experiments. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Spiral Gradient Coil Design for Use in Cylindrical MRI Systems.

PubMed

Wang, Yaohui; Xin, Xuegang; Liu, Feng; Crozier, Stuart

2018-04-01

In magnetic resonance imaging, the stream function based method is commonly used in the design of gradient coils. However, this method can be prone to errors associated with the discretization of continuous current density and wire connections. In this paper, we propose a novel gradient coil design scheme that works directly in the wire space, avoiding the system errors that may appear in the stream function approaches. Specifically, the gradient coil pattern is described with dedicated spiral functions adjusted to allow the coil to produce the required field gradients in the imaging area, minimal stray field, and other engineering terms. The performance of a designed spiral gradient coil was compared with its stream-function counterpart. The numerical evaluation shows that when compared with the conventional solution, the inductance and resistance was reduced by 20.9 and 10.5%, respectively. The overall coil performance (evaluated by the figure of merit (FoM)) was improved up to 26.5% for the x -gradient coil design; for the z-gradient coil design, the inductance and resistance were reduced by 15.1 and 6.7% respectively, and the FoM was increased by 17.7%. In addition, by directly controlling the wire distributions, the spiral gradient coil design was much sparser than conventional coils.

Efficient gradient calibration based on diffusion MRI.

PubMed

Teh, Irvin; Maguire, Mahon L; Schneider, Jürgen E

2017-01-01

To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. The errors in apparent diffusion coefficients along orthogonal axes ranged from -9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and -0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from -5.5% to + 4.5% precalibration and were likewise reduced to -0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170-179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. © 2016 Wiley Periodicals, Inc.

Efficient gradient calibration based on diffusion MRI

PubMed Central

Teh, Irvin; Maguire, Mahon L.

2016-01-01

Purpose To propose a method for calibrating gradient systems and correcting gradient nonlinearities based on diffusion MRI measurements. Methods The gradient scaling in x, y, and z were first offset by up to 5% from precalibrated values to simulate a poorly calibrated system. Diffusion MRI data were acquired in a phantom filled with cyclooctane, and corrections for gradient scaling errors and nonlinearity were determined. The calibration was assessed with diffusion tensor imaging and independently validated with high resolution anatomical MRI of a second structured phantom. Results The errors in apparent diffusion coefficients along orthogonal axes ranged from −9.2% ± 0.4% to + 8.8% ± 0.7% before calibration and −0.5% ± 0.4% to + 0.8% ± 0.3% after calibration. Concurrently, fractional anisotropy decreased from 0.14 ± 0.03 to 0.03 ± 0.01. Errors in geometric measurements in x, y and z ranged from −5.5% to + 4.5% precalibration and were likewise reduced to −0.97% to + 0.23% postcalibration. Image distortions from gradient nonlinearity were markedly reduced. Conclusion Periodic gradient calibration is an integral part of quality assurance in MRI. The proposed approach is both accurate and efficient, can be setup with readily available materials, and improves accuracy in both anatomical and diffusion MRI to within ±1%. Magn Reson Med 77:170–179, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. PMID:26749277

IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH SCHEME WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valdarnini, R., E-mail: valda@sissa.it

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained,more » for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods.« less

A linear recurrent kernel online learning algorithm with sparse updates.

PubMed

Fan, Haijin; Song, Qing

2014-02-01

In this paper, we propose a recurrent kernel algorithm with selectively sparse updates for online learning. The algorithm introduces a linear recurrent term in the estimation of the current output. This makes the past information reusable for updating of the algorithm in the form of a recurrent gradient term. To ensure that the reuse of this recurrent gradient indeed accelerates the convergence speed, a novel hybrid recurrent training is proposed to switch on or off learning the recurrent information according to the magnitude of the current training error. Furthermore, the algorithm includes a data-dependent adaptive learning rate which can provide guaranteed system weight convergence at each training iteration. The learning rate is set as zero when the training violates the derived convergence conditions, which makes the algorithm updating process sparse. Theoretical analyses of the weight convergence are presented and experimental results show the good performance of the proposed algorithm in terms of convergence speed and estimation accuracy. Copyright © 2013 Elsevier Ltd. All rights reserved.

Simulation and mitigation of higher-order ionospheric errors in PPP

NASA Astrophysics Data System (ADS)

Zus, Florian; Deng, Zhiguo; Wickert, Jens

2017-04-01

We developed a rapid and precise algorithm to compute ionospheric phase advances in a realistic electron density field. The electron density field is derived from a plasmaspheric extension of the International Reference Ionosphere (Gulyaeva and Bilitza, 2012) and the magnetic field stems from the International Geomagnetic Reference Field. For specific station locations, elevation and azimuth angles the ionospheric phase advances are stored in a look-up table. The higher-order ionospheric residuals are computed by forming the standard linear combination of the ionospheric phase advances. In a simulation study we examine how the higher-order ionospheric residuals leak into estimated station coordinates, clocks, zenith delays and tropospheric gradients in precise point positioning. The simulation study includes a few hundred globally distributed stations and covers the time period 1990-2015. We take a close look on the estimated zenith delays and tropospheric gradients as they are considered a data source for meteorological and climate related research. We also show how the by product of this simulation study, the look-up tables, can be used to mitigate higher-order ionospheric errors in practise. Gulyaeva, T.L., and Bilitza, D. Towards ISO Standard Earth Ionosphere and Plasmasphere Model. In: New Developments in the Standard Model, edited by R.J. Larsen, pp. 1-39, NOVA, Hauppauge, New York, 2012, available at https://www.novapublishers.com/catalog/product_info.php?products_id=35812

An FPGA Architecture for Extracting Real-Time Zernike Coefficients from Measured Phase Gradients

NASA Astrophysics Data System (ADS)

Moser, Steven; Lee, Peter; Podoleanu, Adrian

2015-04-01

Zernike modes are commonly used in adaptive optics systems to represent optical wavefronts. However, real-time calculation of Zernike modes is time consuming due to two factors: the large factorial components in the radial polynomials used to define them and the large inverse matrix calculation needed for the linear fit. This paper presents an efficient parallel method for calculating Zernike coefficients from phase gradients produced by a Shack-Hartman sensor and its real-time implementation using an FPGA by pre-calculation and storage of subsections of the large inverse matrix. The architecture exploits symmetries within the Zernike modes to achieve a significant reduction in memory requirements and a speed-up of 2.9 when compared to published results utilising a 2D-FFT method for a grid size of 8×8. Analysis of processor element internal word length requirements show that 24-bit precision in precalculated values of the Zernike mode partial derivatives ensures less than 0.5% error per Zernike coefficient and an overall error of <1%. The design has been synthesized on a Xilinx Spartan-6 XC6SLX45 FPGA. The resource utilisation on this device is <3% of slice registers, <15% of slice LUTs, and approximately 48% of available DSP blocks independent of the Shack-Hartmann grid size. Block RAM usage is <16% for Shack-Hartmann grid sizes up to 32×32.

Accuracy Assessment of the Precise Point Positioning for Different Troposphere Models

NASA Astrophysics Data System (ADS)

Oguz Selbesoglu, Mahmut; Gurturk, Mert; Soycan, Metin

2016-04-01

This study investigates the accuracy and repeatability of PPP technique at different latitudes by using different troposphere delay models. Nine IGS stations were selected between 00-800 latitudes at northern hemisphere and southern hemisphere. Coordinates were obtained for 7 days at 1 hour intervals in summer and winter. At first, the coordinates were estimated by using Niell troposphere delay model with and without including north and east gradients in order to investigate the contribution of troposphere delay gradients to the positioning . Secondly, Saastamoinen model was used to eliminate troposphere path delays by using standart atmosphere parameters were extrapolated for all station levels. Finally, coordinates were estimated by using RTCA-MOPS empirical troposphere delay model. Results demonstrate that Niell troposphere delay model with horizontal gradients has better mean values of rms errors 0.09 % and 65 % than the Niell troposphere model without horizontal gradients and RTCA-MOPS model, respectively. Saastamoinen model mean values of rms errors were obtained approximately 4 times bigger than the Niell troposphere delay model with horizontal gradients.

Accuracy estimates for some global analytical models of the Earth's main magnetic field on the basis of data on gradient magnetic surveys at stratospheric balloons

NASA Astrophysics Data System (ADS)

Tsvetkov, Yu. P.; Brekhov, O. M.; Bondar, T. N.; Filippov, S. V.; Petrov, V. G.; Tsvetkova, N. M.; Frunze, A. Kh.

2014-03-01

Two global analytical models of the main magnetic field of the Earth (MFE) have been used to determine their potential in deriving an anomalous MFE from balloon magnetic surveys conducted at altitudes of ˜30 km. The daily mean spherical harmonic model (DMSHM) constructed from satellite data on the day of balloon magnetic surveys was analyzed. This model for the day of magnetic surveys was shown to be almost free of errors associated with secular variations and can be recommended for deriving an anomalous MFE. The error of the enhanced magnetic model (EMM) was estimated depending on the number of harmonics used in the model. The model limited by the first 13 harmonics was shown to be able to lead to errors in the main MFE of around 15 nT. The EMM developed to n = m = 720 and constructed on the basis of satellite and ground-based magnetic data fails to adequately simulate the anomalous MFE at altitudes of 30 km. To construct a representative model developed to m = n = 720, ground-based magnetic data should be replaced by data of balloon magnetic surveys for altitudes of ˜30 km. The results of investigations were confirmed by a balloon experiment conducted by Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of the Russian Academy of Sciences and the Moscow Aviation Institute.

Simulation of co-phase error correction of optical multi-aperture imaging system based on stochastic parallel gradient decent algorithm

NASA Astrophysics Data System (ADS)

He, Xiaojun; Ma, Haotong; Luo, Chuanxin

2016-10-01

The optical multi-aperture imaging system is an effective way to magnify the aperture and increase the resolution of telescope optical system, the difficulty of which lies in detecting and correcting of co-phase error. This paper presents a method based on stochastic parallel gradient decent algorithm (SPGD) to correct the co-phase error. Compared with the current method, SPGD method can avoid detecting the co-phase error. This paper analyzed the influence of piston error and tilt error on image quality based on double-aperture imaging system, introduced the basic principle of SPGD algorithm, and discuss the influence of SPGD algorithm's key parameters (the gain coefficient and the disturbance amplitude) on error control performance. The results show that SPGD can efficiently correct the co-phase error. The convergence speed of the SPGD algorithm is improved with the increase of gain coefficient and disturbance amplitude, but the stability of the algorithm reduced. The adaptive gain coefficient can solve this problem appropriately. This paper's results can provide the theoretical reference for the co-phase error correction of the multi-aperture imaging system.

First-row diatomics: Calculation of the geometry and energetics using self-consistent gradient-functional approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kutzler, F.W.; Painter, G.S.

1992-02-15

A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li{sub 2} through F{sub 2}. Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient correctionsmore » reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li{sub 2}, the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities.« less

Design of a microbial contamination detector and analysis of error sources in its optical path.

PubMed

Zhang, Chao; Yu, Xiang; Liu, Xingju; Zhang, Lei

2014-05-01

Microbial contamination is a growing concern in the food safety today. To effectively control the types and degree of microbial contamination during food production, this paper introduces a design for a microbial contamination detector that can be used for quick in-situ examination. The designed detector can identify the category of microbial contamination by locating its characteristic absorption peak and then can calculate the concentration of the microbial contamination by fitting the absorbance vs. concentration lines of standard samples with gradient concentrations. Based on traditional scanning grating detection system, this design improves the light splitting unit to expand the scanning range and enhance the accuracy of output wavelength. The motor rotation angle φ is designed to have a linear relationship with the output wavelength angle λ, which simplifies the conversion of output spectral curves into wavelength vs. light intensity curves. In this study, we also derive the relationship between the device's major sources of errors and cumulative error of the output wavelengths, and suggest a simple correction for these errors. The proposed design was applied to test pigments and volatile basic nitrogen (VBN) which evaluated microbial contamination degrees of meats, and the deviations between the measured values and the pre-set values were only in a low range of 1.15% - 1.27%.

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Online Coregularization for Multiview Semisupervised Learning

PubMed Central

Li, Guohui; Huang, Kuihua

2013-01-01

We propose a novel online coregularization framework for multiview semisupervised learning based on the notion of duality in constrained optimization. Using the weak duality theorem, we reduce the online coregularization to the task of increasing the dual function. We demonstrate that the existing online coregularization algorithms in previous work can be viewed as an approximation of our dual ascending process using gradient ascent. New algorithms are derived based on the idea of ascending the dual function more aggressively. For practical purpose, we also propose two sparse approximation approaches for kernel representation to reduce the computational complexity. Experiments show that our derived online coregularization algorithms achieve risk and accuracy comparable to offline algorithms while consuming less time and memory. Specially, our online coregularization algorithms are able to deal with concept drift and maintain a much smaller error rate. This paper paves a way to the design and analysis of online coregularization algorithms. PMID:24194680

On the Quality of Point-Clouds Derived from Sfm-Photogrammetry Applied to UAS Imagery

NASA Astrophysics Data System (ADS)

Carbonneau, P.; James, T.

2014-12-01

Structure from Motion photogrammetry (SfM-photogrammetry) recently appeared in environmental sciences as an impressive tool allowing for the creation of topographic data from unstructured imagery. Several authors have tested the performance of SfM-photogrammetry vs that of TLS or dGPS. Whilst the initial results were very promising, there is currently a growing awareness that systematic deformations occur in DEMs and point-clouds derived from SfM-photogrammetry. Notably, some authors have identified a systematic doming manifest as an increasing error vs distance to the model centre. Simulation studies have confirmed that this error is due to errors in the calibration of camera distortions. This work aims to further investigate these effects in the presence of real data. We start with a dataset of 220 images acquired from a sUAS. After obtaining an initial self-calibration of the camera lens with Agisoft Photoscan, our method consists in applying systematic perturbations to 2 key lens parameters: Focal length and the k1 distortion parameter. For each perturbation, a point-cloud was produced and compared to LiDAR data. After deriving the mean and standard deviation of the error residuals (ɛ), a 2nd order polynomial surface was fitted to the errors point-cloud and the peak ɛ defined as the mathematical extrema of this surface. The results are presented in figure 1. This figure shows that lens perturbations can induce a range of errors with systematic behaviours. Peak ɛ is primarily controlled by K1 with a secondary control exerted by the focal length. These results allow us to state that: To limit the peak ɛ to 10cm, the K1 parameter must be calibrated to within 0.00025 and the focal length to within 2.5 pixels (≈10 µm). This level of calibration accuracy can only be achieved with proper design of image acquisition and control network geometry. Our main point is therefore that SfM is not a bypass to a rigorous and well-informed photogrammetric approach. Users of SfM-photogrammetry will still require basic training and knowledge in the fundamentals of photogrammetry. This is especially true for applications where very small topographic changes need to be detected or where gradient-sensitive processes need to be modelled.

Evaluation of a moderate resolution, satellite-based impervious surface map using an independent, high-resolution validation data set

USGS Publications Warehouse

Jones, J.W.; Jarnagin, T.

2009-01-01

Given the relatively high cost of mapping impervious surfaces at regional scales, substantial effort is being expended in the development of moderate-resolution, satellite-based methods for estimating impervious surface area (ISA). To rigorously assess the accuracy of these data products high quality, independently derived validation data are needed. High-resolution data were collected across a gradient of development within the Mid-Atlantic region to assess the accuracy of National Land Cover Data (NLCD) Landsat-based ISA estimates. Absolute error (satellite predicted area - "reference area") and relative error [satellite (predicted area - "reference area")/ "reference area"] were calculated for each of 240 sample regions that are each more than 15 Landsat pixels on a side. The ability to compile and examine ancillary data in a geographic information system environment provided for evaluation of both validation and NLCD data and afforded efficient exploration of observed errors. In a minority of cases, errors could be explained by temporal discontinuities between the date of satellite image capture and validation source data in rapidly changing places. In others, errors were created by vegetation cover over impervious surfaces and by other factors that bias the satellite processing algorithms. On average in the Mid-Atlantic region, the NLCD product underestimates ISA by approximately 5%. While the error range varies between 2 and 8%, this underestimation occurs regardless of development intensity. Through such analyses the errors, strengths, and weaknesses of particular satellite products can be explored to suggest appropriate uses for regional, satellite-based data in rapidly developing areas of environmental significance. ?? 2009 ASCE.

Deterministic convergence of chaos injection-based gradient method for training feedforward neural networks.

PubMed

Zhang, Huisheng; Zhang, Ying; Xu, Dongpo; Liu, Xiaodong

2015-06-01

It has been shown that, by adding a chaotic sequence to the weight update during the training of neural networks, the chaos injection-based gradient method (CIBGM) is superior to the standard backpropagation algorithm. This paper presents the theoretical convergence analysis of CIBGM for training feedforward neural networks. We consider both the case of batch learning as well as the case of online learning. Under mild conditions, we prove the weak convergence, i.e., the training error tends to a constant and the gradient of the error function tends to zero. Moreover, the strong convergence of CIBGM is also obtained with the help of an extra condition. The theoretical results are substantiated by a simulation example.

Assessment of Error in Synoptic-Scale Diagnostics Derived from Wind Profiler and Radiosonde Network Data

NASA Technical Reports Server (NTRS)

Mace, Gerald G.; Ackerman, Thomas P.

1996-01-01

A topic of current practical interest is the accurate characterization of the synoptic-scale atmospheric state from wind profiler and radiosonde network observations. We have examined several related and commonly applied objective analysis techniques for performing this characterization and considered their associated level of uncertainty both from a theoretical and a practical standpoint. A case study is presented where two wind profiler triangles with nearly identical centroids and no common vertices produced strikingly different results during a 43-h period. We conclude that the uncertainty in objectively analyzed quantities can easily be as large as the expected synoptic-scale signal. In order to quantify the statistical precision of the algorithms, we conducted a realistic observing system simulation experiment using output from a mesoscale model. A simple parameterization for estimating the uncertainty in horizontal gradient quantities in terms of known errors in the objectively analyzed wind components and temperature is developed from these results.

Bumps in river profiles: uncertainty assessment and smoothing using quantile regression techniques

NASA Astrophysics Data System (ADS)

Schwanghart, Wolfgang; Scherler, Dirk

2017-12-01

The analysis of longitudinal river profiles is an important tool for studying landscape evolution. However, characterizing river profiles based on digital elevation models (DEMs) suffers from errors and artifacts that particularly prevail along valley bottoms. The aim of this study is to characterize uncertainties that arise from the analysis of river profiles derived from different, near-globally available DEMs. We devised new algorithms - quantile carving and the CRS algorithm - that rely on quantile regression to enable hydrological correction and the uncertainty quantification of river profiles. We find that globally available DEMs commonly overestimate river elevations in steep topography. The distributions of elevation errors become increasingly wider and right skewed if adjacent hillslope gradients are steep. Our analysis indicates that the AW3D DEM has the highest precision and lowest bias for the analysis of river profiles in mountainous topography. The new 12 m resolution TanDEM-X DEM has a very low precision, most likely due to the combined effect of steep valley walls and the presence of water surfaces in valley bottoms. Compared to the conventional approaches of carving and filling, we find that our new approach is able to reduce the elevation bias and errors in longitudinal river profiles.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Automated Processing of Plasma Samples for Lipoprotein Separation by Rate-Zonal Ultracentrifugation.

PubMed

Peters, Carl N; Evans, Iain E J

2016-12-01

Plasma lipoproteins are the primary means of lipid transport among tissues. Defining alterations in lipid metabolism is critical to our understanding of disease processes. However, lipoprotein measurement is limited to specialized centers. Preparation for ultracentrifugation involves the formation of complex density gradients that is both laborious and subject to handling errors. We created a fully automated device capable of forming the required gradient. The design has been made freely available for download by the authors. It is inexpensive relative to commercial density gradient formers, which generally create linear gradients unsuitable for rate-zonal ultracentrifugation. The design can easily be modified to suit user requirements and any potential future improvements. Evaluation of the device showed reliable peristaltic pump accuracy and precision for fluid delivery. We also demonstrate accurate fluid layering with reduced mixing at the gradient layers when compared to usual practice by experienced laboratory personnel. Reduction in layer mixing is of critical importance, as it is crucial for reliable lipoprotein separation. The automated device significantly reduces laboratory staff input and reduces the likelihood of error. Overall, this device creates a simple and effective solution to formation of complex density gradients. © 2015 Society for Laboratory Automation and Screening.

Fundamental performance of transverse wind estimator from Shack-Hartmann wave-front sensor measurements.

PubMed

Li, Zhenghan; Li, Xinyang

2018-04-30

Real time transverse wind estimation contributes to predictive correction which is used to compensate for the time delay error in the control systems of adaptive optics (AO) system. Many methods that apply Shack-Hartmann wave-front sensor to wind profile measurement have been proposed. One of the obvious problems is the lack of a fundamental benchmark to compare the various methods. In this work, we present the fundamental performance limits for transverse wind estimator from Shack-Hartmann wave-front sensor measurements using Cramér-Rao lower bound (CRLB). The bound provides insight into the nature of the transverse wind estimation, thereby suggesting how to design and improve the estimator in the different application scenario. We analyze the theoretical bound and find that factors such as slope measurement noise, wind velocity and atmospheric coherence length r 0 have important influence on the performance. Then, we introduced the non-iterative gradient-based transverse wind estimator. The source of the deterministic bias of the gradient-based transverse wind estimators is analyzed for the first time. Finally, we derived biased CRLB for the gradient-based transverse wind estimators from Shack-Hartmann wave-front sensor measurements and the bound can predict the performance of estimator more accurately.

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Effects of Heterogeneity and Uncertainties in Sources and Initial and Boundary Conditions on Spatiotemporal Variations of Groundwater Levels

NASA Astrophysics Data System (ADS)

Zhang, Y. K.; Liang, X.

2014-12-01

Effects of aquifer heterogeneity and uncertainties in source/sink, and initial and boundary conditions in a groundwater flow model on the spatiotemporal variations of groundwater level, h(x,t), were investigated. Analytical solutions for the variance and covariance of h(x, t) in an unconfined aquifer described by a linearized Boussinesq equation with a white noise source/sink and a random transmissivity field were derived. It was found that in a typical aquifer the error in h(x,t) in early time is mainly caused by the random initial condition and the error reduces as time goes to reach a constant error in later time. The duration during which the effect of the random initial condition is significant may last a few hundred days in most aquifers. The constant error in groundwater in later time is due to the combined effects of the uncertain source/sink and flux boundary: the closer to the flux boundary, the larger the error. The error caused by the uncertain head boundary is limited in a narrow zone near the boundary but it remains more or less constant over time. The effect of the heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The correlation of groundwater level decreases with temporal interval and spatial distance. In addition, the heterogeneity enhances the correlation of groundwater level, especially at larger time intervals and small spatial distances.

Influence of natural temperature gradients on measurements of xylem sap flow with thermal dissipation probes. 1. Field observations and possible remedies.

PubMed

Do, F; Rocheteau, A

2002-06-01

The thermal dissipation method is simple and widely used for measuring sap flow in large stems. As with several other thermal methods, natural temperature gradients are assumed to be negligible in the sapwood being measured. We studied the magnitude and variability of natural temperature gradients in sapwood of Acacia trees growing in the Sahelian zone of Senegal, analyzed their effects on sap flow measurements, and investigated possible solutions. A new measurement approach employing cyclic heating (45 minutes of heating and 15 minutes of cooling; 45/15) was also tested. Three-day measurement sequences that included 1 day without heating, a second day with continuous heating and a third day with cyclic heating were recorded during a 6.5-month period using probes installed at three azimuths in a tree trunk. Natural temperature gradients between the two probes of the sensor unit, spaced 8 to 10 cm vertically, were rarely negligible (i.e., < 0.2 degrees C): they were positive during the night and negative during the day, with an amplitude ranging from 0.3 to 3.5 degrees C depending on trunk azimuth, day and season. These temperature gradients had a direct influence on the signal from the continuously heated sensors, inducing fluctuations in the nighttime reference signal. The resulting errors in sap flow estimates can be greater than 100%. Correction protocols have been proposed in previous studies, but they were unsuitable because of the high spatial and temporal variability of the natural temperature gradients. We found that a measurement signal derived from a noncontinuous heating system could be an attractive solution because it appears to be independent of natural temperature gradients. The magnitude and variability of temperature gradients that we observed were likely exacerbated by the combination of open stand, high solar radiation and low sap flow rate. However, for all applications of the thermal dissipation method, it is wise to check regularly for natural temperature gradients by switching off the heater.

Airborne microwave radar measurements of surface velocity in a tidally-driven inlet

NASA Astrophysics Data System (ADS)

Farquharson, G.; Thomson, J. M.

2012-12-01

A miniaturized dual-beam along-track interferometric (ATI) synthetic aperture radar (SAR), capable of measuring two components of surface velocity at high resolution, was operated during the 2012 Rivers and Inlets Experiment (RIVET) at the New River Inlet in North Carolina. The inlet is predominantly tidally-driven, with little upstream river discharge. Surface velocities in the inlet and nearshore region were measured during ebb and flood tides during a variety of wind and offshore wave conditions. The radar-derived surface velocities range from around ±2~m~s1 during times of maximum flow. We compare these radar-derived surface velocities with surface velocities measured with drifters. The accuracy of the radar-derived velocities is investigated, especially in areas of large velocity gradients where along-track interferometric SAR can show significant differences with surface velocity. The goal of this research is to characterize errors in along-track interferometric SAR velocity so that ATI SAR measurements can be coupled with data assimilative modeling with the goal of developing the capability to adequately constrain nearshore models using remote sensing measurements.

Gradient, contact-free volume transfers minimize compound loss in dose-response experiments.

PubMed

Harris, David; Olechno, Joe; Datwani, Sammy; Ellson, Richard

2010-01-01

More accurate dose-response curves can be constructed by eliminating aqueous serial dilution of compounds. Traditional serial dilutions that use aqueous diluents can result in errors in dose-response values of up to 4 orders of magnitude for a significant percentage of a compound library. When DMSO is used as the diluent, the errors are reduced but not eliminated. The authors use acoustic drop ejection (ADE) to transfer different volumes of model library compounds, directly creating a concentration gradient series in the receiver assay plate. Sample losses and contamination associated with compound handling are therefore avoided or minimized, particularly in the case of less water-soluble compounds. ADE is particularly well suited for assay miniaturization, but gradient volume dispensing is not limited to miniaturized applications.

A directional model of tropospheric horizontal gradients in Global Positioning System and its application for particular weather scenarios

NASA Astrophysics Data System (ADS)

Masoumi, Salim; McClusky, Simon; Koulali, Achraf; Tregoning, Paul

2017-04-01

Improper modeling of horizontal tropospheric gradients in GPS analysis induces errors in estimated parameters, with the largest impact on heights and tropospheric zenith delays. The conventional two-axis tilted plane model of horizontal gradients fails to provide an accurate representation of tropospheric gradients under weather conditions with asymmetric horizontal changes of refractivity. A new parametrization of tropospheric gradients whereby an arbitrary number of gradients are estimated as discrete directional wedges is shown via simulations to significantly improve the accuracy of recovered tropospheric zenith delays in asymmetric gradient scenarios. In a case study of an extreme rain event that occurred in September 2002 in southern France, the new directional parametrization is able to isolate the strong gradients in particular azimuths around the GPS stations consistent with the "V" shape spatial pattern of the observed precipitation. In another study of a network of GPS stations in the Sierra Nevada region where highly asymmetric tropospheric gradients are known to exist, the new directional model significantly improves the repeatabilities of the stations in asymmetric gradient situations while causing slightly degraded repeatabilities for the stations in normal symmetric gradient conditions. The average improvement over the entire network is ˜31%, while the improvement for one of the worst affected sites P631 is ˜49% (from 8.5 mm to 4.3 mm) in terms of weighted root-mean-square (WRMS) error and ˜82% (from -1.1 to -0.2) in terms of skewness. At the same station, the use of the directional model changes the estimates of zenith wet delay by 15 mm (˜25%).

Topographical gradients of semantics and phonology revealed by temporal lobe stimulation.

PubMed

Miozzo, Michele; Williams, Alicia C; McKhann, Guy M; Hamberger, Marla J

2017-02-01

Word retrieval is a fundamental component of oral communication, and it is well established that this function is supported by left temporal cortex. Nevertheless, the specific temporal areas mediating word retrieval and the particular linguistic processes these regions support have not been well delineated. Toward this end, we analyzed over 1000 naming errors induced by left temporal cortical stimulation in epilepsy surgery patients. Errors were primarily semantic (lemon → "pear"), phonological (horn → "corn"), non-responses, and delayed responses (correct responses after a delay), and each error type appeared predominantly in a specific region: semantic errors in mid-middle temporal gyrus (TG), phonological errors and delayed responses in middle and posterior superior TG, and non-responses in anterior inferior TG. To the extent that semantic errors, phonological errors and delayed responses reflect disruptions in different processes, our results imply topographical specialization of semantic and phonological processing. Specifically, results revealed an inferior-to-superior gradient, with more superior regions associated with phonological processing. Further, errors were increasingly semantically related to targets toward posterior temporal cortex. We speculate that detailed semantic input is needed to support phonological retrieval, and thus, the specificity of semantic input increases progressively toward posterior temporal regions implicated in phonological processing. Hum Brain Mapp 38:688-703, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Automation of workplace lifting hazard assessment for musculoskeletal injury prevention.

PubMed

Spector, June T; Lieblich, Max; Bao, Stephen; McQuade, Kevin; Hughes, Margaret

2014-01-01

Existing methods for practically evaluating musculoskeletal exposures such as posture and repetition in workplace settings have limitations. We aimed to automate the estimation of parameters in the revised United States National Institute for Occupational Safety and Health (NIOSH) lifting equation, a standard manual observational tool used to evaluate back injury risk related to lifting in workplace settings, using depth camera (Microsoft Kinect) and skeleton algorithm technology. A large dataset (approximately 22,000 frames, derived from six subjects) of simultaneous lifting and other motions recorded in a laboratory setting using the Kinect (Microsoft Corporation, Redmond, Washington, United States) and a standard optical motion capture system (Qualysis, Qualysis Motion Capture Systems, Qualysis AB, Sweden) was assembled. Error-correction regression models were developed to improve the accuracy of NIOSH lifting equation parameters estimated from the Kinect skeleton. Kinect-Qualysis errors were modelled using gradient boosted regression trees with a Huber loss function. Models were trained on data from all but one subject and tested on the excluded subject. Finally, models were tested on three lifting trials performed by subjects not involved in the generation of the model-building dataset. Error-correction appears to produce estimates for NIOSH lifting equation parameters that are more accurate than those derived from the Microsoft Kinect algorithm alone. Our error-correction models substantially decreased the variance of parameter errors. In general, the Kinect underestimated parameters, and modelling reduced this bias, particularly for more biased estimates. Use of the raw Kinect skeleton model tended to result in falsely high safe recommended weight limits of loads, whereas error-corrected models gave more conservative, protective estimates. Our results suggest that it may be possible to produce reasonable estimates of posture and temporal elements of tasks such as task frequency in an automated fashion, although these findings should be confirmed in a larger study. Further work is needed to incorporate force assessments and address workplace feasibility challenges. We anticipate that this approach could ultimately be used to perform large-scale musculoskeletal exposure assessment not only for research but also to provide real-time feedback to workers and employers during work method improvement activities and employee training.

Torus Approach in Gravity Field Determination from Simulated GOCE Gravity Gradients

NASA Astrophysics Data System (ADS)

Liu, Huanling; Wen, Hanjiang; Xu, Xinyu; Zhu, Guangbin

2016-08-01

In Torus approach, observations are projected to the nominal orbits with constant radius and inclination, lumped coefficients provides a linear relationship between observations and spherical harmonic coefficients. Based on the relationship, two-dimensional FFT and block-diagonal least-squares adjustment are used to recover Earth's gravity field model. The Earth's gravity field model complete to degree and order 200 is recovered using simulated satellite gravity gradients on a torus grid, and the degree median error is smaller than 10-18, which shows the effectiveness of Torus approach. EGM2008 is employed as a reference model and the gravity field model is resolved using the simulated observations without noise given on GOCE orbits of 61 days. The error from reduction and interpolation can be mitigated by iterations. Due to polar gap, the precision of low-order coefficients is lower. Without considering these coefficients the maximum geoid degree error and cumulative error are 0.022mm and 0.099mm, respectively. The Earth's gravity field model is also recovered from simulated observations with white noise 5mE/Hz1/2, which is compared to that from direct method. In conclusion, it is demonstrated that Torus approach is a valid method for processing massive amount of GOCE gravity gradients.

Implementation of a flow-dependent background error correlation length scale formulation in the NEMOVAR OSTIA system

NASA Astrophysics Data System (ADS)

Fiedler, Emma; Mao, Chongyuan; Good, Simon; Waters, Jennifer; Martin, Matthew

2017-04-01

OSTIA is the Met Office's Operational Sea Surface Temperature (SST) and Ice Analysis system, which produces L4 (globally complete, gridded) analyses on a daily basis. Work is currently being undertaken to replace the original OI (Optimal Interpolation) data assimilation scheme with NEMOVAR, a 3D-Var data assimilation method developed for use with the NEMO ocean model. A dual background error correlation length scale formulation is used for SST in OSTIA, as implemented in NEMOVAR. Short and long length scales are combined according to the ratio of the decomposition of the background error variances into short and long spatial correlations. The pre-defined background error variances vary spatially and seasonally, but not on shorter time-scales. If the derived length scales applied to the daily analysis are too long, SST features may be smoothed out. Therefore a flow-dependent component to determining the effective length scale has also been developed. The total horizontal gradient of the background SST field is used to identify regions where the length scale should be shortened. These methods together have led to an improvement in the resolution of SST features compared to the previous OI analysis system, without the introduction of spurious noise. This presentation will show validation results for feature resolution in OSTIA using the OI scheme, the dual length scale NEMOVAR scheme, and the flow-dependent implementation.

Error decomposition and estimation of inherent optical properties.

PubMed

Salama, Mhd Suhyb; Stein, Alfred

2009-09-10

We describe a methodology to quantify and separate the errors of inherent optical properties (IOPs) derived from ocean-color model inversion. Their total error is decomposed into three different sources, namely, model approximations and inversion, sensor noise, and atmospheric correction. Prior information on plausible ranges of observation, sensor noise, and inversion goodness-of-fit are employed to derive the posterior probability distribution of the IOPs. The relative contribution of each error component to the total error budget of the IOPs, all being of stochastic nature, is then quantified. The method is validated with the International Ocean Colour Coordinating Group (IOCCG) data set and the NASA bio-Optical Marine Algorithm Data set (NOMAD). The derived errors are close to the known values with correlation coefficients of 60-90% and 67-90% for IOCCG and NOMAD data sets, respectively. Model-induced errors inherent to the derived IOPs are between 10% and 57% of the total error, whereas atmospheric-induced errors are in general above 43% and up to 90% for both data sets. The proposed method is applied to synthesized and in situ measured populations of IOPs. The mean relative errors of the derived values are between 2% and 20%. A specific error table to the Medium Resolution Imaging Spectrometer (MERIS) sensor is constructed. It serves as a benchmark to evaluate the performance of the atmospheric correction method and to compute atmospheric-induced errors. Our method has a better performance and is more appropriate to estimate actual errors of ocean-color derived products than the previously suggested methods. Moreover, it is generic and can be applied to quantify the error of any derived biogeophysical parameter regardless of the used derivation.

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks.

PubMed

Li, Zhijun; Ge, Shuzhi Sam; Liu, Sibang

2014-08-01

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

A New Approach for Identifying Ionospheric Gradients in the Context of the Gagan System

NASA Astrophysics Data System (ADS)

Kudala, Ravi Chandra

2012-10-01

The Indian Space Research Organization and the Airports Authority of India are jointly implementing the Global Positioning System (GPS) aided GEO Augmented Navigation (GAGAN) system in order to meet the following required navigation performance (RNP) parameters: integrity, continuity, accuracy, and availability (for aircraft operations). Such a system provides the user with orbit, clock, and ionospheric corrections in addition to ranging signals via the geostationary earth orbit satellite (GEOSAT). The equatorial ionization anomaly (EIA), due to rapid non-uniform electron-ion recombination that persists on the Indian subcontinent, causes ionospheric gradients. Ionospheric gradients represent the most severe threat to high-integrity differential GNSS systems such as GAGAN. In order to ensure integrity under conditions of an ionospheric storm, the following three objectives must be met: careful monitoring, error bounding, and sophisticated storm-front modeling. The first objective is met by continuously tracking data due to storms, and, on quiet days, determining precise estimates of the threat parameters from reference monitoring stations. The second objective is met by quantifying the above estimates of threat parameters due to storms through maximum and minimum typical thresholds. In the context GAGAN, this work proposes a new method for identifying ionospheric gradients, in addition to determining an appropriate upper bound, in order to sufficiently understand error during storm days. Initially, carrier phase data of the GAGAN network from Indian TEC stations for both storm and quiet days was used for estimating ionospheric spatial and temporal gradients (the vertical ionospheric gradient (σVIG) and the rate of the TEC index (ROTI), respectively) in multiple viewing directions. Along similar lines, using the carrier to noise ratio (C/N0) for the same data, the carrier to noise ratio index (σCNRI) was derived. Subsequently, the one-toone relationship between σVIG and σCNRI was examined. High values of σVIG were determined for strong noise signals and corresponded to minimal σCNRI, indicating poor phase estimations and, in turn, an erroneous location. On the other hand, low values of σVIG were produced for weak noise signals and corresponded to maximum σCNRI, indicating strong phase estimations and, in turn, accurate locations. In other words, if a gradient persists in the line of sight direction of GEOSAT for aviation users, the down link L- band signal itself becomes erroneous. As a result, the en-route aviation user fails to receive a SBAS correction message leading to deprivation for the main objective of GAGAN. On the other hand, since the proposed approach enhances the receivers of both the aviation user and the reference monitoring station in terms of their performance, based on σCNRI, the integrity of SBAS messages themselves can be analyzed and considered for forward corrections.

Estimation of perspective errors in 2D2C-PIV measurements for 3D concentrated vortices

NASA Astrophysics Data System (ADS)

Ma, Bao-Feng; Jiang, Hong-Gang

2018-06-01

Two-dimensional planar PIV (2D2C) is still extensively employed in flow measurement owing to its availability and reliability, although more advanced PIVs have been developed. It has long been recognized that there exist perspective errors in velocity fields when employing the 2D2C PIV to measure three-dimensional (3D) flows, the magnitude of which depends on out-of-plane velocity and geometric layouts of the PIV. For a variety of vortex flows, however, the results are commonly represented by vorticity fields, instead of velocity fields. The present study indicates that the perspective error in vorticity fields relies on gradients of the out-of-plane velocity along a measurement plane, instead of the out-of-plane velocity itself. More importantly, an estimation approach to the perspective error in 3D vortex measurements was proposed based on a theoretical vortex model and an analysis on physical characteristics of the vortices, in which the gradient of out-of-plane velocity is uniquely determined by the ratio of the maximum out-of-plane velocity to maximum swirling velocity of the vortex; meanwhile, the ratio has upper limits for naturally formed vortices. Therefore, if the ratio is imposed with the upper limits, the perspective error will only rely on the geometric layouts of PIV that are known in practical measurements. Using this approach, the upper limits of perspective errors of a concentrated vortex can be estimated for vorticity and other characteristic quantities of the vortex. In addition, the study indicates that the perspective errors in vortex location, vortex strength, and vortex radius can be all zero for axisymmetric vortices if they are calculated by proper methods. The dynamic mode decomposition on an oscillatory vortex indicates that the perspective errors of each DMD mode are also only dependent on the gradient of out-of-plane velocity if the modes are represented by vorticity.

Scaling fixed-field alternating gradient accelerators with a small orbit excursion.

PubMed

Machida, Shinji

2009-10-16

A novel scaling type of fixed-field alternating gradient (FFAG) accelerator is proposed that solves the major problems of conventional scaling and nonscaling types. This scaling FFAG accelerator can achieve a much smaller orbit excursion by taking a larger field index k. A triplet focusing structure makes it possible to set the operating point in the second stability region of Hill's equation with a reasonable sensitivity to various errors. The orbit excursion is about 5 times smaller than in a conventional scaling FFAG accelerator and the beam size growth due to typical errors is at most 10%.

Efficient and precise calculation of the b-matrix elements in diffusion-weighted imaging pulse sequences.

PubMed

Zubkov, Mikhail; Stait-Gardner, Timothy; Price, William S

2014-06-01

Precise NMR diffusion measurements require detailed knowledge of the cumulative dephasing effect caused by the numerous gradient pulses present in most NMR pulse sequences. This effect, which ultimately manifests itself as the diffusion-related NMR signal attenuation, is usually described by the b-value or the b-matrix in the case of multidirectional diffusion weighting, the latter being common in diffusion-weighted NMR imaging. Neglecting some of the gradient pulses introduces an error in the calculated diffusion coefficient reaching in some cases 100% of the expected value. Therefore, ensuring the b-matrix calculation includes all the known gradient pulses leads to significant error reduction. Calculation of the b-matrix for simple gradient waveforms is rather straightforward, yet it grows cumbersome when complexly shaped and/or numerous gradient pulses are introduced. Making three broad assumptions about the gradient pulse arrangement in a sequence results in an efficient framework for calculation of b-matrices as well providing some insight into optimal gradient pulse placement. The framework allows accounting for the diffusion-sensitising effect of complexly shaped gradient waveforms with modest computational time and power. This is achieved by using the b-matrix elements of the simple unmodified pulse sequence and minimising the integration of the complexly shaped gradient waveform in the modified sequence. Such re-evaluation of the b-matrix elements retains all the analytical relevance of the straightforward approach, yet at least halves the amount of symbolic integration required. The application of the framework is demonstrated with the evaluation of the expression describing the diffusion-sensitizing effect, caused by different bipolar gradient pulse modules. Copyright © 2014 Elsevier Inc. All rights reserved.

Mitigation of Engine Inlet Distortion Through Adjoint-Based Design

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Rallabhandi, Sriram; Nielsen, Eric J.; Diskin, Boris

2017-01-01

The adjoint-based design capability in FUN3D is extended to allow efficient gradient- based optimization and design of concepts with highly integrated aero-propulsive systems. A circumferential distortion calculation, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. This newly implemented distortion calculation can be used not only for design but also to drive the existing mesh adaptation process and reduce the error associated with the fan distortion calculation. The design capability is demonstrated by the shape optimization of an in-house aircraft concept equipped with an aft fuselage propulsor. The optimization objective is the minimization of flow distortion at the aerodynamic interface plane of this aft fuselage propulsor.

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

NASA Technical Reports Server (NTRS)

Thomas, James

2008-01-01

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Assessment of Ionospheric Gradient Impacts on Ground-Based Augmentation System (GBAS) Data in Guangdong Province, China

PubMed Central

Wang, Zhipeng; Wang, Shujing; Zhu, Yanbo; Xin, Pumin

2017-01-01

Ionospheric delay is one of the largest and most variable sources of error for Ground-Based Augmentation System (GBAS) users because inospheric activity is unpredictable. Under normal conditions, GBAS eliminates ionospheric delays, but during extreme ionospheric storms, GBAS users and GBAS ground facilities may experience different ionospheric delays, leading to considerable differential errors and threatening the safety of users. Therefore, ionospheric monitoring and assessment are important parts of GBAS integrity monitoring. To study the effects of the ionosphere on the GBAS of Guangdong Province, China, GPS data collected from 65 reference stations were processed using the improved “Simple Truth” algorithm. In addition, the ionospheric characteristics of Guangdong Province were calculated and an ionospheric threat model was established. Finally, we evaluated the influence of the standard deviation and maximum ionospheric gradient on GBAS. The results show that, under normal ionospheric conditions, the vertical protection level of GBAS was increased by 0.8 m for the largest over bound σvig (sigma of vertical ionospheric gradient), and in the case of the maximum ionospheric gradient conditions, the differential correction error may reach 5 m. From an airworthiness perspective, when the satellite is at a low elevation, this interference does not cause airworthiness risks, but when the satellite is at a high elevation, this interference can cause airworthiness risks. PMID:29019953

Assessment of Ionospheric Gradient Impacts on Ground-Based Augmentation System (GBAS) Data in Guangdong Province, China.

PubMed

Wang, Zhipeng; Wang, Shujing; Zhu, Yanbo; Xin, Pumin

2017-10-11

Ionospheric delay is one of the largest and most variable sources of error for Ground-Based Augmentation System (GBAS) users because inospheric activity is unpredictable. Under normal conditions, GBAS eliminates ionospheric delays, but during extreme ionospheric storms, GBAS users and GBAS ground facilities may experience different ionospheric delays, leading to considerable differential errors and threatening the safety of users. Therefore, ionospheric monitoring and assessment are important parts of GBAS integrity monitoring. To study the effects of the ionosphere on the GBAS of Guangdong Province, China, GPS data collected from 65 reference stations were processed using the improved "Simple Truth" algorithm. In addition, the ionospheric characteristics of Guangdong Province were calculated and an ionospheric threat model was established. Finally, we evaluated the influence of the standard deviation and maximum ionospheric gradient on GBAS. The results show that, under normal ionospheric conditions, the vertical protection level of GBAS was increased by 0.8 m for the largest over bound σ v i g (sigma of vertical ionospheric gradient), and in the case of the maximum ionospheric gradient conditions, the differential correction error may reach 5 m. From an airworthiness perspective, when the satellite is at a low elevation, this interference does not cause airworthiness risks, but when the satellite is at a high elevation, this interference can cause airworthiness risks.

Algorithm for ion beam figuring of low-gradient mirrors.

PubMed

Jiao, Changjun; Li, Shengyi; Xie, Xuhui

2009-07-20

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 lambda.

Domain Derivatives in Dielectric Rough Surface Scattering

DTIC Science & Technology

2015-01-01

and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite...differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single...derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

NASA Technical Reports Server (NTRS)

Vatsa, Veer N.

2004-01-01

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Derivatives of logarithmic stationary distributions for policy gradient reinforcement learning.

PubMed

Morimura, Tetsuro; Uchibe, Eiji; Yoshimoto, Junichiro; Peters, Jan; Doya, Kenji

2010-02-01

Most conventional policy gradient reinforcement learning (PGRL) algorithms neglect (or do not explicitly make use of) a term in the average reward gradient with respect to the policy parameter. That term involves the derivative of the stationary state distribution that corresponds to the sensitivity of its distribution to changes in the policy parameter. Although the bias introduced by this omission can be reduced by setting the forgetting rate gamma for the value functions close to 1, these algorithms do not permit gamma to be set exactly at gamma = 1. In this article, we propose a method for estimating the log stationary state distribution derivative (LSD) as a useful form of the derivative of the stationary state distribution through backward Markov chain formulation and a temporal difference learning framework. A new policy gradient (PG) framework with an LSD is also proposed, in which the average reward gradient can be estimated by setting gamma = 0, so it becomes unnecessary to learn the value functions. We also test the performance of the proposed algorithms using simple benchmark tasks and show that these can improve the performances of existing PG methods.

A Wavelet Based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Auger, Ludovic; Tangborn, Andrew; Atlas, Robert (Technical Monitor)

2002-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.

Performance analysis of a GPS Interferometric attitude determination system for a gravity gradient stabilized spacecraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Stoll, John C.

1995-01-01

The performance of an unaided attitude determination system based on GPS interferometry is examined using linear covariance analysis. The modelled system includes four GPS antennae onboard a gravity gradient stabilized spacecraft, specifically the Air Force's RADCAL satellite. The principal error sources are identified and modelled. The optimal system's sensitivities to these error sources are examined through an error budget and by varying system parameters. The effects of two satellite selection algorithms, Geometric and Attitude Dilution of Precision (GDOP and ADOP, respectively) are examined. The attitude performance of two optimal-suboptimal filters is also presented. Based on this analysis, the limiting factors in attitude accuracy are the knowledge of the relative antenna locations, the electrical path lengths from the antennae to the receiver, and the multipath environment. The performance of the system is found to be fairly insensitive to torque errors, orbital inclination, and the two satellite geometry figures-of-merit tested.

Distinguishing discrete and gradient category structure in language: Insights from verb-particle constructions.

PubMed

Brehm, Laurel; Goldrick, Matthew

2017-10-01

The current work uses memory errors to examine the mental representation of verb-particle constructions (VPCs; e.g., make up the story, cut up the meat). Some evidence suggests that VPCs are represented by a cline in which the relationship between the VPC and its component elements ranges from highly transparent (cut up) to highly idiosyncratic (make up). Other evidence supports a multiple class representation, characterizing VPCs as belonging to discretely separated classes differing in semantic and syntactic structure. We outline a novel paradigm to investigate the representation of VPCs in which we elicit illusory conjunctions, or memory errors sensitive to syntactic structure. We then use a novel application of piecewise regression to demonstrate that the resulting error pattern follows a cline rather than discrete classes. A preregistered replication verifies these findings, and a final preregistered study verifies that these errors reflect syntactic structure. This provides evidence for gradient rather than discrete representations across levels of representation in language processing. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Rapid Measurement and Correction of Phase Errors from B0 Eddy Currents: Impact on Image Quality for Non-Cartesian Imaging

PubMed Central

Brodsky, Ethan K.; Klaers, Jessica L.; Samsonov, Alexey A.; Kijowski, Richard; Block, Walter F.

2014-01-01

Non-Cartesian imaging sequences and navigational methods can be more sensitive to scanner imperfections that have little impact on conventional clinical sequences, an issue which has repeatedly complicated the commercialization of these techniques by frustrating transitions to multi-center evaluations. One such imperfection is phase errors caused by resonant frequency shifts from eddy currents induced in the cryostat by time-varying gradients, a phenomemon known as B0 eddy currents. These phase errors can have a substantial impact on sequences that use ramp sampling, bipolar gradients, and readouts at varying azimuthal angles. We present a method for measuring and correcting phase errors from B0 eddy currents and examine the results on two different scanner models. This technique yields significant improvements in image quality for high-resolution joint imaging on certain scanners. The results suggest that correction of short time B0 eddy currents in manufacturer provided service routines would simplify adoption of non-Cartesian sampling methods. PMID:22488532

Calibration of Gephyrocapsa Coccolith Abundance in Holocene Sediments for Paleo-temperature Assessment

NASA Astrophysics Data System (ADS)

Bollmann, J.; Brabec, B.

2001-12-01

Abundance and assemblage compositions of microplankton, together with their chemical and stable isotopic composition, have been among the most successful methods in paleoceanography. One of the most frequently applied techniques for reconstruction of paleo-temperature is a transfer function using the relative abundance of planktic foraminifera in sediment samples. Here we present evidence, suggesting that absolute sea surface temperature for a given location can be also calculated from the relative abundance of Gephyrocapsa morphotypes in sediment samples with an accuracy comparable to foraminifera transfer functions. By extrapolating this finding, paleo-enviromental interpretations can be obtained for the Late Pleistocene and discrepancies between the different currently used methods (e.g., foraminifer, alkenone and Ca/Mg derived temperature estimates) might be resolved. Eighty-one Holocene sediment samples were selected from the Pacific, Indian and Atlantic Oceans covering a temperature gradient from 13.4° C to 29.4° C, a salinity gradient from 32.21 to 37.34 and a productivity gradient of 0.045 to 0.492μ g chlorophyll/L. Standard multiple linear regression analyses were applied to this data set, linking the relative abundance of Gephyrocapsa morphotypes to mean sea surface temperature. The best model revealed an r2 of 0.8 with a standard residual error of 1.8° C for calculation of the mean sea surface temperature.

The 630 nm MIG and the vertical neutral wind in the low latitude nighttime thermosphere

NASA Technical Reports Server (NTRS)

Herrero, F. A.; Meriwether, J. W., Jr.

1994-01-01

It is shown that large negative divergences (gradients) in the horizontal neutral wind in the equatorial thermosphere can support downward neutral winds in excess of 20 m/s. With attention to the meridional and vertical winds only, the pressure tendency equation is used to derive the expression U(sub z0) approximately equals (Partial derivative U(sub y)/Partial derivative y)H for the vertical wind U(sub z0) at the reference altitude for the pressure tendency equation; H is the atmospheric density scale height, and (Partial derivative U(sub y)/Partial derivative y) is the meridional wind gradient. The velocity gradient associated with the Meridional Intensity Gradient (MIG) of the O((sup 1)D) emission (630 nm) at low latitudes is used to estimate the vertical neutral wind in the MIG region. Velocity gradients derived from MIG data are about 0.5 (m/s)/km) or more, indicating that the MIG region may contain downward neutral winds in excess of 20 m/s. Though direct measurements of the vertical wind are scarce, Fabry-Perot interferometer data of the equatorial F-region above Natal, Brazil, showed downward winds of 30 m/s occurring during a strong meridional wind convergence in 1982. In-situ measurements with the WATS instrument on the DE-2 satellite also show large vertical neutral winds in the equatorial region.

Expressions of the fundamental equation of gradient elution and a numerical solution of these equations under any gradient profile.

PubMed

Nikitas, P; Pappa-Louisi, A

2005-09-01

The original work carried out by Freiling and Drake in gradient liquid chromatography is rewritten in the current language of reversed-phase liquid chromatography. This allows for the rigorous derivation of the fundamental equation for gradient elution and the development of two alternative expressions of this equation, one of which is free from the constraint that the holdup time must be constant. In addition, the above derivation results in a very simple numerical solution of the various equations of gradient elution under any gradient profile. The theory was tested using eight catechol-related solutes in mobile phases modified with methanol, acetonitrile, or 2-propanol. It was found to be a satisfactory prediction of solute gradient retention behavior even if we used a simple linear description for the isocratic elution of these solutes.

Large Uncertainty in Estimating pCO2 From Carbonate Equilibria in Lakes

NASA Astrophysics Data System (ADS)

Golub, Malgorzata; Desai, Ankur R.; McKinley, Galen A.; Remucal, Christina K.; Stanley, Emily H.

2017-11-01

Most estimates of carbon dioxide (CO2) evasion from freshwaters rely on calculating partial pressure of aquatic CO2 (pCO2) from two out of three CO2-related parameters using carbonate equilibria. However, the pCO2 uncertainty has not been systematically evaluated across multiple lake types and equilibria. We quantified random errors in pH, dissolved inorganic carbon, alkalinity, and temperature from the North Temperate Lakes Long-Term Ecological Research site in four lake groups across a broad gradient of chemical composition. These errors were propagated onto pCO2 calculated from three carbonate equilibria, and for overlapping observations, compared against uncertainties in directly measured pCO2. The empirical random errors in CO2-related parameters were mostly below 2% of their median values. Resulting random pCO2 errors ranged from ±3.7% to ±31.5% of the median depending on alkalinity group and choice of input parameter pairs. Temperature uncertainty had a negligible effect on pCO2. When compared with direct pCO2 measurements, all parameter combinations produced biased pCO2 estimates with less than one third of total uncertainty explained by random pCO2 errors, indicating that systematic uncertainty dominates over random error. Multidecadal trend of pCO2 was difficult to reconstruct from uncertain historical observations of CO2-related parameters. Given poor precision and accuracy of pCO2 estimates derived from virtually any combination of two CO2-related parameters, we recommend direct pCO2 measurements where possible. To achieve consistently robust estimates of CO2 emissions from freshwater components of terrestrial carbon balances, future efforts should focus on improving accuracy and precision of CO2-related parameters (including direct pCO2) measurements and associated pCO2 calculations.

Generalized Analysis Tools for Multi-Spacecraft Missions

NASA Astrophysics Data System (ADS)

Chanteur, G. M.

2011-12-01

Analysis tools for multi-spacecraft missions like CLUSTER or MMS have been designed since the end of the 90's to estimate gradients of fields or to characterize discontinuities crossed by a cluster of spacecraft. Different approaches have been presented and discussed in the book "Analysis Methods for Multi-Spacecraft Data" published as Scientific Report 001 of the International Space Science Institute in Bern, Switzerland (G. Paschmann and P. Daly Eds., 1998). On one hand the approach using methods of least squares has the advantage to apply to any number of spacecraft [1] but is not convenient to perform analytical computation especially when considering the error analysis. On the other hand the barycentric approach is powerful as it provides simple analytical formulas involving the reciprocal vectors of the tetrahedron [2] but appears limited to clusters of four spacecraft. Moreover the barycentric approach allows to derive theoretical formulas for errors affecting the estimators built from the reciprocal vectors [2,3,4]. Following a first generalization of reciprocal vectors proposed by Vogt et al [4] and despite the present lack of projects with more than four spacecraft we present generalized reciprocal vectors for a cluster made of any number of spacecraft : each spacecraft is given a positive or nul weight. The non-coplanarity of at least four spacecraft with strictly positive weights is a necessary and sufficient condition for this analysis to be enabled. Weights given to spacecraft allow to minimize the influence of some spacecraft if its location or the quality of its data are not appropriate, or simply to extract subsets of spacecraft from the cluster. Estimators presented in [2] are generalized within this new frame except for the error analysis which is still under investigation. References [1] Harvey, C. C.: Spatial Gradients and the Volumetric Tensor, in: Analysis Methods for Multi-Spacecraft Data, G. Paschmann and P. Daly (eds.), pp. 307-322, ISSI SR-001, 1998. [2] Chanteur, G.: Spatial Interpolation for Four Spacecraft: Theory, in: Analysis Methods for Multi-Spacecraft Data, G. Paschmann and P. Daly (eds.), pp. 371-393, ISSI SR-001, 1998. [3] Chanteur, G.: Accuracy of field gradient estimations by Cluster: Explanation of its dependency upon elongation and planarity of the tetrahedron, pp. 265-268, ESA SP-449, 2000. [4] Vogt, J., Paschmann, G., and Chanteur, G.: Reciprocal Vectors, pp. 33-46, ISSI SR-008, 2008.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

VLBI-derived troposphere parameters during CONT08

NASA Astrophysics Data System (ADS)

Heinkelmann, R.; Böhm, J.; Bolotin, S.; Engelhardt, G.; Haas, R.; Lanotte, R.; MacMillan, D. S.; Negusini, M.; Skurikhina, E.; Titov, O.; Schuh, H.

2011-07-01

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays ( ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12-26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6 mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3 mm (unweighted), 4.4 mm (diagonal), 8.6 mm [variance component (VC) estimation], and 8.6 mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended.

Consistent lattice Boltzmann methods for incompressible axisymmetric flows

NASA Astrophysics Data System (ADS)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

2016-08-01

In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

Reinforcement learning state estimator.

PubMed

Morimoto, Jun; Doya, Kenji

2007-03-01

In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.

Gradient-based interpolation method for division-of-focal-plane polarimeters.

PubMed

Gao, Shengkui; Gruev, Viktor

2013-01-14

Recent advancements in nanotechnology and nanofabrication have allowed for the emergence of the division-of-focal-plane (DoFP) polarization imaging sensors. These sensors capture polarization properties of the optical field at every imaging frame. However, the DoFP polarization imaging sensors suffer from large registration error as well as reduced spatial-resolution output. These drawbacks can be improved by applying proper image interpolation methods for the reconstruction of the polarization results. In this paper, we present a new gradient-based interpolation method for DoFP polarimeters. The performance of the proposed interpolation method is evaluated against several previously published interpolation methods by using visual examples and root mean square error (RMSE) comparison. We found that the proposed gradient-based interpolation method can achieve better visual results while maintaining a lower RMSE than other interpolation methods under various dynamic ranges of a scene ranging from dim to bright conditions.

Optimized distortion correction technique for echo planar imaging.

PubMed

Chen , N K; Wyrwicz, A M

2001-03-01

A new phase-shifted EPI pulse sequence is described that encodes EPI phase errors due to all off-resonance factors, including B(o) field inhomogeneity, eddy current effects, and gradient waveform imperfections. Combined with the previously proposed multichannel modulation postprocessing algorithm (Chen and Wyrwicz, MRM 1999;41:1206-1213), the encoded phase error information can be used to effectively remove geometric distortions in subsequent EPI scans. The proposed EPI distortion correction technique has been shown to be effective in removing distortions due to gradient waveform imperfections and phase gradient-induced eddy current effects. In addition, this new method retains advantages of the earlier method, such as simultaneous correction of different off-resonance factors without use of a complicated phase unwrapping procedure. The effectiveness of this technique is illustrated with EPI studies on phantoms and animal subjects. Implementation to different versions of EPI sequences is also described. Magn Reson Med 45:525-528, 2001. Copyright 2001 Wiley-Liss, Inc.

Data-driven gradient algorithm for high-precision quantum control

NASA Astrophysics Data System (ADS)

Wu, Re-Bing; Chu, Bing; Owens, David H.; Rabitz, Herschel

2018-04-01

In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.

Investigation of Ionospheric Spatial Gradients for Gagan Error Correction

NASA Astrophysics Data System (ADS)

Chandra, K. Ravi

In India, Indian Space Research Organization (ISRO) has established with an objective to develop space technology and its application to various national tasks. The national tasks include, establishment of major space systems such as Indian National Satellites (INSAT) for communication, television broadcasting and meteorological services, Indian Remote Sensing Satellites (IRS), etc. Apart from these, to cater to the needs of civil aviation applications, GPS Aided Geo Augmented Navigation (GAGAN) system is being jointly implemented along with Airports Authority of India (AAI) over the Indian region. The most predominant parameter affecting the navigation accuracy of GAGAN is ionospheric delay which is a function of total number of electrons present in one square meter cylindrical cross-sectional area in the line of site direction between the satellite and the user on the earth, i.e. Total Electron Content (TEC). In the equatorial and low latitude regions such as India, TEC is often quite high with large spatial gradients. Carrier phase data from the GAGAN network of Indian TEC Stations is used for estimating and identifying ionospheric spatial gradients inmultiple viewing directions. In this paper amongst the satellite signals arriving in multipledirections,Vertical ionospheric gradients (σVIG) are calculated, inturn spatial ionospheric gradients are identified. In addition, estimated temporal gradients, i.e. rate of TEC Index is also compared. These aspects which contribute to errors can be treated for improved GAGAN system performance.

Computational trigonometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gustafson, K.

1994-12-31

By means of the author`s earlier theory of antieigenvalues and antieigenvectors, a new computational approach to iterative methods is presented. This enables an explicit trigonometric understanding of iterative convergence and provides new insights into the sharpness of error bounds. Direct applications to Gradient descent, Conjugate gradient, GCR(k), Orthomin, CGN, GMRES, CGS, and other matrix iterative schemes will be given.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Yiting; Dong, Bin; Wang, Bing

Purpose: Effective and accurate segmentation of the aortic valve (AV) from sequenced ultrasound (US) images remains a technical challenge because of intrinsic factors of ultrasound images that impact the quality and the continuous changes of shape and position of segmented objects. In this paper, a novel shape-constraint gradient Chan-Vese (GCV) model is proposed for segmenting the AV from time serial echocardiography. Methods: The GCV model is derived by incorporating the energy of the gradient vector flow into a CV model framework, where the gradient vector energy term is introduced by calculating the deviation angle between the inward normal force ofmore » the evolution contour and the gradient vector force. The flow force enlarges the capture range and enhances the blurred boundaries of objects. This is achieved by adding a circle-like contour (constructed using the AV structure region as a constraint shape) as an energy item to the GCV model through the shape comparison function. This shape-constrained energy can enhance the image constraint force by effectively connecting separate gaps of the object edge as well as driving the evolution contour to quickly approach the ideal object. Because of the slight movement of the AV in adjacent frames, the initial constraint shape is defined by users, with the other constraint shapes being derived from the segmentation results of adjacent sequence frames after morphological filtering. The AV is segmented from the US images by minimizing the proposed energy function. Results: To evaluate the performance of the proposed method, five assessment parameters were used to compare it with manual delineations performed by radiologists (gold standards). Three hundred and fifteen images acquired from nine groups were analyzed in the experiment. The area-metric overlap error rate was 6.89% ± 2.88%, the relative area difference rate 3.94% ± 2.63%, the average symmetric contour distance 1.08 ± 0.43 mm, the root mean square symmetric contour distance 1.37 ± 0.52 mm, and the maximum symmetric contour distance was 3.57 ± 1.72 mm. Conclusions: Compared with the CV model, as a result of the combination of the gradient vector and neighborhood shape information, this semiautomatic segmentation method significantly improves the accuracy and robustness of AV segmentation, making it feasible for improved segmentation of aortic valves from US images that have fuzzy boundaries.« less

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons

PubMed Central

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2012-01-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π. PMID:24027379

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2013-08-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.

Three filters for visualization of phase objects with large variations of phase gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sagan, Arkadiusz; Antosiewicz, Tomasz J.; Szoplik, Tomasz

2009-02-20

We propose three amplitude filters for visualization of phase objects. They interact with the spectra of pure-phase objects in the frequency plane and are based on tangent and error functions as well as antisymmetric combination of square roots. The error function is a normalized form of the Gaussian function. The antisymmetric square-root filter is composed of two square-root filters to widen its spatial frequency spectral range. Their advantage over other known amplitude frequency-domain filters, such as linear or square-root graded ones, is that they allow high-contrast visualization of objects with large variations of phase gradients.

SU-C-BRA-02: Gradient Based Method of Target Delineation On PET/MR Image of Head and Neck Cancer Patients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dance, M; Chera, B; Falchook, A

2015-06-15

Purpose: Validate the consistency of a gradient-based segmentation tool to facilitate accurate delineation of PET/CT-based GTVs in head and neck cancers by comparing against hybrid PET/MR-derived GTV contours. Materials and Methods: A total of 18 head and neck target volumes (10 primary and 8 nodal) were retrospectively contoured using a gradient-based segmentation tool by two observers. Each observer independently contoured each target five times. Inter-observer variability was evaluated via absolute percent differences. Intra-observer variability was examined by percentage uncertainty. All target volumes were also contoured using the SUV percent threshold method. The thresholds were explored case by case so itsmore » derived volume matched with the gradient-based volume. Dice similarity coefficients (DSC) were calculated to determine overlap of PET/CT GTVs and PET/MR GTVs. Results: The Levene’s test showed there was no statistically significant difference of the variances between the observer’s gradient-derived contours. However, the absolute difference between the observer’s volumes was 10.83%, with a range from 0.39% up to 42.89%. PET-avid regions with qualitatively non-uniform shapes and intensity levels had a higher absolute percent difference near 25%, while regions with uniform shapes and intensity levels had an absolute percent difference of 2% between observers. The average percentage uncertainty between observers was 4.83% and 7%. As the volume of the gradient-derived contours increased, the SUV threshold percent needed to match the volume decreased. Dice coefficients showed good agreement of the PET/CT and PET/MR GTVs with an average DSC value across all volumes at 0.69. Conclusion: Gradient-based segmentation of PET volume showed good consistency in general but can vary considerably for non-uniform target shapes and intensity levels. PET/CT-derived GTV contours stemming from the gradient-based tool show good agreement with the anatomically and metabolically more accurate PET/MR-derived GTV contours, but tumor delineation accuracy can be further improved with the use PET/MR.« less

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Evaluation of B1 inhomogeneity effect on DCE-MRI data analysis of brain tumor patients at 3T.

PubMed

Sengupta, Anirban; Gupta, Rakesh Kumar; Singh, Anup

2017-12-02

Dynamic-contrast-enhanced (DCE) MRI data acquired using gradient echo based sequences is affected by errors in flip angle (FA) due to transmit B 1 inhomogeneity (B 1 inh). The purpose of the study was to evaluate the effect of B 1 inh on quantitative analysis of DCE-MRI data of human brain tumor patients and to evaluate the clinical significance of B 1 inh correction of perfusion parameters (PPs) on tumor grading. An MRI study was conducted on 35 glioma patients at 3T. The patients had histologically confirmed glioma with 23 high-grade (HG) and 12 low-grade (LG). Data for B 1 -mapping, T 1 -mapping and DCE-MRI were acquired. Relative B 1 maps (B 1rel ) were generated using the saturated-double-angle method. T 1 -maps were computed using the variable flip-angle method. Post-processing was performed for conversion of signal-intensity time (S(t)) curve to concentration-time (C(t)) curve followed by tracer kinetic analysis (K trans , Ve, Vp, Kep) and first pass analysis (CBV, CBF) using the general tracer-kinetic model. DCE-MRI data was analyzed without and with B 1 inh correction and errors in PPs were computed. Receiver-operating-characteristic (ROC) analysis was performed on HG and LG patients. Simulations were carried out to understand the effect of B 1 inhomogeneity on DCE-MRI data analysis in a systematic way. S(t) curves mimicking those in tumor tissue, were generated and FA errors were introduced followed by error analysis of PPs. Dependence of FA-based errors on the concentration of contrast agent and on the duration of DCE-MRI data was also studied. Simulations were also done to obtain K trans of glioma patients at different B 1rel values and see whether grading is affected or not. Current study shows that B 1rel value higher than nominal results in an overestimation of C(t) curves as well as derived PPs and vice versa. Moreover, at same B 1rel values, errors were large for larger values of C(t). Simulation results showed that grade of patients can change because of B 1 inh. B 1 inh in the human brain at 3T-MRI can introduce substantial errors in PPs derived from DCE-MRI data that might affect the accuracy of tumor grading, particularly for border zone cases. These errors can be mitigated using B 1 inh correction during DCE-MRI data analysis.

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Correction of Thermal Gradient Errors in Stem Thermocouple Hygrometers

PubMed Central

Michel, Burlyn E.

1979-01-01

Stem thermocouple hygrometers were subjected to transient and stable thermal gradients while in contact with reference solutions of NaCl. Both dew point and psychrometric voltages were directly related to zero offset voltages, the latter reflecting the size of the thermal gradient. Although slopes were affected by absolute temperature, they were not affected by water potential. One hygrometer required a correction of 1.75 bars water potential per microvolt of zero offset, a value that was constant from 20 to 30 C. PMID:16660685

Method of Lines Transpose an Implicit Vlasov Maxwell Solver for Plasmas

DTIC Science & Technology

2015-04-17

boundary crossings should be rare. Numerical results for the Bennett pinch are given in Figure 9. In order to resolve large gradients near the center of the...contributing to the large error at the center of the beam due to large gradients there) and with the finite beam cut-off radius and the outflow boundary...usable time step size can be limited by the numerical accuracy of the method when there are large gradients (high-frequency content) in the solution. We

Prediction of gradient retention data for hydrophilic interaction liquid chromatographic separation of native and fluorescently labeled oligosaccharides.

PubMed

Vaňková, Nikola; Česla, Petr

2017-02-17

In this work, we have investigated the predictive properties of mixed-mode retention model and oligomeric mixed-mode model, taking into account the contribution of monomeric units to the retention, in hydrophilic interaction liquid chromatography. The gradient retention times of native maltooligosaccharides and their fluorescent derivatives were predicted in the oligomeric series with number of monomeric glucose units in the range from two to seven. The maltooligosaccharides were separated on a packed column with carbamoyl-bonded silica stationary phase and 15 gradient profiles with different initial and final mobile phase composition were used with the gradient times 5; 7.5 and 10min. The predicted gradient retention times were compared for calculations based on isocratic retention data and gradient retention data, which provided better accuracy of the results. By comparing two different mobile phase additives, the more accurate retention times were predicted in mobile phases containing ammonium acetate. The acidic derivatives, prepared by reaction of an oligosaccharide with 2-aminobenzoic acid or 8-aminonaphthalene-1,3,6-trisulfonic acid, provided more accurate predictions of the retention data in comparison to native oligosaccharides or their neutral derivatives. The oligomeric mixed-mode model allowed prediction of gradient retention times using only one gradient profile, which significantly speeded-up the method development. Copyright © 2017 Elsevier B.V. All rights reserved.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system.

PubMed

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-21

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

On the derivation of empirical limits on the helium abundance in coronal holes below 1.5 solar radius

NASA Technical Reports Server (NTRS)

Habbal, Shadia Rifai; Esser, Ruth

1994-01-01

We present a simple technique describing how limits on the helium abundance, alpha, defined as the ratio of helium to proton number density, can be inferred from measurements of the electron density and temperature below 1.5 solar radius. As an illustration, we apply this technique to two different data sets: emission-line intensities in the extreme ultraviolet (EUV) and white-light observations, both measured in polar coronal holes. For the EUV data, the temperature gradient is derived from line intensity ratios, and the density gradient is replaced by the gradient of the line intensity. The lower limit on alpha derived from these data is 0.2-0.3 at 1 solar radius and drops very sharply to interplanetary values of a few percent below 1.06 solar radius. The white-light observations yield density gradients in the inner corona beyond 1.25 solar radius but do not have corresponding temperature gradients. In this case we consider an isothermal atmosphere, and derive an upper limit of 0.2 for alpha. These examples are used to illustrate how this technique could be applicable to the more extensive data to be obtained with the upcoming SOHO mission. Although only ranges on alpha can be derived, the application of the technique to data currently available merely points to the fact that alpha can be significantly large in the inner corona.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

NASA Technical Reports Server (NTRS)

Tsaoussi, Lucia S.; Koblinsky, Chester J.

1994-01-01

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Estimation of diastolic intraventricular pressure gradients by Doppler M-mode echocardiography

NASA Technical Reports Server (NTRS)

Greenberg, N. L.; Vandervoort, P. M.; Firstenberg, M. S.; Garcia, M. J.; Thomas, J. D.

2001-01-01

Previous studies have shown that small intraventricular pressure gradients (IVPG) are important for efficient filling of the left ventricle (LV) and as a sensitive marker for ischemia. Unfortunately, there has previously been no way of measuring these noninvasively, severely limiting their research and clinical utility. Color Doppler M-mode (CMM) echocardiography provides a spatiotemporal velocity distribution along the inflow tract throughout diastole, which we hypothesized would allow direct estimation of IVPG by using the Euler equation. Digital CMM images, obtained simultaneously with intracardiac pressure waveforms in six dogs, were processed by numerical differentiation for the Euler equation, then integrated to estimate IVPG and the total (left atrial to left ventricular apex) pressure drop. CMM-derived estimates agreed well with invasive measurements (IVPG: y = 0.87x + 0.22, r = 0.96, P < 0.001, standard error of the estimate = 0.35 mmHg). Quantitative processing of CMM data allows accurate estimation of IVPG and tracking of changes induced by beta-adrenergic stimulation. This novel approach provides unique information on LV filling dynamics in an entirely noninvasive way that has previously not been available for assessment of diastolic filling and function.

Validation of an improved 'diffeomorphic demons' algorithm for deformable image registration in image-guided radiation therapy.

PubMed

Zhou, Lu; Zhou, Linghong; Zhang, Shuxu; Zhen, Xin; Yu, Hui; Zhang, Guoqian; Wang, Ruihao

2014-01-01

Deformable image registration (DIR) was widely used in radiation therapy, such as in automatic contour generation, dose accumulation, tumor growth or regression analysis. To achieve higher registration accuracy and faster convergence, an improved 'diffeomorphic demons' registration algorithm was proposed and validated. Based on Brox et al.'s gradient constancy assumption and Malis's efficient second-order minimization (ESM) algorithm, a grey value gradient similarity term and a transformation error term were added into the demons energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function so that the iteration number could be determined automatically. The proposed algorithm was validated using mathematically deformed images and physically deformed phantom images. Compared with the original 'diffeomorphic demons' algorithm, the registration method proposed achieve a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. In such a case, the improved demons algorithm can achieve faster and more accurate radiotherapy.

Ionospheric Impacts on UHF Space Surveillance

NASA Astrophysics Data System (ADS)

Jones, J. C.

2017-12-01

Earth's atmosphere contains regions of ionized plasma caused by the interaction of highly energetic solar radiation. This region of ionization is called the ionosphere and varies significantly with altitude, latitude, local solar time, season, and solar cycle. Significant ionization begins at about 100 km (E layer) with a peak in the ionization at about 300 km (F2 layer). Above the F2 layer, the atmosphere is mostly ionized but the ion and electron densities are low due to the unavailability of neutral molecules for ionization so the density decreases exponentially with height to well over 1000 km. The gradients of these variations in the ionosphere play a significant role in radio wave propagation. These gradients induce variations in the index of refraction and cause some radio waves to refract. The amount of refraction depends on the magnitude and direction of the electron density gradient and the frequency of the radio wave. The refraction is significant at HF frequencies (3-30 MHz) with decreasing effects toward the UHF (300-3000 MHz) range. UHF is commonly used for tracking of space objects in low Earth orbit (LEO). While ionospheric refraction is small for UHF frequencies, it can cause errors in range, azimuth angle, and elevation angle estimation by ground-based radars tracking space objects. These errors can cause significant errors in precise orbit determinations. For radio waves transiting the ionosphere, it is important to understand and account for these effects. Using a sophisticated radio wave propagation tool suite and an empirical ionospheric model, we calculate the errors induced by the ionosphere in a simulation of a notional space surveillance radar tracking objects in LEO. These errors are analyzed to determine daily, monthly, annual, and solar cycle trends. Corrections to surveillance radar measurements can be adapted from our simulation capability.

Manipulating the Gradient

ERIC Educational Resources Information Center

Gaze, Eric C.

2005-01-01

We introduce a cooperative learning, group lab for a Calculus III course to facilitate comprehension of the gradient vector and directional derivative concepts. The lab is a hands-on experience allowing students to manipulate a tangent plane and empirically measure the effect of partial derivatives on the direction of optimal ascent. (Contains 7…

Reductive amination of glutaraldehyde 2,4-dinitrophenylhydrazone using 2-picoline borane and high-performance liquid chromatographic analysis.

PubMed

Uchiyama, Shigehisa; Sakamoto, Hironari; Ohno, Akiko; Inaba, Yohei; Nakagome, Hideki; Kunugita, Naoki

2012-09-21

A typical method for the measurement of glutaraldehyde (GLA) employs 2,4-dinitrophenylhydrazine (DNPH) to form GLA-DNPhydrazone derivatives. However, this method is subject to analytical errors because GLA-DNPhydrazone is a quaternary bis-derivative and forms three geometric isomers (E-E, E-Z and Z-Z) as a result of the two C[double bond, length as m-dash]N double bonds. To overcome this issue, a method for transforming the C[double bond, length as m-dash]N double bond into a C-N single bond, using reductive amination of DNPhydrazone derivatives, has been applied. The amination reaction of GLA-DNPhydrazones with 2-picoline borane is accelerated with catalytic amounts of acid and is completed within 10 minutes in the presence of 100 mmol L(-1) phosphoric acid. Reduction of GLA-DNPhydrazone by 2-picoline borane is unique and results in the formation of N-(2,4-dinitrophenyl)-1-piperidinamine (DNPPA). NMR and LC-APCI-MS data confirmed the product identification. DNPPA is very stable and did not change when stored for at least four weeks at room temperature. DNPPA has excellent solubility of 14.6 g L(-1) at 20 °C in acetonitrile. The absorption maximum wavelength and the molar absorptivity of DNPPA were 351 nm and 4.2 × 10(4) L mol(-1) cm(-1) respectively. Complete separation between the reduced forms of C1-C10 aldehyde DNPhydrazones, including DNPPA, can be achieved by operating the reversed-phase high-performance liquid chromatograph at 351 nm in gradient mode using a C18 amide column. The reductive amination method for GLA overcomes analytical errors caused by E-E, E-Z and Z-Z geometrical isomers.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Magnetic field of longitudinal gradient bend

NASA Astrophysics Data System (ADS)

Aiba, Masamitsu; Böge, Michael; Ehrlichman, Michael; Streun, Andreas

2018-06-01

The longitudinal gradient bend is an effective method for reducing the natural emittance in light sources. It is, however, not a common element. We have analyzed its magnetic field and derived a set of formulae. Based on the derivation, we discuss how to model the longitudinal gradient bend in accelerator codes that are used for designing electron storage rings. Strengths of multipole components can also be evaluated from the formulae, and we investigate the impact of higher order multipole components in a very low emittance lattice.

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Edge profile analysis of Joint European Torus (JET) Thomson scattering data: Quantifying the systematic error due to edge localised mode synchronisation.

PubMed

Leyland, M J; Beurskens, M N A; Flanagan, J C; Frassinetti, L; Gibson, K J; Kempenaars, M; Maslov, M; Scannell, R

2016-01-01

The Joint European Torus (JET) high resolution Thomson scattering (HRTS) system measures radial electron temperature and density profiles. One of the key capabilities of this diagnostic is measuring the steep pressure gradient, termed the pedestal, at the edge of JET plasmas. The pedestal is susceptible to limiting instabilities, such as Edge Localised Modes (ELMs), characterised by a periodic collapse of the steep gradient region. A common method to extract the pedestal width, gradient, and height, used on numerous machines, is by performing a modified hyperbolic tangent (mtanh) fit to overlaid profiles selected from the same region of the ELM cycle. This process of overlaying profiles, termed ELM synchronisation, maximises the number of data points defining the pedestal region for a given phase of the ELM cycle. When fitting to HRTS profiles, it is necessary to incorporate the diagnostic radial instrument function, particularly important when considering the pedestal width. A deconvolved fit is determined by a forward convolution method requiring knowledge of only the instrument function and profiles. The systematic error due to the deconvolution technique incorporated into the JET pedestal fitting tool has been documented by Frassinetti et al. [Rev. Sci. Instrum. 83, 013506 (2012)]. This paper seeks to understand and quantify the systematic error introduced to the pedestal width due to ELM synchronisation. Synthetic profiles, generated with error bars and point-to-point variation characteristic of real HRTS profiles, are used to evaluate the deviation from the underlying pedestal width. We find on JET that the ELM synchronisation systematic error is negligible in comparison to the statistical error when assuming ten overlaid profiles (typical for a pre-ELM fit to HRTS profiles). This confirms that fitting a mtanh to ELM synchronised profiles is a robust and practical technique for extracting the pedestal structure.

Assessment of the derivative-moment transformation method for unsteady-load estimation

NASA Astrophysics Data System (ADS)

Mohebbian, Ali; Rival, David E.

2012-08-01

It is often difficult, if not impossible, to measure the aerodynamic or hydrodynamic forces on a moving body. For this reason, a classical control-volume technique is typically applied to extract the unsteady forces. However, measuring the acceleration term within the volume of interest using particle image velocimetry (PIV) can be limited by optical access, reflections, as well as shadows. Therefore, in this study, an alternative approach, termed the derivative-moment transformation (DMT) method, is introduced and tested on a synthetic data set produced using numerical simulations. The test case involves the unsteady loading of a flat plate in a two-dimensional, laminar periodic gust. The results suggest that the DMT method can accurately predict the acceleration term so long as appropriate spatial and temporal resolutions are maintained. The major deficiency, which is more dominant for the direction of drag, was found to be the determination of pressure and unsteady terms in the wake. The effect of control-volume size was investigated, suggesting that larger domains work best by minimizing the associated error in the determination of the pressure field. When decreasing the control-volume size, wake vortices, which produce high gradients across the control surfaces, are found to substantially increase the level of error. On the other hand, it was shown that for large control volumes, and with realistic spatial resolution, the accuracy of the DMT method would also suffer. Therefore, a delicate compromise is required when selecting control-volume size in future experiments.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Artificial Vector Calibration Method for Differencing Magnetic Gradient Tensor Systems

PubMed Central

Li, Zhining; Zhang, Yingtang; Yin, Gang

2018-01-01

The measurement error of the differencing (i.e., using two homogenous field sensors at a known baseline distance) magnetic gradient tensor system includes the biases, scale factors, nonorthogonality of the single magnetic sensor, and the misalignment error between the sensor arrays, all of which can severely affect the measurement accuracy. In this paper, we propose a low-cost artificial vector calibration method for the tensor system. Firstly, the error parameter linear equations are constructed based on the single-sensor’s system error model to obtain the artificial ideal vector output of the platform, with the total magnetic intensity (TMI) scalar as a reference by two nonlinear conversions, without any mathematical simplification. Secondly, the Levenberg–Marquardt algorithm is used to compute the integrated model of the 12 error parameters by nonlinear least-squares fitting method with the artificial vector output as a reference, and a total of 48 parameters of the system is estimated simultaneously. The calibrated system outputs along the reference platform-orthogonal coordinate system. The analysis results show that the artificial vector calibrated output can track the orientation fluctuations of TMI accurately, effectively avoiding the “overcalibration” problem. The accuracy of the error parameters’ estimation in the simulation is close to 100%. The experimental root-mean-square error (RMSE) of the TMI and tensor components is less than 3 nT and 20 nT/m, respectively, and the estimation of the parameters is highly robust. PMID:29373544

Simple method for RF pulse measurement using gradient reversal.

PubMed

Landes, Vanessa L; Nayak, Krishna S

2018-05-01

To develop and evaluate a simple method for measuring the envelope of small-tip radiofrequency (RF) excitation waveforms in MRI, without extra hardware or synchronization. Gradient reversal approach to evaluate RF (GRATER) involves RF excitation with a constant gradient and reversal of that gradient during signal reception to acquire the time-reversed version of an RF envelope. An outer-volume suppression prepulse is used optionally to preselect a uniform volume. GRATER was evaluated in phantom and in vivo experiments. It was compared with the programmed waveform and the traditional pick-up coil method. In uniform phantom experiments, pick-up coil, GRATER, and outer-volume suppression + GRATER matched the programmed waveforms to less than 2.1%, less than 6.1%, and less than 2.4% normalized root mean square error, respectively, for real RF pulses with flip angle less than or equal to 30°, time-bandwidth product 2 to 8, and two to five excitation bands. For flip angles greater than 30°, GRATER measurement error increased as predicted by Bloch simulation. Fat-water phantom and in vivo experiments with outer-volume suppression + GRATER demonstrated less than 6.4% normalized root mean square error. The GRATER sequence measures small-tip RF envelopes without extra hardware or synchronization in just over two times the RF duration. The sequence may be useful in prescan calibration and for measurement and precompensation of RF amplifier nonlinearity. Magn Reson Med 79:2642-2651, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

PubMed

Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai

2016-06-10

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

A constrained-gradient method to control divergence errors in numerical MHD

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2016-10-01

In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.

Applying additive modeling and gradient boosting to assess the effects of watershed and reach characteristics on riverine assemblages

USGS Publications Warehouse

Maloney, Kelly O.; Schmid, Matthias; Weller, Donald E.

2012-01-01

Issues with ecological data (e.g. non-normality of errors, nonlinear relationships and autocorrelation of variables) and modelling (e.g. overfitting, variable selection and prediction) complicate regression analyses in ecology. Flexible models, such as generalized additive models (GAMs), can address data issues, and machine learning techniques (e.g. gradient boosting) can help resolve modelling issues. Gradient boosted GAMs do both. Here, we illustrate the advantages of this technique using data on benthic macroinvertebrates and fish from 1573 small streams in Maryland, USA.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

Performance Evaluation and Requirements Assessment for Gravity Gradient Referenced Navigation

PubMed Central

Lee, Jisun; Kwon, Jay Hyoun; Yu, Myeongjong

2015-01-01

In this study, simulation tests for gravity gradient referenced navigation (GGRN) are conducted to verify the effects of various factors such as database (DB) and sensor errors, flight altitude, DB resolution, initial errors, and measurement update rates on the navigation performance. Based on the simulation results, requirements for GGRN are established for position determination with certain target accuracies. It is found that DB and sensor errors and flight altitude have strong effects on the navigation performance. In particular, a DB and sensor with accuracies of 0.1 E and 0.01 E, respectively, are required to determine the position more accurately than or at a level similar to the navigation performance of terrain referenced navigation (TRN). In most cases, the horizontal position error of GGRN is less than 100 m. However, the navigation performance of GGRN is similar to or worse than that of a pure inertial navigation system when the DB and sensor errors are 3 E or 5 E each and the flight altitude is 3000 m. Considering that the accuracy of currently available gradiometers is about 3 E or 5 E, GGRN does not show much advantage over TRN at present. However, GGRN is expected to exhibit much better performance in the near future when accurate DBs and gravity gradiometer are available. PMID:26184212

A general strategy for performing temperature-programming in high performance liquid chromatography--further improvements in the accuracy of retention time predictions of segmented temperature gradients.

PubMed

Wiese, Steffen; Teutenberg, Thorsten; Schmidt, Torsten C

2012-01-27

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed for systematic method development in high-temperature liquid chromatography (HT-HPLC). The ability to predict isothermal retention times based on temperature-gradient as well as isothermal input data was investigated. For a small temperature interval of ΔT=40°C, both approaches result in very similar predictions. Average relative errors of predicted retention times of 2.7% and 1.9% were observed for simulations based on isothermal and temperature-gradient measurements, respectively. Concurrently, it was investigated whether the accuracy of retention time predictions of segmented temperature gradients can be further improved by temperature dependent calculation of the parameter S(T) of the LES relationship. It was found that the accuracy of retention time predictions of multi-step temperature gradients can be improved to around 1.5%, if S(T) was also calculated temperature dependent. The adjusted experimental design making use of four temperature-gradient measurements was applied for systematic method development of selected food additives by high-temperature liquid chromatography. Method development was performed within a temperature interval from 40°C to 180°C using water as mobile phase. Two separation methods were established where selected food additives were baseline separated. In addition, a good agreement between simulation and experiment was observed, because an average relative error of predicted retention times of complex segmented temperature gradients less than 5% was observed. Finally, a schedule of recommendations to assist the practitioner during systematic method development in high-temperature liquid chromatography was established. Copyright © 2011 Elsevier B.V. All rights reserved.

Adaptive filter design using recurrent cerebellar model articulation controller.

PubMed

Lin, Chih-Min; Chen, Li-Yang; Yeung, Daniel S

2010-07-01

A novel adaptive filter is proposed using a recurrent cerebellar-model-articulation-controller (CMAC). The proposed locally recurrent globally feedforward recurrent CMAC (RCMAC) has favorable properties of small size, good generalization, rapid learning, and dynamic response, thus it is more suitable for high-speed signal processing. To provide fast training, an efficient parameter learning algorithm based on the normalized gradient descent method is presented, in which the learning rates are on-line adapted. Then the Lyapunov function is utilized to derive the conditions of the adaptive learning rates, so the stability of the filtering error can be guaranteed. To demonstrate the performance of the proposed adaptive RCMAC filter, it is applied to a nonlinear channel equalization system and an adaptive noise cancelation system. The advantages of the proposed filter over other adaptive filters are verified through simulations.

Influence of measuring algorithm on shape accuracy in the compensating turning of high gradient thin-wall parts

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Guilin; Zhu, Dengchao; Li, Shengyi

2015-02-01

In order to meet the requirement of aerodynamics, the infrared domes or windows with conformal and thin-wall structure becomes the development trend of high-speed aircrafts in the future. But these parts usually have low stiffness, the cutting force will change along with the axial position, and it is very difficult to meet the requirement of shape accuracy by single machining. Therefore, on-machine measurement and compensating turning are used to control the shape errors caused by the fluctuation of cutting force and the change of stiffness. In this paper, on the basis of ultra precision diamond lathe, a contact measuring system with five DOFs is developed to achieve on-machine measurement of conformal thin-wall parts with high accuracy. According to high gradient surface, the optimizing algorithm is designed on the distribution of measuring points by using the data screening method. The influence rule of sampling frequency is analyzed on measuring errors, the best sampling frequency is found out based on planning algorithm, the effect of environmental factors and the fitting errors are controlled within lower range, and the measuring accuracy of conformal dome is greatly improved in the process of on-machine measurement. According to MgF2 conformal dome with high gradient, the compensating turning is implemented by using the designed on-machine measuring algorithm. The shape error is less than PV 0.8μm, greatly superior compared with PV 3μm before compensating turning, which verifies the correctness of measuring algorithm.

Improving Maritime Domain Awareness Using Neural Networks for Target of Interest Classification

DTIC Science & Technology

2015-03-01

spreading SCG scaled conjugate gradient xv THIS PAGE INTENTIONALLY LEFT BLANK xvi EXECUTIVE SUMMARY The research detailed in this thesis is a...algorithms were explored for training the neural networks: resilient backpropagation (RP) and scaled conjugate gradient backpropagation ( SCG ). The...results of the neural network training performance are presented using mean squared error convergence plots. In all implementations, the SCG learning

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

NASA Astrophysics Data System (ADS)

Wladyslawski, Mark; Nooijen, Marcel

The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit equations for the wavefunction amplitudes, the Lagrange multipliers, and the analytical gradient via the perturbation-independent generalized Hellmann-Feynman effective density matrix. This systematic automated derivation procedure is applied to obtain the detailed gradient equations for the excitation energy (EE-), double ionization potential (DIP-), and double electron affinity (DEA-) similarity transformed equation-of-motion coupled-cluster singles-and-doubles (STEOM-CCSD) methods. In addition, the derivatives of the closed-shell-reference excitation energy (EE-), ionization potential (IP-), and electron affinity (EA-) equation-of-motion coupled-cluster singles-and-doubles (EOM-CCSD) methods are derived. Furthermore, the perturbative EOM-PT and STEOM-PT gradients are obtained. The algebraic derivative expressions for these dozen methods are all derived here uniformly through the automated Lagrange multiplier process and are expressed compactly in a chain-rule/intermediate-density formulation, which facilitates a unified modular implementation of analytic energy gradients for CCSD/PT-based electronic methods. The working equations for these analytical gradients are presented in full detail, and their factorization and implementation into an efficient computer code are discussed.

Upscaling from particle models to entropic gradient flows

NASA Astrophysics Data System (ADS)

Dirr, Nicolas; Laschos, Vaios; Zimmer, Johannes

2012-06-01

We prove that, for the case of Gaussians on the real line, the functional derived by a time discretization of the diffusion equation as entropic gradient flow is asymptotically equivalent to the rate functional derived from the underlying microscopic process. This result strengthens a conjecture that the same statement is actually true for all measures with second finite moment.

Snake River Plain Geothermal Play Fairway Analysis - Phase 1 Raster Files

DOE Data Explorer

John Shervais

2015-10-09

Snake River Plain Play Fairway Analysis - Phase 1 CRS Raster Files. This dataset contains raster files created in ArcGIS. These raster images depict Common Risk Segment (CRS) maps for HEAT, PERMEABILITY, AND SEAL, as well as selected maps of Evidence Layers. These evidence layers consist of either Bayesian krige functions or kernel density functions, and include: (1) HEAT: Heat flow (Bayesian krige map), Heat flow standard error on the krige function (data confidence), volcanic vent distribution as function of age and size, groundwater temperature (equivalue interval and natural breaks bins), and groundwater T standard error. (2) PERMEABILTY: Fault and lineament maps, both as mapped and as kernel density functions, processed for both dilational tendency (TD) and slip tendency (ST), along with data confidence maps for each data type. Data types include mapped surface faults from USGS and Idaho Geological Survey data bases, as well as unpublished mapping; lineations derived from maximum gradients in magnetic, deep gravity, and intermediate depth gravity anomalies. (3) SEAL: Seal maps based on presence and thickness of lacustrine sediments and base of SRP aquifer. Raster size is 2 km. All files generated in ArcGIS.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

Robust Optimal Adaptive Control Method with Large Adaptive Gain

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2009-01-01

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.

Identification method of laser gyro error model under changing physical field

NASA Astrophysics Data System (ADS)

Wang, Qingqing; Niu, Zhenzhong

2018-04-01

In this paper, the influence mechanism of temperature, temperature changing rate and temperature gradient on the inertial devices is studied. The two-order model of zero bias and the three-order model of the calibration factor of lster gyro under temperature variation are deduced. The calibration scheme of temperature error is designed, and the experiment is carried out. Two methods of stepwise regression analysis and BP neural network are used to identify the parameters of the temperature error model, and the effectiveness of the two methods is proved by the temperature error compensation.

Applications of seismic spatial wavefield gradient and rotation data in exploration seismology

NASA Astrophysics Data System (ADS)

Schmelzbach, C.; Van Renterghem, C.; Sollberger, D.; Häusler, M.; Robertsson, J. O. A.

2017-12-01

Seismic spatial wavefield gradient and rotation data have the potential to open up new ways to address long-standing problems in land-seismic exploration such as identifying and separating P-, S-, and surface waves. Gradient-based acquisition and processing techniques could enable replacing large arrays of densely spaced receivers by sparse spatially-compact receiver layouts or even one single multicomponent station with dedicated instruments (e.g., rotational seismometers). Such approaches to maximize the information content of single-station recordings are also of significant interest for seismic measurements at sites with limited access such as boreholes, the sea bottom, and extraterrestrial seismology. Arrays of conventional three-component (3C) geophones enable measuring not only the particle velocity in three dimensions but also estimating their spatial gradients. Because the free-surface condition allows to express vertical derivatives in terms of horizontal derivatives, the full gradient tensor and, hence, curl and divergence of the wavefield can be computed. In total, three particle velocity components, three rotational components, and divergence, result seven-component (7C) seismic data. Combined particle velocity and gradient data can be used to isolate the incident P- or S-waves at the land surface or the sea bottom using filtering techniques based on the elastodynamic representation theorem. Alternatively, as only S-waves exhibit rotational motion, rotational measurements can directly be used to identify S-waves. We discuss the derivations of the gradient-based filters as well as their application to synthetic and field data, demonstrating that rotational data can be of particular interest to S-wave reflection and P-to-S-wave conversion imaging. The concept of array-derived gradient estimation can be extended to source arrays as well. Therefore, source arrays allow us to emulate rotational (curl) and dilatational (divergence) sources. Combined with 7C recordings, a total of 49 components of the seismic wavefield can be excited and recorded. Such data potentially allow to further improve wavefield separation and may find application in directional imaging and coherent noise suppression.

A Modified Magnetic Gradient Contraction Based Method for Ferromagnetic Target Localization

PubMed Central

Wang, Chen; Zhang, Xiaojuan; Qu, Xiaodong; Pan, Xiao; Fang, Guangyou; Chen, Luzhao

2016-01-01

The Scalar Triangulation and Ranging (STAR) method, which is based upon the unique properties of magnetic gradient contraction, is a high real-time ferromagnetic target localization method. Only one measurement point is required in the STAR method and it is not sensitive to changes in sensing platform orientation. However, the localization accuracy of the method is limited by the asphericity errors and the inaccurate value of position leads to larger errors in the estimation of magnetic moment. To improve the localization accuracy, a modified STAR method is proposed. In the proposed method, the asphericity errors of the traditional STAR method are compensated with an iterative algorithm. The proposed method has a fast convergence rate which meets the requirement of high real-time localization. Simulations and field experiments have been done to evaluate the performance of the proposed method. The results indicate that target parameters estimated by the modified STAR method are more accurate than the traditional STAR method. PMID:27999322

Turboprop+: enhanced Turboprop diffusion-weighted imaging with a new phase correction.

PubMed

Lee, Chu-Yu; Li, Zhiqiang; Pipe, James G; Debbins, Josef P

2013-08-01

Faster periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) diffusion-weighted imaging acquisitions, such as Turboprop and X-prop, remain subject to phase errors inherent to a gradient echo readout, which ultimately limits the applied turbo factor (number of gradient echoes between each pair of radiofrequency refocusing pulses) and, thus, scan time reductions. This study introduces a new phase correction to Turboprop, called Turboprop+. This technique employs calibration blades, which generate 2-D phase error maps and are rotated in accordance with the data blades, to correct phase errors arising from off-resonance and system imperfections. The results demonstrate that with a small increase in scan time for collecting calibration blades, Turboprop+ had a superior immunity to the off-resonance-related artifacts when compared to standard Turboprop and recently proposed X-prop with the high turbo factor (turbo factor = 7). Thus, low specific absorption rate and short scan time can be achieved in Turboprop+ using a high turbo factor, whereas off-resonance related artifacts are minimized. © 2012 Wiley Periodicals, Inc.

Analysis of Online Composite Mirror Descent Algorithm.

PubMed

Lei, Yunwen; Zhou, Ding-Xuan

2017-03-01

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Two-dimensional simulation of eccentric photorefraction images for ametropes: factors influencing the measurement.

PubMed

Wu, Yifei; Thibos, Larry N; Candy, T Rowan

2018-05-07

Eccentric photorefraction and Purkinje image tracking are used to estimate refractive state and eye position simultaneously. Beyond vision screening, they provide insight into typical and atypical visual development. Systematic analysis of the effect of refractive error and spectacles on photorefraction data is needed to gauge the accuracy and precision of the technique. Simulation of two-dimensional, double-pass eccentric photorefraction was performed (Zemax). The inward pass included appropriate light sources, lenses and a single surface pupil plane eye model to create an extended retinal image that served as the source for the outward pass. Refractive state, as computed from the luminance gradient in the image of the pupil captured by the model's camera, was evaluated for a range of refractive errors (-15D to +15D), pupil sizes (3 mm to 7 mm) and two sets of higher-order monochromatic aberrations. Instrument calibration was simulated using -8D to +8D trial lenses at the spectacle plane for: (1) vertex distances from 3 mm to 23 mm, (2) uncorrected and corrected hyperopic refractive errors of +4D and +7D, and (3) uncorrected and corrected astigmatism of 4D at four different axes. Empirical calibration of a commercial photorefractor was also compared with a wavefront aberrometer for human eyes. The pupil luminance gradient varied linearly with refractive state for defocus less than approximately 4D (5 mm pupil). For larger errors, the gradient magnitude saturated and then reduced, leading to under-estimation of refractive state. Additional inaccuracy (up to 1D for 8D of defocus) resulted from spectacle magnification in the pupil image, which would reduce precision in situations where vertex distance is variable. The empirical calibration revealed a constant offset between the two clinical instruments. Computational modelling demonstrates the principles and limitations of photorefraction to help users avoid potential measurement errors. Factors that could cause clinically significant errors in photorefraction estimates include high refractive error, vertex distance and magnification effects of a spectacle lens, increased higher-order monochromatic aberrations, and changes in primary spherical aberration with accommodation. The impact of these errors increases with increasing defocus. © 2018 The Authors Ophthalmic & Physiological Optics © 2018 The College of Optometrists.

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

A New Correction Technique for Strain-Gage Measurements Acquired in Transient-Temperature Environments

NASA Technical Reports Server (NTRS)

Richards, W. Lance

1996-01-01

Significant strain-gage errors may exist in measurements acquired in transient-temperature environments if conventional correction methods are applied. As heating or cooling rates increase, temperature gradients between the strain-gage sensor and substrate surface increase proportionally. These temperature gradients introduce strain-measurement errors that are currently neglected in both conventional strain-correction theory and practice. Therefore, the conventional correction theory has been modified to account for these errors. A new experimental method has been developed to correct strain-gage measurements acquired in environments experiencing significant temperature transients. The new correction technique has been demonstrated through a series of tests in which strain measurements were acquired for temperature-rise rates ranging from 1 to greater than 100 degrees F/sec. Strain-gage data from these tests have been corrected with both the new and conventional methods and then compared with an analysis. Results show that, for temperature-rise rates greater than 10 degrees F/sec, the strain measurements corrected with the conventional technique produced strain errors that deviated from analysis by as much as 45 percent, whereas results corrected with the new technique were in good agreement with analytical results.

In Vitro Polarization of Colonoids to Create an Intestinal Stem Cell Compartment

PubMed Central

Attayek, Peter J.; Ahmad, Asad A.; Wang, Yuli; Williamson, Ian; Sims, Christopher E.; Magness, Scott T.; Allbritton, Nancy L.

2016-01-01

The polarity of proliferative and differentiated cellular compartments of colonic crypts is believed to be specified by gradients of key mitogens and morphogens. Indirect evidence demonstrates a tight correlation between Wnt- pathway activity and the basal-luminal patterning; however, to date there has been no direct experimental manipulation demonstrating that a chemical gradient of signaling factors can produce similar patterning under controlled conditions. In the current work, colonic organoids (colonoids) derived from cultured, multicellular organoid fragments or single stem cells were exposed in culture to steep linear gradients of two Wnt-signaling ligands, Wnt-3a and R-spondin1. The use of a genetically engineered Sox9-Sox9EGFP:CAGDsRED reporter gene mouse model and EdU-based labeling enabled crypt patterning to be quantified in the developing colonoids. Colonoids derived from multicellular fragments cultured for 5 days under a Wnt-3a or a combined Wnt-3a and R-spondin1 gradient were highly polarized with proliferative cells localizing to the region of the higher morphogen concentration. In a Wnt-3a gradient, Sox9EGFP polarization was 7.3 times greater than that of colonoids cultured in the absence of a gradient; and the extent of EdU polarization was 2.2 times greater than that in the absence of a gradient. Under a Wnt-3a/R-spondin1 gradient, Sox9EGFP polarization was 8.2 times greater than that of colonoids cultured in the absence of a gradient while the extent of EdU polarization was 10 times greater than that in the absence of a gradient. Colonoids derived from single stem cells cultured in Wnt-3a/R-spondin1 gradients were most highly polarized demonstrated by a Sox9EGFP polarization 20 times that of colonoids grown in the absence of a gradient. This data provides direct evidence that a linear gradient of Wnt signaling factors applied to colonic stem cells is sufficient to direct patterning of the colonoid unit in culture. PMID:27100890

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

PubMed Central

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-01

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26-cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients. PMID:28033119

Statistics of velocity gradients in two-dimensional Navier-Stokes and ocean turbulence.

PubMed

Schorghofer, Norbert; Gille, Sarah T

2002-02-01

Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from TOPEX satellite altimeter measurements. The simulations use rapid forcing on large scales, characteristic of surface winds. The probability distributions of transverse velocity derivatives from the ocean observations agree with the forced simulations, although they differ from unforced simulations reported elsewhere. The distribution and cross correlation of velocity derivatives provide clear evidence that large coherent eddies play only a minor role in generating the observed statistics.

Minimizing hot spot temperature in asymmetric gradient coil design.

PubMed

While, Peter T; Forbes, Larry K; Crozier, Stuart

2011-08-01

Heating caused by gradient coils is a considerable concern in the operation of magnetic resonance imaging (MRI) scanners. Hot spots can occur in regions where the gradient coil windings are closely spaced. These problem areas are particularly common in the design of gradient coils with asymmetrically located target regions. In this paper, an extension of an existing coil design method is described, to enable the design of asymmetric gradient coils with reduced hot spot temperatures. An improved model is presented for predicting steady-state spatial temperature distributions for gradient coils. A great amount of flexibility is afforded by this model to consider a wide range of geometries and system material properties. A feature of the temperature distribution related to the temperature gradient is used in a relaxed fixed point iteration routine for successively altering coil windings to have a lower hot spot temperature. Results show that significant reductions in peak temperature are possible at little or no cost to coil performance when compared to minimum power coils of equivalent field error.

[Application of general retention time formula for gradient liquid chromatography in the studies of ladder-like gradient elution].

PubMed

Sun, Xiaoli; Hao, Weiqiang; Wang, Junde; Di, Bin; Chen, Qiang; Zhuang, Wei; Yu, Qiang; Zhang, Peipei

2013-08-01

By not explicitly specifying the type of solvent strength model, the features of ladder-like gradient elution were studied based on the general retention time formula that was derived in our previous work. For the case where the solute is eluted at like gradient, we derived the expression that connects the mobile phase composition (phiR), at which the solute is eluted from the column, with the gradient slope (B). It was shown that phiR will increase with the increase of B in this case. For the case where the solute is eluted at the last isocratic segment of the ladder-like gradient, it was proven that the retention time (tR) will correlate linearly with the reciprocal of the gradient slope (1/B) when the initial and final mobile phase compositions are set to be constant. In experiments, by taking biphenyl as the sample, the values of retention time in isocratic and gradient elution were measured on a C18 column by using a mixture of methanol and water as the mobile phase. The experimental values were found to be well consistent with the theoretical values that were calculated from the expressions. These expressions will be helpful to understand the features of the ladder-like gradient in practice.

Filtering Airborne LIDAR Data by AN Improved Morphological Method Based on Multi-Gradient Analysis

NASA Astrophysics Data System (ADS)

Li, Y.

2013-05-01

The technology of airborne Light Detection And Ranging (LIDAR) is capable of acquiring dense and accurate 3D geospatial data. Although many related efforts have been made by a lot of researchers in the last few years, LIDAR data filtering is still a challenging task, especially for area with high relief or hybrid geographic features. In order to address the bare-ground extraction from LIDAR point clouds of complex landscapes, a novel morphological filtering algorithm is proposed based on multi-gradient analysis in terms of the characteristic of LIDAR data distribution in this paper. Firstly, point clouds are organized by an index mesh. Then, the multigradient of each point is calculated using the morphological method. And, objects are removed gradually by choosing some points to carry on an improved opening operation constrained by multi-gradient iteratively. 15 sample data provided by ISPRS Working Group III/3 are employed to test the filtering algorithm proposed. These sample data include those environments that may lead to filtering difficulty. Experimental results show that filtering algorithm proposed by this paper is of high adaptability to various scenes including urban and rural areas. Omission error, commission error and total error can be simultaneously controlled in a relatively small interval. This algorithm can efficiently remove object points while preserves ground points to a great degree.

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Tangborn, Andrew; Auger, Ludovic

2003-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Gradient Learning Algorithms for Ontology Computing

PubMed Central

Gao, Wei; Zhu, Linli

2014-01-01

The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting. PMID:25530752

Compensating for magnetic field inhomogeneity in multigradient-echo-based MR thermometry.

PubMed

Simonis, Frank F J; Petersen, Esben T; Bartels, Lambertus W; Lagendijk, Jan J W; van den Berg, Cornelis A T

2015-03-01

MR thermometry (MRT) is a noninvasive method for measuring temperature that can potentially be used for radio frequency (RF) safety monitoring. This application requires measuring absolute temperature. In this study, a multigradient-echo (mGE) MRT sequence was used for that purpose. A drawback of this sequence, however, is that its accuracy is affected by background gradients. In this article, we present a method to minimize this effect and to improve absolute temperature measurements using MRI. By determining background gradients using a B0 map or by combining data acquired with two opposing readout directions, the error can be removed in a homogenous phantom, thus improving temperature maps. All scans were performed on a 3T system using ethylene glycol-filled phantoms. Background gradients were varied, and one phantom was uniformly heated to validate both compensation approaches. Independent temperature recordings were made with optical probes. Errors correlated closely to the background gradients in all experiments. Temperature distributions showed a much smaller standard deviation when the corrections were applied (0.21°C vs. 0.45°C) and correlated well with thermo-optical probes. The corrections offer the possibility to measure RF heating in phantoms more precisely. This allows mGE MRT to become a valuable tool in RF safety assessment. © 2014 Wiley Periodicals, Inc.

Using the full tensor of GOCE gravity gradients for regional gravity field modelling

NASA Astrophysics Data System (ADS)

Lieb, Verena; Bouman, Johannes; Dettmering, Denise; Fuchs, Martin; Schmidt, Michael

2013-04-01

With its 3-axis gradiometer GOCE delivers 3-dimensional (3D) information of the Earth's gravity field. This essential advantage - e.g. compared with the 1D gravity field information from GRACE - can be used for research on the Earth's interior and for geophysical exploration. To benefit from this multidimensional measurement system, the combination of all 6 GOCE gradients and additionally the consistent combination with other gravity observations mean an innovative challenge for regional gravity field modelling. As the individual gravity gradients reflect the gravity field depending on different spatial directions, observation equations are formulated separately for each of these components. In our approach we use spherical localizing base functions to display the gravity field for specified regions. Therefore the series expansions based on Legendre polynomials have to be adopted to obtain mathematical expressions for the second derivatives of the gravitational potential which are observed by GOCE in the Cartesian Gradiometer Reference Frame (GRF). We (1) have to transform the equations from the spherical terrestrial into a Cartesian Local North-Oriented Reference Frame (LNOF), (2) to set up a 3x3 tensor of observation equations and (3) finally to rotate the tensor defined in the terrestrial LNOF into the GRF. Thus we ensure the use of the original non-rotated and unaffected GOCE measurements within the analysis procedure. As output from the synthesis procedure we then obtain the second derivatives of the gravitational potential for all combinations of the xyz Cartesian coordinates in the LNOF. Further the implementation of variance component estimation provides a flexible tool to diversify the influence of the input gradiometer observations. On the one hand the less accurate xy and yz measurements are nearly excluded by estimating large variance components. On the other hand the yy measurements, which show systematic errors increasing at high latitudes, could be manually down-weighted in the corresponding regions. We choose different test areas to compute regional gravity field models at mean GOCE altitudes for different spectral resolutions and varying relative weights for the observations. Further we compare the regional models with the static global GOCO03S model. Especially the flexible handling and combination of the 3D measurements promise a great benefit for geophysical applications from GOCE gravity gradients, as they contain information on radial as well as on lateral gravity changes.

Reduction of shading-derived artifacts in skin chromophore imaging without measurements or assumptions about the shape of the subject

NASA Astrophysics Data System (ADS)

Yoshida, Kenichiro; Nishidate, Izumi; Ojima, Nobutoshi; Iwata, Kayoko

2014-01-01

To quantitatively evaluate skin chromophores over a wide region of curved skin surface, we propose an approach that suppresses the effect of the shading-derived error in the reflectance on the estimation of chromophore concentrations, without sacrificing the accuracy of that estimation. In our method, we use multiple regression analysis, assuming the absorbance spectrum as the response variable and the extinction coefficients of melanin, oxygenated hemoglobin, and deoxygenated hemoglobin as the predictor variables. The concentrations of melanin and total hemoglobin are determined from the multiple regression coefficients using compensation formulae (CF) based on the diffuse reflectance spectra derived from a Monte Carlo simulation. To suppress the shading-derived error, we investigated three different combinations of multiple regression coefficients for the CF. In vivo measurements with the forearm skin demonstrated that the proposed approach can reduce the estimation errors that are due to shading-derived errors in the reflectance. With the best combination of multiple regression coefficients, we estimated that the ratio of the error to the chromophore concentrations is about 10%. The proposed method does not require any measurements or assumptions about the shape of the subjects; this is an advantage over other studies related to the reduction of shading-derived errors.

Prostate Localization on Daily Cone-Beam Computed Tomography Images: Accuracy Assessment of Similarity Metrics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jinkoo, E-mail: jkim3@hfhs.or; Hammoud, Rabih; Pradhan, Deepak

2010-07-15

Purpose: To evaluate different similarity metrics (SM) using natural calcifications and observation-based measures to determine the most accurate prostate and seminal vesicle localization on daily cone-beam CT (CBCT) images. Methods and Materials: CBCT images of 29 patients were retrospectively analyzed; 14 patients with prostate calcifications (calcification data set) and 15 patients without calcifications (no-calcification data set). Three groups of test registrations were performed. Test 1: 70 CT/CBCT pairs from calcification dataset were registered using 17 SMs (6,580 registrations) and compared using the calcification mismatch error as an endpoint. Test 2: Using the four best SMs from Test 1, 75 CT/CBCTmore » pairs in the no-calcification data set were registered (300 registrations). Accuracy of contour overlays was ranked visually. Test 3: For the best SM from Tests 1 and 2, accuracy was estimated using 356 CT/CBCT registrations. Additionally, target expansion margins were investigated for generating registration regions of interest. Results: Test 1-Incremental sign correlation (ISC), gradient correlation (GC), gradient difference (GD), and normalized cross correlation (NCC) showed the smallest errors ({mu} {+-} {sigma}: 1.6 {+-} 0.9 {approx} 2.9 {+-} 2.1 mm). Test 2-Two of the three reviewers ranked GC higher. Test 3-Using GC, 96% of registrations showed <3-mm error when calcifications were filtered. Errors were left/right: 0.1 {+-} 0.5mm, anterior/posterior: 0.8 {+-} 1.0mm, and superior/inferior: 0.5 {+-} 1.1 mm. The existence of calcifications increased the success rate to 97%. Expansion margins of 4-10 mm were equally successful. Conclusion: Gradient-based SMs were most accurate. Estimated error was found to be <3 mm (1.1 mm SD) in 96% of the registrations. Results suggest that the contour expansion margin should be no less than 4 mm.« less

SAGE: The Self-Adaptive Grid Code. 3

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1999-01-01

The multi-dimensional self-adaptive grid code, SAGE, is an important tool in the field of computational fluid dynamics (CFD). It provides an efficient method to improve the accuracy of flow solutions while simultaneously reducing computer processing time. Briefly, SAGE enhances an initial computational grid by redistributing the mesh points into more appropriate locations. The movement of these points is driven by an equal-error-distribution algorithm that utilizes the relationship between high flow gradients and excessive solution errors. The method also provides a balance between clustering points in the high gradient regions and maintaining the smoothness and continuity of the adapted grid, The latest version, Version 3, includes the ability to change the boundaries of a given grid to more efficiently enclose flow structures and provides alternative redistribution algorithms.

Lateral velocity estimation bias due to beamforming delay errors (Conference Presentation)

NASA Astrophysics Data System (ADS)

Rodriguez-Molares, Alfonso; Fadnes, Solveig; Swillens, Abigail; Løvstakken, Lasse

2017-03-01

An artefact has recently been reported [1,2] in the estimation of the lateral blood velocity using speckle tracking. This artefact shows as a net velocity bias in presence of strong spatial velocity gradients such as those that occur at the edges of the filling jets in the heart. Even though this artifact has been found both in vitro and in simulated data, its causes are still undescribed. Here we demonstrate that a potential source of this artefact can be traced to smaller errors in the beamforming setup. By inserting a small offset in the beamforming delay, one can artificially create a net lateral movement in the speckle in areas of high velocity gradient. That offset does not have a strong impact in the image quality and can easily go undetected.

First-order approximation error analysis of Risley-prism-based beam directing system.

PubMed

Zhao, Yanyan; Yuan, Yan

2014-12-01

To improve the performance of a Risley-prism system for optical detection and measuring applications, it is necessary to be able to determine the direction of the outgoing beam with high accuracy. In previous works, error sources and their impact on the performance of the Risley-prism system have been analyzed, but their numerical approximation accuracy was not high. Besides, pointing error analysis of the Risley-prism system has provided results for the case when the component errors, prism orientation errors, and assembly errors are certain. In this work, the prototype of a Risley-prism system was designed. The first-order approximations of the error analysis were derived and compared with the exact results. The directing errors of a Risley-prism system associated with wedge-angle errors, prism mounting errors, and bearing assembly errors were analyzed based on the exact formula and the first-order approximation. The comparisons indicated that our first-order approximation is accurate. In addition, the combined errors produced by the wedge-angle errors and mounting errors of the two prisms together were derived and in both cases were proved to be the sum of errors caused by the first and the second prism separately. Based on these results, the system error of our prototype was estimated. The derived formulas can be implemented to evaluate beam directing errors of any Risley-prism beam directing system with a similar configuration.

A search for stability gradients in North American breeding bird communities

USGS Publications Warehouse

Noon, B.R.; Dawson, D.K.; Kelly, J.P.

1985-01-01

To search for the existence of stability gradients in North American breeding land bird communities we operationally defined stability (after Jarvinen 1979) as year-to-year persistence in species composition and distribution of species abundances. From the census data for 174 study plots we derived nine indices that estimate the annual variability of species composition, the species abundance distribution, diversity, and breeding density. The resulting matrix of study plot by stability indices was used to estimate the correlation structure of the stability indices. The correlation matrix was, in turn, subjected to a principal components analysis to derive synthetic gradients of variation. We then searched for patterns of variation in these stability gradients associated with either geographic location or habitat type. Three independent principal component axes reproduced most of the variation in the initial data and were interpreted as gradients of variation in species turnover, diversity, and breeding abundance. Thus, the annual stability of community structure apparently responds independently to species and abundance variation. Despite the clarity of the derived gradients, few patterns emerged when the plots were ordinated by either habitat or geographic location. In general, grasslands showed greater annual variation in diversity than forested habitats, and, for some habitats, northern communities were less stable than more southern communities. However, few of these patterns were very strong, and we interpret them cautiously.

Correlational approach to study interactions between dust Brownian particles in a plasma

NASA Astrophysics Data System (ADS)

Lisin, E. A.; Vaulina, O. S.; Petrov, O. F.

2018-01-01

A general approach to the correlational analysis of Brownian motion of strongly coupled particles in open dissipative systems is described. This approach can be applied to the theoretical description of various non-ideal statistically equilibrium systems (including non-Hamiltonian systems), as well as for the analysis of experimental data. In this paper, we consider an application of the correlational approach to the problem of experimental exploring the wake-mediated nonreciprocal interactions in complex plasmas. We derive simple analytic equations, which allows one to calculate the gradients of forces acting on a microparticle due to each of other particles as well as the gradients of external field, knowing only the information on time-averaged correlations of particles displacements and velocities. We show the importance of taking dissipative and random processes into account, without which consideration of a system with a nonreciprocal interparticle interaction as linearly coupled oscillators leads to significant errors in determining the characteristic frequencies in a system. In the examples of numerical simulations, we demonstrate that the proposed original approach could be an effective instrument in exploring the longitudinal wake structure of a microparticle in a plasma. Unlike the previous attempts to study the wake-mediated interactions in complex plasmas, our method does not require any external perturbations and is based on Brownian motion analysis only.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

PubMed

Qin, Shanlin; Liu, Fawang; Turner, Ian W; Yu, Qiang; Yang, Qianqian; Vegh, Viktor

2017-04-01

To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Fast higher-order MR image reconstruction using singular-vector separation.

PubMed

Wilm, Bertram J; Barmet, Christoph; Pruessmann, Klaas P

2012-07-01

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Distance error correction for time-of-flight cameras

NASA Astrophysics Data System (ADS)

Fuersattel, Peter; Schaller, Christian; Maier, Andreas; Riess, Christian

2017-06-01

The measurement accuracy of time-of-flight cameras is limited due to properties of the scene and systematic errors. These errors can accumulate to multiple centimeters which may limit the applicability of these range sensors. In the past, different approaches have been proposed for improving the accuracy of these cameras. In this work, we propose a new method that improves two important aspects of the range calibration. First, we propose a new checkerboard which is augmented by a gray-level gradient. With this addition it becomes possible to capture the calibration features for intrinsic and distance calibration at the same time. The gradient strip allows to acquire a large amount of distance measurements for different surface reflectivities, which results in more meaningful training data. Second, we present multiple new features which are used as input to a random forest regressor. By using random regression forests, we circumvent the problem of finding an accurate model for the measurement error. During application, a correction value for each individual pixel is estimated with the trained forest based on a specifically tailored feature vector. With our approach the measurement error can be reduced by more than 40% for the Mesa SR4000 and by more than 30% for the Microsoft Kinect V2. In our evaluation we also investigate the impact of the individual forest parameters and illustrate the importance of the individual features.

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients.

PubMed

Jin, Shuo; Li, Dengwang; Wang, Hongjun; Yin, Yong

2013-01-07

Accurate registration of 18F-FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from (18)F-FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information-based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application.

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients

PubMed Central

Jin, Shuo; Li, Dengwang; Yin, Yong

2013-01-01

Accurate registration of  18F−FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from  18F−FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information‐based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application. PACS numbers: 87.57.nj, 87.57.Q‐, 87.57.uk PMID:23318381

Toward development of mobile application for hand arthritis screening.

PubMed

Akhbardeh, Farhad; Vasefi, Fartash; Tavakolian, Kouhyar; Bradley, David; Fazel-Rezai, Reza

2015-01-01

Arthritis is one of the most common health problems affecting people throughout the world. The goal of the work presented in this paper is to provide individuals, who may be developing or have developed arthritis, with a mobile application to assess and monitor the progress of their disease using their smartphone. The image processing algorithm includes finger border detection algorithm to monitor joint thickness and angular deviation abnormalities, which are common symptoms of arthritis. In this work, we have analyzed and compared gradient, thresholding and Canny algorithms for border detection. The effect of image spatial resolution (down-sampling) is also investigated. The results calculated based on 36 joint measurements show that the mean errors for gradient, thresholding, and Canny methods are 0.20, 2.13, and 2.03 mm, respectively. In addition, the average error for different image resolutions is analyzed and the minimum required resolution is determined for each method. The results confirm that recent smartphone imaging capabilities can provide enough accuracy for hand border detection and finger joint analysis based on gradient method.

Effective Inertial Frame in an Atom Interferometric Test of the Equivalence Principle

NASA Astrophysics Data System (ADS)

Overstreet, Chris; Asenbaum, Peter; Kovachy, Tim; Notermans, Remy; Hogan, Jason M.; Kasevich, Mark A.

2018-05-01

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δ g /g ≈6 ×10-11 per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 1 013 , these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

NASA Astrophysics Data System (ADS)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Control of Complex Dynamic Systems by Neural Networks

NASA Technical Reports Server (NTRS)

Spall, James C.; Cristion, John A.

1993-01-01

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Non-invasive assessment of pulsatile intracranial pressure with phase-contrast magnetic resonance imaging

PubMed Central

Lindstrøm, Erika Kristina; Vatnehol, Svein Are Sirirud; Mardal, Kent-André; Emblem, Kyrre Eeg; Eide, Per Kristian

2017-01-01

Invasive monitoring of pulsatile intracranial pressure can accurately predict shunt response in patients with idiopathic normal pressure hydrocephalus, but may potentially cause complications such as bleeding and infection. We tested how a proposed surrogate parameter for pulsatile intracranial pressure, the phase-contrast magnetic resonance imaging derived pulse pressure gradient, compared with its invasive counterpart. In 22 patients with suspected idiopathic normal pressure hydrocephalus, preceding invasive intracranial pressure monitoring, and any surgical shunt procedure, we calculated the pulse pressure gradient from phase-contrast magnetic resonance imaging derived cerebrospinal fluid flow velocities obtained at the upper cervical spinal canal using a simplified Navier-Stokes equation. Repeated measurements of the pulse pressure gradient were also undertaken in four healthy controls. Of 17 shunted patients, 16 responded, indicating high proportion of “true” normal pressure hydrocephalus in the patient cohort. However, there was no correlation between the magnetic resonance imaging derived pulse pressure gradient and pulsatile intracranial pressure (R = -.18, P = .43). Pulse pressure gradients were also similar in patients and healthy controls (P = .26), and did not differ between individuals with pulsatile intracranial pressure above or below established thresholds for shunt treatment (P = .97). Assessment of pulse pressure gradient at level C2 was therefore not found feasible to replace invasive monitoring of pulsatile intracranial pressure in selection of patients with idiopathic normal pressure hydrocephalus for surgical shunting. Unlike invasive, overnight monitoring, the pulse pressure gradient from magnetic resonance imaging comprises short-term pressure fluctuations only. Moreover, complexity of cervical cerebrospinal fluid flow and -pulsatility at the upper cervical spinal canal may render the pulse pressure gradient a poor surrogate marker for intracranial pressure pulsations. PMID:29190788

Non-invasive assessment of pulsatile intracranial pressure with phase-contrast magnetic resonance imaging.

PubMed

Ringstad, Geir; Lindstrøm, Erika Kristina; Vatnehol, Svein Are Sirirud; Mardal, Kent-André; Emblem, Kyrre Eeg; Eide, Per Kristian

2017-01-01

Invasive monitoring of pulsatile intracranial pressure can accurately predict shunt response in patients with idiopathic normal pressure hydrocephalus, but may potentially cause complications such as bleeding and infection. We tested how a proposed surrogate parameter for pulsatile intracranial pressure, the phase-contrast magnetic resonance imaging derived pulse pressure gradient, compared with its invasive counterpart. In 22 patients with suspected idiopathic normal pressure hydrocephalus, preceding invasive intracranial pressure monitoring, and any surgical shunt procedure, we calculated the pulse pressure gradient from phase-contrast magnetic resonance imaging derived cerebrospinal fluid flow velocities obtained at the upper cervical spinal canal using a simplified Navier-Stokes equation. Repeated measurements of the pulse pressure gradient were also undertaken in four healthy controls. Of 17 shunted patients, 16 responded, indicating high proportion of "true" normal pressure hydrocephalus in the patient cohort. However, there was no correlation between the magnetic resonance imaging derived pulse pressure gradient and pulsatile intracranial pressure (R = -.18, P = .43). Pulse pressure gradients were also similar in patients and healthy controls (P = .26), and did not differ between individuals with pulsatile intracranial pressure above or below established thresholds for shunt treatment (P = .97). Assessment of pulse pressure gradient at level C2 was therefore not found feasible to replace invasive monitoring of pulsatile intracranial pressure in selection of patients with idiopathic normal pressure hydrocephalus for surgical shunting. Unlike invasive, overnight monitoring, the pulse pressure gradient from magnetic resonance imaging comprises short-term pressure fluctuations only. Moreover, complexity of cervical cerebrospinal fluid flow and -pulsatility at the upper cervical spinal canal may render the pulse pressure gradient a poor surrogate marker for intracranial pressure pulsations.

Toward an improved determination of Earth's lithospheric magnetic field from satellite observations

NASA Astrophysics Data System (ADS)

Kotsiaros, S.

2016-12-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into Γ(1) = {[∇B]rθ,[∇B]rφ} resp. Γ(2) = {[∇B]θθ-[∇B]φφ, 2[∇B]θφ}. It is shown that the estimated combinations Γ(1) and Γ(2) produce similar signal content as the theoretical radial gradient [∇B]rr. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations Γ(1) and Γ(2) and compared with models derived from traditional vector and gradient data. The model resulting from Γ(1) leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e. a full set of vector, North-South and East-West gradients. ReferencesRummel, R., and M. van Gelderen (1992), Spectral analysis of the full gravity tensor, Geophysical Journal International, 111 (1), 159-169.

Displacement fields from point cloud data: Application of particle imaging velocimetry to landslide geodesy

USGS Publications Warehouse

Aryal, Arjun; Brooks, Benjamin A.; Reid, Mark E.; Bawden, Gerald W.; Pawlak, Geno

2012-01-01

Acquiring spatially continuous ground-surface displacement fields from Terrestrial Laser Scanners (TLS) will allow better understanding of the physical processes governing landslide motion at detailed spatial and temporal scales. Problems arise, however, when estimating continuous displacement fields from TLS point-clouds because reflecting points from sequential scans of moving ground are not defined uniquely, thus repeat TLS surveys typically do not track individual reflectors. Here, we implemented the cross-correlation-based Particle Image Velocimetry (PIV) method to derive a surface deformation field using TLS point-cloud data. We estimated associated errors using the shape of the cross-correlation function and tested the method's performance with synthetic displacements applied to a TLS point cloud. We applied the method to the toe of the episodically active Cleveland Corral Landslide in northern California using TLS data acquired in June 2005–January 2007 and January–May 2010. Estimated displacements ranged from decimeters to several meters and they agreed well with independent measurements at better than 9% root mean squared (RMS) error. For each of the time periods, the method provided a smooth, nearly continuous displacement field that coincides with independently mapped boundaries of the slide and permits further kinematic and mechanical inference. For the 2010 data set, for instance, the PIV-derived displacement field identified a diffuse zone of displacement that preceded by over a month the development of a new lateral shear zone. Additionally, the upslope and downslope displacement gradients delineated by the dense PIV field elucidated the non-rigid behavior of the slide.

The Dropout Learning Algorithm

PubMed Central

Baldi, Pierre; Sadowski, Peter

2014-01-01

Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations. PMID:24771879

The SFR-M∗ main sequence archetypal star-formation history and analytical models

NASA Astrophysics Data System (ADS)

Ciesla, L.; Elbaz, D.; Fensch, J.

2017-12-01

The star-formation history (SFH) of galaxies is a key assumption to derive their physical properties and can lead to strong biases. In this work, we derive the SFH of main sequence (MS) galaxies and show how the peak SFH of a galaxy depends on its seed mass at, for example, z = 5. This seed mass reflects the galaxy's underlying dark matter (DM) halo environment. We show that, following the MS, galaxies undergo a drastic slow down of their stellar mass growth after reaching the peak of their SFH. According to abundance matching, these masses correspond to hot and massive DM halos which state could result in less efficient gas inflows on the galaxies and thus could be the origin of limited stellar mass growth. As a result, we show that galaxies, still on the MS, can enter the passive region of the UVJ diagram while still forming stars. The best fit to the MS SFH is provided by a right skew peak function for which we provide parameters depending on the seed mass of the galaxy. The ability of the classical analytical SFHs to retrieve the star-formation rate (SFR) of galaxies from spectral energy distribution (SED) fitting is studied. Due to mathematical limitations, the exponentially declining and delayed SFH struggle to model high SFR, which starts to be problematic at z > 2. The exponentially rising and log-normal SFHs exhibit the opposite behavior with the ability to reach very high SFR, and thus model starburst galaxies, but they are not able to model low values such as those expected at low redshift for massive galaxies. By simulating galaxies SED from the MS SFH, we show that these four analytical forms recover the SFR of MS galaxies with an error dependent on the model and the redshift. They are, however, sensitive enough to probe small variations of SFR within the MS, with an error ranging from 5 to 40% depending on the SFH assumption and redshift; but all the four fail to recover the SFR of rapidly quenched galaxies. However, these SFHs lead to an artificial gradient of age, parallel to the MS, which is not exhibited by the simulated sample. This gradient is also produced on real data as we show using a sample of real galaxies with redshifts between 1.5 and 2.5. Here, we propose an SFH composed of a delayed form to model the bulk of stellar population with the addition of a flexibility in the recent SFH. This SFH provides very good estimates of the SFR of MS, starbursts, and rapidly quenched galaxies at all redshift. Furthermore, when used on the real sample, the age gradient disappears which show its dependency on the SFH assumption made to perform the SED fitting.

Theoretical analysis on the measurement errors of local 2D DIC: Part I temporal and spatial uncertainty quantification of displacement measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yueqi; Lava, Pascal; Reu, Phillip

This study presents a theoretical uncertainty quantification of displacement measurements by subset-based 2D-digital image correlation. A generalized solution to estimate the random error of displacement measurement is presented. The obtained solution suggests that the random error of displacement measurements is determined by the image noise, the summation of the intensity gradient in a subset, the subpixel part of displacement, and the interpolation scheme. The proposed method is validated with virtual digital image correlation tests.

Theoretical analysis on the measurement errors of local 2D DIC: Part I temporal and spatial uncertainty quantification of displacement measurements

DOE PAGES

Wang, Yueqi; Lava, Pascal; Reu, Phillip; ...

2015-12-23

This study presents a theoretical uncertainty quantification of displacement measurements by subset-based 2D-digital image correlation. A generalized solution to estimate the random error of displacement measurement is presented. The obtained solution suggests that the random error of displacement measurements is determined by the image noise, the summation of the intensity gradient in a subset, the subpixel part of displacement, and the interpolation scheme. The proposed method is validated with virtual digital image correlation tests.

Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data

NASA Technical Reports Server (NTRS)

Gottlieb, Robert G.

1993-01-01

Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.

A simple ecohydrological model captures essentials of seasonal leaf dynamics in semi-arid tropical grasslands

NASA Astrophysics Data System (ADS)

Choler, P.; Sea, W.; Briggs, P.; Raupach, M.; Leuning, R.

2009-09-01

Modelling leaf phenology in water-controlled ecosystems remains a difficult task because of high spatial and temporal variability in the interaction of plant growth and soil moisture. Here, we move beyond widely used linear models to examine the performance of low-dimensional, nonlinear ecohydrological models that couple the dynamics of plant cover and soil moisture. The study area encompasses 400 000 km2 of semi-arid perennial tropical grasslands, dominated by C4 grasses, in the Northern Territory and Queensland (Australia). We prepared 8 yr time series (2001-2008) of climatic variables and estimates of fractional vegetation cover derived from MODIS Normalized Difference Vegetation Index (NDVI) for 400 randomly chosen sites, of which 25% were used for model calibration and 75% for model validation. We found that the mean absolute error of linear and nonlinear models did not markedly differ. However, nonlinear models presented key advantages: (1) they exhibited far less systematic error than their linear counterparts; (2) their error magnitude was consistent throughout a precipitation gradient while the performance of linear models deteriorated at the driest sites, and (3) they better captured the sharp transitions in leaf cover that are observed under high seasonality of precipitation. Our results showed that low-dimensional models including feedbacks between soil water balance and plant growth adequately predict leaf dynamics in semi-arid perennial grasslands. Because these models attempt to capture fundamental ecohydrological processes, they should be the favoured approach for prognostic models of phenology.

A simple ecohydrological model captures essentials of seasonal leaf dynamics in semi-arid tropical grasslands

NASA Astrophysics Data System (ADS)

Choler, P.; Sea, W.; Briggs, P.; Raupach, M.; Leuning, R.

2010-03-01

Modelling leaf phenology in water-controlled ecosystems remains a difficult task because of high spatial and temporal variability in the interaction of plant growth and soil moisture. Here, we move beyond widely used linear models to examine the performance of low-dimensional, nonlinear ecohydrological models that couple the dynamics of plant cover and soil moisture. The study area encompasses 400 000 km2 of semi-arid perennial tropical grasslands, dominated by C4 grasses, in the Northern Territory and Queensland (Australia). We prepared 8-year time series (2001-2008) of climatic variables and estimates of fractional vegetation cover derived from MODIS Normalized Difference Vegetation Index (NDVI) for 400 randomly chosen sites, of which 25% were used for model calibration and 75% for model validation. We found that the mean absolute error of linear and nonlinear models did not markedly differ. However, nonlinear models presented key advantages: (1) they exhibited far less systematic error than their linear counterparts; (2) their error magnitude was consistent throughout a precipitation gradient while the performance of linear models deteriorated at the driest sites, and (3) they better captured the sharp transitions in leaf cover that are observed under high seasonality of precipitation. Our results showed that low-dimensional models including feedbacks between soil water balance and plant growth adequately predict leaf dynamics in semi-arid perennial grasslands. Because these models attempt to capture fundamental ecohydrological processes, they should be the favoured approach for prognostic models of phenology.

Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

NASA Astrophysics Data System (ADS)

Katsoulakis, Markos A.; Vlachos, Dionisios G.

2003-11-01

We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.

On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study.

PubMed

Michael, J Robert; Koritsanszky, Tibor

2017-05-28

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study

NASA Astrophysics Data System (ADS)

Michael, J. Robert; Koritsanszky, Tibor

2017-05-01

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

Microwave and physical properties of sea ice in the winter marginal ice zone

NASA Technical Reports Server (NTRS)

Tucker, W. B., III; Perovich, D. K.; Gow, A. J.; Grenfell, T. C.; Onstott, R. G.

1991-01-01

Surface-based active and passive microwave measurements were made in conjunction with ice property measurements for several distinct ice types in the Fram Strait during March and April 1987. Synthesis aperture radar imagery downlinked from an aircraft was used to select study sites. The surface-based radar scattering cross section and emissivity spectra generally support previously inferred qualitative relationships between ice types, exhibiting expected separation between young, first-year and multiyear ice. Gradient ratios, calculated for both active and passive data, appear to allow clear separation of ice types when used jointly. Surface flooding of multiyear floes, resulting from excessive loading and perhaps wave action, causes both active and passive signatures to resemble those of first-year ice. This effect could possibly cause estimates of ice type percentages in the marginal ice zone to be in error when derived from aircraft- or satellite-born sensors.

Case studies using GOES infrared data and a planetary boundary layer model to infer regional scale variations in soil moisture. M.S. Thesis

NASA Technical Reports Server (NTRS)

Rose, F. G.

1983-01-01

Modeled temperature data from a one-dimensional, time-dependent, initial value, planetary boundary layer model for 16 separate model runs with varying initial values of moisture availability are applied, by the use of a regression equation, to longwave infrared GOES satellite data to infer moisture availability over a regional area in the central U.S. This was done for several days during the summers of 1978 and 1980 where a large gradient in the antecedent precipitation index (API) represented the boundary between a drought area and a region of near normal precipitation. Correlations between satellite derived moisture availability and API were found to exist. Errors from the presence of clouds, water vapor and other spatial inhomogeneities made the use of the measurement for anything except the relative degree of moisture availability dubious.

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas

We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 methodmore » and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.« less

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

NASA Technical Reports Server (NTRS)

Long, S. A. T.

1974-01-01

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Comment on ``Turbulent equipartition theory of toroidal momentum pinch'' [Phys. Plasmas 15, 055902 (2008)

NASA Astrophysics Data System (ADS)

Peeters, A. G.; Angioni, C.; Strintzi, D.

2009-03-01

The comment addresses questions raised on the derivation of the momentum pinch velocity due to the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)]. These concern the definition of the gradient, and the scaling with the density gradient length. It will be shown that the turbulent equipartition mechanism is included within the derivation using the Coriolis drift, with the density gradient scaling being the consequence of drift terms not considered in [T. S. Hahm et al., Phys. Plasmas 15, 055902 (2008)]. Finally the accuracy of the analytic models is assessed through a comparison with the full gyrokinetic solution.

Gradient descent learning algorithm overview: a general dynamical systems perspective.

PubMed

Baldi, P

1995-01-01

Gives a unified treatment of gradient descent learning algorithms for neural networks using a general framework of dynamical systems. This general approach organizes and simplifies all the known algorithms and results which have been originally derived for different problems (fixed point/trajectory learning), for different models (discrete/continuous), for different architectures (forward/recurrent), and using different techniques (backpropagation, variational calculus, adjoint methods, etc.). The general approach can also be applied to derive new algorithms. The author then briefly examines some of the complexity issues and limitations intrinsic to gradient descent learning. Throughout the paper, the author focuses on the problem of trajectory learning.

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

A model-assisted radio occultation data inversion method based on data ingestion into NeQuick

NASA Astrophysics Data System (ADS)

Shaikh, M. M.; Nava, B.; Kashcheyev, A.

2017-01-01

Inverse Abel transform is the most common method to invert radio occultation (RO) data in the ionosphere and it is based on the assumption of the spherical symmetry for the electron density distribution in the vicinity of an occultation event. It is understood that this 'spherical symmetry hypothesis' could fail, above all, in the presence of strong horizontal electron density gradients. As a consequence, in some cases wrong electron density profiles could be obtained. In this work, in order to incorporate the knowledge of horizontal gradients, we have suggested an inversion technique based on the adaption of the empirical ionospheric model, NeQuick2, to RO-derived TEC. The method relies on the minimization of a cost function involving experimental and model-derived TEC data to determine NeQuick2 input parameters (effective local ionization parameters) at specific locations and times. These parameters are then used to obtain the electron density profile along the tangent point (TP) positions associated with the relevant RO event using NeQuick2. The main focus of our research has been laid on the mitigation of spherical symmetry effects from RO data inversion without using external data such as data from global ionospheric maps (GIM). By using RO data from Constellation Observing System for Meteorology Ionosphere and Climate (FORMOSAT-3/COSMIC) mission and manually scaled peak density data from a network of ionosondes along Asian and American longitudinal sectors, we have obtained a global improvement of 5% with 7% in Asian longitudinal sector (considering the data used in this work), in the retrieval of peak electron density (NmF2) with model-assisted inversion as compared to the Abel inversion. Mean errors of NmF2 in Asian longitudinal sector are calculated to be much higher compared to American sector.

Modeling energy flow and nutrient cycling in natural semiarid grassland ecosystems with the aid of thematic mapper data

NASA Technical Reports Server (NTRS)

Lewis, James K.

1987-01-01

Energy flow and nutrient cycling were modeled as affected by herbivory on selected intensive sites along gradients of precipitation and soils, validating the model output by monitoring selected parameters with data derived from the Thematic Mapper (TM). Herbivore production was modeled along the gradient of soils and herbivory, and validated with data derived from TM in a spatial data base.

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

Processing the image gradient field using a topographic primal sketch approach.

PubMed

Gambaruto, A M

2015-03-01

The spatial derivatives of the image intensity provide topographic information that may be used to identify and segment objects. The accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution. This paper focuses on accurate computation of spatial derivatives and their subsequent use to process an image gradient field directly, from which an image with improved characteristics can be reconstructed. The improvements include noise reduction, contrast enhancement, thinning object contours and the preservation of edges. Processing the gradient field directly instead of the image is shown to have numerous benefits. The approach is developed such that the steps are modular, allowing the overall method to be improved and possibly tailored to different applications. As presented, the approach relies on a topographic representation and primal sketch of an image. Comparisons with existing image processing methods on a synthetic image and different medical images show improved results and accuracy in segmentation. Here, the focus is on objects with low spatial resolution, which is often the case in medical images. The methods developed show the importance of improved accuracy in derivative calculation and the potential in processing the image gradient field directly. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Detection of ferromagnetic target based on mobile magnetic gradient tensor system

NASA Astrophysics Data System (ADS)

Gang, Y. I. N.; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

2016-03-01

Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source-sensor displacement vector. Secondly, unit source-sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source-sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source-sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source-sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

PubMed

Pan, Zhao; Whitehead, Jared; Thomson, Scott; Truscott, Tadd

2016-08-01

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Atmospheric gradients from very long baseline interferometry observations

NASA Technical Reports Server (NTRS)

Macmillan, D. S.

1995-01-01

Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Daily average gradient effects can be as large as 50 mm of delay at a 7 deg elevation. To model gradients, the constrained estimation of gradient paramters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990-1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990-1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties.

Integral Field Spectroscopy Surveys: Oxygen Abundance Gradients

NASA Astrophysics Data System (ADS)

Sánchez, S. F.; Sánchez-Menguiano, L.

2017-07-01

We present here the recent results on our understanding of oxygen abundance gradients derived using Integral Field Spectroscopic surveys. In particular we analyzed more than 2124 datacubes corresponding to individual objects observed by the CALIFA (˜ 734 objects) and the public data by MaNGA (˜ 1390 objects), deriving the oxygen abundance gradient for each galaxy. We confirm previous results that indicate that the shape of this gradient is very similar for all galaxies with masses above 109.5M⊙, presenting in average a very similar slope of ˜ -0.04 dex within 0.5-2.0 re, with a possible drop in the inner regions (r<0.5re) and a flattennig in the outer regions. For lower masses (>109.5M⊙) the gradient seems to be flatter than for more massive ones. All these results agree with an inside-out growth of massive galaxies and indicate that low mass ones may still be growing in an outside in phase.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

PubMed

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

PubMed

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Errores fotométricos debido al uso del filtro anular de mediana en imágenes CCD

NASA Astrophysics Data System (ADS)

Gil-Hutton, R.; Cañada, M.; Noel, N.

El filtro anular de mediana tiene la importante propiedad de tener una escala claramente definida, lo que permite remover de una imagen CCD todos los objetos con tamaños menores a esta escala, independientemente de su morfología particular, y reemplazarlos por el correspondiente ``background" local. Este filtro es de gran utilidad para remover gradientes de fondo, ``fringing" y halos de objetos extendidos mediante el simple procedimiento de restar a la imagen original una imagen filtrada, repitiendo el proceso las veces que sea necesario. En este trabajo se presentan resultados sobre los errores que introduce este filtro en la fotometría de objetos con diferente relación S/N y su aplicación a imágenes con gradientes de fondo y ``fringing".

Puzzles in modern biology. V. Why are genomes overwired?

PubMed

Frank, Steven A

2017-01-01

Many factors affect eukaryotic gene expression. Transcription factors, histone codes, DNA folding, and noncoding RNA modulate expression. Those factors interact in large, broadly connected regulatory control networks. An engineer following classical principles of control theory would design a simpler regulatory network. Why are genomes overwired? Neutrality or enhanced robustness may lead to the accumulation of additional factors that complicate network architecture. Dynamics progresses like a ratchet. New factors get added. Genomes adapt to the additional complexity. The newly added factors can no longer be removed without significant loss of fitness. Alternatively, highly wired genomes may be more malleable. In large networks, most genomic variants tend to have a relatively small effect on gene expression and trait values. Many small effects lead to a smooth gradient, in which traits may change steadily with respect to underlying regulatory changes. A smooth gradient may provide a continuous path from a starting point up to the highest peak of performance. A potential path of increasing performance promotes adaptability and learning. Genomes gain by the inductive process of natural selection, a trial and error learning algorithm that discovers general solutions for adapting to environmental challenge. Similarly, deeply and densely connected computational networks gain by various inductive trial and error learning procedures, in which the networks learn to reduce the errors in sequential trials. Overwiring alters the geometry of induction by smoothing the gradient along the inductive pathways of improving performance. Those overwiring benefits for induction apply to both natural biological networks and artificial deep learning networks.

Can partial coherence interferometry be used to determine retinal shape?

PubMed

Atchison, David A; Charman, W Neil

2011-05-01

To determine likely errors in estimating retinal shape using partial coherence interferometric instruments when no allowance is made for optical distortion. Errors were estimated using Gullstrand no. 1 schematic eye and variants which included a 10 diopter (D) axial myopic eye, an emmetropic eye with a gradient-index lens, and a 10.9 D accommodating eye with a gradient-index lens. Performance was simulated for two commercial instruments, the IOLMaster (Carl Zeiss Meditec) and the Lenstar LS 900 (Haag-Streit AG). The incident beam was directed toward either the center of curvature of the anterior cornea (corneal-direction method) or the center of the entrance pupil (pupil-direction method). Simple trigonometry was used with the corneal intercept and the incident beam angle to estimate retinal contour. Conics were fitted to the estimated contours. The pupil-direction method gave estimates of retinal contour that were much too flat. The cornea-direction method gave similar results for IOLMaster and Lenstar approaches. The steepness of the retinal contour was slightly overestimated, the exact effects varying with the refractive error, gradient index, and accommodation. These theoretical results suggest that, for field angles ≤30°, partial coherence interferometric instruments are of use in estimating retinal shape by the corneal-direction method with the assumptions of a regular retinal shape and no optical distortion. It may be possible to improve on these estimates out to larger field angles by using optical modeling to correct for distortion.

Retrieval of Water Vapor Anisotropy using the Japanese Nationwide GPS Array and its Potential for Monitoring of Convective Precipitation

NASA Astrophysics Data System (ADS)

Shoji, Y.

2012-12-01

Procedures for retrieving two indices indicating the degree of anisotropy of water vapor using the carrier phase of a Global Positioning System (GPS) are introduced. One index describes the spatial concentration of water vapor; the other indicates higher-order water vapor inhomogeneity. GPS analysis can provide more atmospheric information than just PWV. Following MacMillan (1995), the slant path delay (SPD) between a GPS satellite and a receiver at the elevation angle θ and direction angle φ can be written in the following form: SPD(θ,φ)=m(θ)[ZTD+cotθ(Gncosφ+Gesinφ)]+ɛ, where ɛ is postfit residual. The postfit residuals contain information on higher-order atmospheric inhomogeneity (HI). However, other errors that do not originate from the atmosphere are also included (e.g., antenna phase center variation (PCV), signal scattering, multipath, and satellite orbit errors). Therefore, in order to estimate SPD accurately, it is necessary to remove all errors not due to atmospheric inhomogeneity. Shoji et al. (2004) demonstrated that the horizontal scale of the ZTD can be considered as about 600 km, the gradient component (Gn and Ge) as 60 km, and the HI as 2 to 3 km. This result insists that ZTD, Gn and Ge, and HI relate to atmospheric motion of the meso- , meso- , and meso- scales, respectively. The fact allows us defining two new atmospheric indices from GPS SPD as: (1) Water vapor concentration (WVC) index Inner product of nabla operator and gradient vector (Gn and Ge) (2) Water vapor inhomogeneity (WVI) index Standard deviation of ɛ after removing non-atmospheric noises The characteristics of the water vapor field over Japan in August 2011 were studied using the temporal-spatial variation in the two indices along with GPS-derived precipitable water vapor (PWV). The monthly averaged indices indicate distinct diurnal variation in the mountainous region of central Honshu and coincidence with the diurnal variation in precipitation frequencies in the area. The relationships between these indices and precipitation were examined statistically. The results indicate that the anisotropy indices are more strongly correlated with strong rainfall than PWV, whereas PWV seems to be related to weak and/or modest precipitation. These relations hold true for both present and upcoming precipitation. The spatial-temporal variation in the indices for a thunderstorm on 11 August 2011 was also examined. Both water vapor concentration and higher-order inhomogeneity showed an increase ahead of the initiation of convective precipitation. The results suggest that the two GPS-derived indices of water vapor anisotropy reflect local variation in water vapor associated with convection phenomena and can be potentially used for the monitoring of thunderstorms.

Improved Remote Sensing Retrieval of Land Surface Temperature in the Thermal Infrared (TIR) Using Visible/Short Wave Infrared (VSWIR) Imaging Spectrometer Estimated Water Vapor

NASA Astrophysics Data System (ADS)

Grigsby, S.; Hulley, G. C.; Roberts, D. A.; Scheele, C. J.; Ustin, S.; Alsina, M. M.

2014-12-01

Land surface temperature (LST) is an important parameter in many ecological studies, where processes such as evapotranspiration have impacts at temperature gradients less than 1 K. Current errors in standard MODIS and ASTER LST products are greater than 1 K, and for ASTER can be greater than 2 K in humid conditions due to incomplete atmospheric correction of atmospheric water vapor. Estimates of water vapor, either derived from visible-to-shortwave-infrared (VSWIR) remote sensing data or taken from weather simulation data such as NCEP, can be combined with coincident Thermal-Infrared (TIR) remote sensing data to yield improved accuracy in LST measurements. This study compares LST retrieval accuracies derived using the standard JPL MASTER Temperature Emissivity Separation (TES) algorithm, and the Water Vapor Scaling (WVS) atmospheric correction method proposed for the Hyperspectral Infrared Imager, or HyspIRI, mission with ground observations. The 2011 ER-2 Delano/Lost Hills flights acquired TIR data from the MODIS/ASTER Simulator (MASTER) and VSWIR data from Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) instruments flown concurrently. The TES and WVS retrieval methods are run with and without high spatial resolution AVIRIS-derived water vapor maps to assess the improvement using VSWIR water vapor estimates. We find improvement using VSWIR derived water vapor maps in both cases, with the WVS method being most accurate overall. For closed canopy agricultural vegetation we observed canopy temperature retrieval RMSEs of 0.49 K and 0.70 K using the WVS method on MASTER data with and without AVIRIS derived water vapor, respectively.

Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

PubMed

Bozkaya, Uğur

2018-03-15

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Integrating ecosystem sampling, gradient modeling, remote sensing, and ecosystem simulation to create spatially explicit landscape inventories

Treesearch

Robert E. Keane; Matthew G. Rollins; Cecilia H. McNicoll; Russell A. Parsons

2002-01-01

Presented is a prototype of the Landscape Ecosystem Inventory System (LEIS), a system for creating maps of important landscape characteristics for natural resource planning. This system uses gradient-based field inventories coupled with gradient modeling remote sensing, ecosystem simulation, and statistical analyses to derive spatial data layers required for ecosystem...

WE-AB-BRA-01: 3D-2D Image Registration for Target Localization in Spine Surgery: Comparison of Similarity Metrics Against Robustness to Content Mismatch

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Silva, T; Ketcha, M; Siewerdsen, J H

Purpose: In image-guided spine surgery, mapping 3D preoperative images to 2D intraoperative images via 3D-2D registration can provide valuable assistance in target localization. However, the presence of surgical instrumentation, hardware implants, and soft-tissue resection/displacement causes mismatches in image content, confounding existing registration methods. Manual/semi-automatic methods to mask such extraneous content is time consuming, user-dependent, error prone, and disruptive to clinical workflow. We developed and evaluated 2 novel similarity metrics within a robust registration framework to overcome such challenges in target localization. Methods: An IRB-approved retrospective study in 19 spine surgery patients included 19 preoperative 3D CT images and 50 intraoperativemore » mobile radiographs in cervical, thoracic, and lumbar spine regions. A neuroradiologist provided truth definition of vertebral positions in CT and radiography. 3D-2D registration was performed using the CMA-ES optimizer with 4 gradient-based image similarity metrics: (1) gradient information (GI); (2) gradient correlation (GC); (3) a novel variant referred to as gradient orientation (GO); and (4) a second variant referred to as truncated gradient correlation (TGC). Registration accuracy was evaluated in terms of the projection distance error (PDE) of the vertebral levels. Results: Conventional similarity metrics were susceptible to gross registration error and failure modes associated with the presence of surgical instrumentation: for GI, the median PDE and interquartile range was 33.0±43.6 mm; similarly for GC, PDE = 23.0±92.6 mm respectively. The robust metrics GO and TGC, on the other hand, demonstrated major improvement in PDE (7.6 ±9.4 mm and 8.1± 18.1 mm, respectively) and elimination of gross failure modes. Conclusion: The proposed GO and TGC similarity measures improve registration accuracy and robustness to gross failure in the presence of strong image content mismatch. Such registration capability could offer valuable assistance in target localization without disruption of clinical workflow. G. Kleinszig and S. Vogt are employees of Siemens Healthcare.« less

Metallicity gradients in local field star-forming galaxies: insights on inflows, outflows, and the coevolution of gas, stars and metals

NASA Astrophysics Data System (ADS)

Ho, I.-Ting; Kudritzki, Rolf-Peter; Kewley, Lisa J.; Zahid, H. Jabran; Dopita, Michael A.; Bresolin, Fabio; Rupke, David S. N.

2015-04-01

We present metallicity gradients in 49 local field star-forming galaxies. We derive gas-phase oxygen abundances using two widely adopted metallicity calibrations based on the [O III]/Hβ, [N II]/Hα, and [N II]/[O II] line ratios. The two derived metallicity gradients are usually in good agreement within ± 0.14 dex R_{25}^{-1} (R25 is the B-band iso-photoal radius), but the metallicity gradients can differ significantly when the ionization parameters change systematically with radius. We investigate the metallicity gradients as a function of stellar mass (8 < log (M*/M⊙) < 11) and absolute B-band luminosity (-16 > MB > -22). When the metallicity gradients are expressed in dex kpc-1, we show that galaxies with lower mass and luminosity, on average, have steeper metallicity gradients. When the metallicity gradients are expressed in dex R_{25}^{-1}, we find no correlation between the metallicity gradients, and stellar mass and luminosity. We provide a local benchmark metallicity gradient of field star-forming galaxies useful for comparison with studies at high redshifts. We investigate the origin of the local benchmark gradient using simple chemical evolution models and observed gas and stellar surface density profiles in nearby field spiral galaxies. Our models suggest that the local benchmark gradient is a direct result of the coevolution of gas and stellar disc under virtually closed-box chemical evolution when the stellar-to-gas mass ratio becomes high (≫0.3). These models imply low current mass accretion rates ( ≲ 0.3 × SFR), and low-mass outflow rates ( ≲ 3 × SFR) in local field star-forming galaxies.

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

NASA Astrophysics Data System (ADS)

Chen, Yue; Cunningham, Gregory; Henderson, Michael

2016-09-01

This study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Second, using a newly developed proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ˜ 2°, than those from the three empirical models with averaged errors > ˜ 5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. This study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

DOE PAGES

Chen, Yue; Cunningham, Gregory; Henderson, Michael

2016-09-21

Our study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Furthermore, using a newly developedmore » proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ~2°, than those from the three empirical models with averaged errors > ~5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. Finally, this study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.« less

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yue; Cunningham, Gregory; Henderson, Michael

Our study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Furthermore, using a newly developedmore » proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ~2°, than those from the three empirical models with averaged errors > ~5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. Finally, this study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.« less

A Comparison of Four Indices for Combining Distance and Dose Differences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomas, Simon J., E-mail: simon.thomas@addenbrookes.nhs.uk; Cowley, Ian R.

2012-04-01

Purpose: When one is comparing two dose distributions, a number of methods have been published to combine dose difference and distance to agreement into a single measure. Some have been defined as pass/fail indices and some as numeric indices. We show that the pass/fail indices can all be used to derive numeric indices, and we compare the results of using these indices to evaluate one-dimensional (1D) and three-dimensional (3D) dose distributions, with the aim of selecting the most appropriate index for use in different circumstances. Methods and Materials: The indices compared are the gamma index, the kappa index, the indexmore » in International Commission on Radiation Units and Measurements Report 83, and a box index. Comparisons are made for 1D and 3D distributions. The 1D distribution is chosen to have a variety of dose gradients. The 3D distribution is taken from a clinical treatment plan. The effect of offsetting distributions by known distances and doses is studied. Results: The International Commission on Radiation Units and Measurements Report 83 index causes large discontinuities unless the dose gradient cutoff is set to equal the ratio of the dose tolerance to the distance tolerance. If it is so set, it returns identical results to the kappa index. Where the gradient is very high or very low, all the indices studied in this article give similar results for the same tolerance values. For moderate gradients, they differ, with the box index being the least strict, followed by the gamma index, and with the kappa index being the most strict. Conclusions: If the clinical tolerances are much greater than the uncertainties of the measuring system, the kappa index should be used, with tolerance values determined by the clinical tolerances. In cases where the uncertainties of the measuring system dominate, the box index will be best able to determine errors in the delivery system.« less

Satellite gravity gradient grids for geophysics

PubMed Central

Bouman, Johannes; Ebbing, Jörg; Fuchs, Martin; Sebera, Josef; Lieb, Verena; Szwillus, Wolfgang; Haagmans, Roger; Novak, Pavel

2016-01-01

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite aimed at determining the Earth’s mean gravity field. GOCE delivered gravity gradients containing directional information, which are complicated to use because of their error characteristics and because they are given in a rotating instrument frame indirectly related to the Earth. We compute gravity gradients in grids at 225 km and 255 km altitude above the reference ellipsoid corresponding to the GOCE nominal and lower orbit phases respectively, and find that the grids may contain additional high-frequency content compared with GOCE-based global models. We discuss the gradient sensitivity for crustal depth slices using a 3D lithospheric model of the North-East Atlantic region, which shows that the depth sensitivity differs from gradient to gradient. In addition, the relative signal power for the individual gradient component changes comparing the 225 km and 255 km grids, implying that using all components at different heights reduces parameter uncertainties in geophysical modelling. Furthermore, since gravity gradients contain complementary information to gravity, we foresee the use of the grids in a wide range of applications from lithospheric modelling to studies on dynamic topography, and glacial isostatic adjustment, to bedrock geometry determination under ice sheets. PMID:26864314

M Dwarfs from Hubble Space Telescope Star Counts. IV.

NASA Astrophysics Data System (ADS)

Zheng, Zheng; Flynn, Chris; Gould, Andrew; Bahcall, John N.; Salim, Samir

2001-07-01

We study a sample of about 1400 disk M dwarfs that are found in 148 fields observed with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and 162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 of the WFC2 fields are newly analyzed. The method of maximum likelihood is applied to derive the luminosity function and the Galactic disk parameters. At first, we use a local color-magnitude relation and a locally determined mass-luminosity relation in our analysis. The results are consistent with those of previous work but with considerably reduced statistical errors. These small statistical errors motivate us to investigate the systematic uncertainties. Considering the metallicity gradient above the Galactic plane, we introduce a modified color-magnitude relation that is a function of Galactic height. The resultant M dwarf luminosity function has a shape similar to that derived using the local color-magnitude relation but with a higher peak value. The peak occurs at MV~12, and the luminosity function drops sharply toward MV~14. We then apply a height-dependent mass-luminosity function interpolated from theoretical models with different metallicities to calculate the mass function. Unlike the mass function obtained using local relations, which has a power-law index α=0.47, the one derived from the height-dependent relations tends to be flat (α=-0.10). The resultant local surface density of disk M dwarfs (12.2+/-1.6 Msolar pc-2) is somewhat smaller than the one obtained using local relations (14.3+/-1.3 Msolar pc-2). Our measurement favors a short disk scale length, H=2.75+/-0.16 (statistical)+/-0.25 (systematic) kpc. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

Instabilities in mimetic matter perturbations

NASA Astrophysics Data System (ADS)

Firouzjahi, Hassan; Gorji, Mohammad Ali; Mansoori, Seyed Ali Hosseini

2017-07-01

We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

Atmospheric gradients from GNSS, VLBI, and DORIS analyses and from Numerical Weather Models during CONT14

NASA Astrophysics Data System (ADS)

Heinkelmann, Robert; Dick, Galina; Nilsson, Tobias; Soja, Benedikt; Wickert, Jens; Zus, Florian; Schuh, Harald

2015-04-01

Observations from space-geodetic techniques are nowadays increasingly used to derive atmospheric information for various commercial and scientific applications. A prominent example is the operational use of GNSS data to improve global and regional weather forecasts, which was started in 2006. Atmosphere gradients describe the azimuthal asymmetry of zenith delays. Estimates of geodetic and other parameters significantly improve when atmosphere gradients are determined in addition. Here we assess the capability of several space geodetic techniques (GNSS, VLBI, DORIS) to determine atmosphere gradients of refractivity. For this purpose we implement and compare various strategies for gradient estimation, such as different values for the temporal resolution and the corresponding parameter constraints. Applying least squares estimation the gradients are usually deterministically modelled as constants or piece-wise linear functions. In our study we compare this approach with a stochastic approach modelling atmosphere gradients as random walk processes and applying a Kalman Filter for parameter estimation. The gradients, derived from space geodetic techniques are verified by comparison with those derived from Numerical Weather Models (NWM). These model data were generated using raytracing calculations based on European Centre for Medium-Range Weather Forecast (ECMWF) and National Centers for Environmental Prediction (NCEP) analyses with different spatial resolutions. The investigation of the differences between the ECMWF and NCEP gradients hereby in addition allow for an empirical assessment of the quality of model gradients and how suitable the NWM data are for verification. CONT14 (2014-05-06 until 2014-05-20) is the youngest two week long continuous VLBI campaign carried out by IVS (International VLBI Service for Geodesy and Astrometry). It presents the state-of-the-art VLBI performance in terms of number of stations and number of observations and presents thus an excellent test period for comparisons with other space geodetic techniques. During the VLBI campaign CONT14 the HOBART12 and HOBART26 (Hobart, Tasmania, Australia) VLBI antennas were involved that co-locate with each other. The investigation of the gradient estimate differences from these co-located antennas allows for a valuable empirical quality assessment. Another quality criterion for gradient estimates are the differences of parameters at the borders of adjacent 24h-sessions. Both are investigated in our study.

Performance of local optimization in single-plane fluoroscopic analysis for total knee arthroplasty.

PubMed

Prins, A H; Kaptein, B L; Stoel, B C; Lahaye, D J P; Valstar, E R

2015-11-05

Fluoroscopy-derived joint kinematics plays an important role in the evaluation of knee prostheses. Fluoroscopic analysis requires estimation of the 3D prosthesis pose from its 2D silhouette in the fluoroscopic image, by optimizing a dissimilarity measure. Currently, extensive user-interaction is needed, which makes analysis labor-intensive and operator-dependent. The aim of this study was to review five optimization methods for 3D pose estimation and to assess their performance in finding the correct solution. Two derivative-free optimizers (DHSAnn and IIPM) and three gradient-based optimizers (LevMar, DoNLP2 and IpOpt) were evaluated. For the latter three optimizers two different implementations were evaluated: one with a numerically approximated gradient and one with an analytically derived gradient for computational efficiency. On phantom data, all methods were able to find the 3D pose within 1mm and 1° in more than 85% of cases. IpOpt had the highest success-rate: 97%. On clinical data, the success rates were higher than 85% for the in-plane positions, but not for the rotations. IpOpt was the most expensive method and the application of an analytically derived gradients accelerated the gradient-based methods by a factor 3-4 without any differences in success rate. In conclusion, 85% of the frames can be analyzed automatically in clinical data and only 15% of the frames require manual supervision. The optimal success-rate on phantom data (97% with IpOpt) on phantom data indicates that even less supervision may become feasible. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adaptive Flight Control Design with Optimal Control Modification on an F-18 Aircraft Model

NASA Technical Reports Server (NTRS)

Burken, John J.; Nguyen, Nhan T.; Griffin, Brian J.

2010-01-01

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to as the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly; however, a large adaptive gain can lead to high-frequency oscillations which can adversely affect the robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient robustness. A damping term (v) is added in the modification to increase damping as needed. Simulations were conducted on a damaged F-18 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) with both the standard baseline dynamic inversion controller and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model.

Fisher classifier and its probability of error estimation

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

Computationally efficient expressions are derived for estimating the probability of error using the leave-one-out method. The optimal threshold for the classification of patterns projected onto Fisher's direction is derived. A simple generalization of the Fisher classifier to multiple classes is presented. Computational expressions are developed for estimating the probability of error of the multiclass Fisher classifier.

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Limitations of Dower's inverse transform for the study of atrial loops during atrial fibrillation.

PubMed

Guillem, María S; Climent, Andreu M; Bollmann, Andreas; Husser, Daniela; Millet, José; Castells, Francisco

2009-08-01

Spatial characteristics of atrial fibrillatory waves have been extracted by using a vectorcardiogram (VCG) during atrial fibrillation (AF). However, the VCG is usually not recorded in clinical practice and atrial loops are derived from the 12-lead electrocardiogram (ECG). We evaluated the suitability of the reconstruction of orthogonal leads from the 12-lead ECG for fibrillatory waves in AF. We used the Physikalisch-Technische Bundesanstalt diagnostic ECG database, which contains 15 simultaneously recorded signals (12-lead ECG and three Frank orthogonal leads) of 13 patients during AF. Frank leads were derived from the 12-lead ECG by using Dower's inverse transform. Derived leads were then compared to true Frank leads in terms of the relative error achieved. We calculated the orientation of AF loops of both recorded orthogonal leads and derived leads and measured the difference in estimated orientation. Also, we investigated the relationship of errors in derivation with fibrillatory wave amplitude, frequency, wave residuum, and fit to a plane of the AF loops. Errors in derivation of AF loops were 68 +/- 31% and errors in the estimation of orientation were 35.85 +/- 20.43 degrees . We did not find any correlation among these errors and amplitude, frequency, or other parameters. In conclusion, Dower's inverse transform should not be used for the derivation of orthogonal leads from the 12-lead ECG for the analysis of fibrillatory wave loops in AF. Spatial parameters obtained after this derivation may differ from those obtained from recorded orthogonal leads.

Flight Investigation of Prescribed Simultaneous Independent Surface Excitations for Real-Time Parameter Identification

NASA Technical Reports Server (NTRS)

Moes, Timothy R.; Smith, Mark S.; Morelli, Eugene A.

2003-01-01

Near real-time stability and control derivative extraction is required to support flight demonstration of Intelligent Flight Control System (IFCS) concepts being developed by NASA, academia, and industry. Traditionally, flight maneuvers would be designed and flown to obtain stability and control derivative estimates using a postflight analysis technique. The goal of the IFCS concept is to be able to modify the control laws in real time for an aircraft that has been damaged in flight. In some IFCS implementations, real-time parameter identification (PID) of the stability and control derivatives of the damaged aircraft is necessary for successfully reconfiguring the control system. This report investigates the usefulness of Prescribed Simultaneous Independent Surface Excitations (PreSISE) to provide data for rapidly obtaining estimates of the stability and control derivatives. Flight test data were analyzed using both equation-error and output-error PID techniques. The equation-error PID technique is known as Fourier Transform Regression (FTR) and is a frequency-domain real-time implementation. Selected results were compared with a time-domain output-error technique. The real-time equation-error technique combined with the PreSISE maneuvers provided excellent derivative estimation in the longitudinal axis. However, the PreSISE maneuvers as presently defined were not adequate for accurate estimation of the lateral-directional derivatives.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

NASA Astrophysics Data System (ADS)

Qamar, Anisa; Ata-ur-Rahman, Mirza, Arshad M.

2012-05-01

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

A Requirements-Driven Optimization Method for Acoustic Liners Using Analytic Derivatives

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.; Lopes, Leonard V.

2017-01-01

More than ever, there is flexibility and freedom in acoustic liner design. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. In a previous paper on this subject, a method deriving the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground was described. A simple code-wrapping approach was used to evaluate a community noise objective function for an external optimizer. Gradients were evaluated using a finite difference formula. The subject of this paper is an application of analytic derivatives that supply precise gradients to an optimization process. Analytic derivatives improve the efficiency and accuracy of gradient-based optimization methods and allow consideration of more design variables. In addition, the benefit of variable impedance liners is explored using a multi-objective optimization.

Advances and Limitations of Atmospheric Boundary Layer Observations with GPS Occultation over Southeast Pacific Ocean

NASA Technical Reports Server (NTRS)

Xie, F.; Wu, D. L.; Ao, C. O.; Mannucci, A. J.; Kursinski, E. R.

2012-01-01

The typical atmospheric boundary layer (ABL) over the southeast (SE) Pacific Ocean is featured with a strong temperature inversion and a sharp moisture gradient across the ABL top. The strong moisture and temperature gradients result in a sharp refractivity gradient that can be precisely detected by the Global Positioning System (GPS) radio occultation (RO) measurements. In this paper, the Constellation Observing System for Meteorology, Ionosphere & Climate (COSMIC) GPS RO soundings, radiosondes and the high-resolution ECMWF analysis over the SE Pacific are analyzed. COSMIC RO is able to detect a wide range of ABL height variations (1-2 kilometer) as observed from the radiosondes. However, the ECMWF analysis systematically underestimates the ABL heights. The sharp refractivity gradient at the ABL top frequently exceeds the critical refraction (e.g., -157 N-unit per kilometer) and becomes the so-called ducting condition, which results in a systematic RO refractivity bias (or called N-bias) inside the ABL. Simulation study based on radiosonde profiles reveals the magnitudes of the N-biases are vertical resolution dependent. The N-bias is also the primary cause of the systematically smaller refractivity gradient (rarely exceeding -110 N-unit per kilometer) at the ABL top from RO measurement. However, the N-bias seems not affect the ABL height detection. Instead, the very large RO bending angle and the sharp refractivity gradient due to ducting allow reliable detection of the ABL height from GPS RO. The seasonal mean climatology of ABL heights derived from a nine-month composite of COSMIC RO soundings over the SE Pacific reveals significant differences from the ECMWF analysis. Both show an increase of ABL height from the shallow stratocumulus near the coast to a much higher trade wind inversion further off the coast. However, COSMIC RO shows an overall deeper ABL and reveals different locations of the minimum and maximum ABL heights as compared to the ECMWF analysis. At low latitudes, despite the decreasing number of COSMIC RO soundings and the lower percentage of soundings that penetrate into the lowest 500-m above the mean-sea-level, there are small sampling errors in the mean ABL height climatology. The difference of ABL height climatology between COSMIC RO and ECMWF analysis over SE Pacific is significant and requires further studies.

Regional evapotranspiration from an image-based implementation of the Surface Temperature Initiated Closure (STIC1.2) model and its validation across an aridity gradient in the conterminous US

NASA Astrophysics Data System (ADS)

Bhattarai, Nishan; Mallick, Kaniska; Brunsell, Nathaniel A.; Sun, Ge; Jain, Meha

2018-04-01

Recent studies have highlighted the need for improved characterizations of aerodynamic conductance and temperature (gA and T0) in thermal remote-sensing-based surface energy balance (SEB) models to reduce uncertainties in regional-scale evapotranspiration (ET) mapping. By integrating radiometric surface temperature (TR) into the Penman-Monteith (PM) equation and finding analytical solutions of gA and T0, this need was recently addressed by the Surface Temperature Initiated Closure (STIC) model. However, previous implementations of STIC were confined to the ecosystem-scale using flux tower observations of infrared temperature. This study demonstrates the first regional-scale implementation of the most recent version of the STIC model (STIC1.2) that integrates the Moderate Resolution Imaging Spectroradiometer (MODIS) derived TR and ancillary land surface variables in conjunction with NLDAS (North American Land Data Assimilation System) atmospheric variables into a combined structure of the PM and Shuttleworth-Wallace (SW) framework for estimating ET at 1 km × 1 km spatial resolution. Evaluation of STIC1.2 at 13 core AmeriFlux sites covering a broad spectrum of climates and biomes across an aridity gradient in the conterminous US suggests that STIC1.2 can provide spatially explicit ET maps with reliable accuracies from dry to wet extremes. When observed ET from one wet, one dry, and one normal precipitation year from all sites were combined, STIC1.2 explained 66 % of the variability in observed 8-day cumulative ET with a root mean square error (RMSE) of 7.4 mm/8-day, mean absolute error (MAE) of 5 mm/8-day, and percent bias (PBIAS) of -4 %. These error statistics showed relatively better accuracies than a widely used but previous version of the SEB-based Surface Energy Balance System (SEBS) model, which utilized a simple NDVI-based parameterization of surface roughness (zOM), and the PM-based MOD16 ET. SEBS was found to overestimate (PBIAS = 28 %) and MOD16 was found to underestimate ET (PBIAS = -26 %). The performance of STIC1.2 was better in forest and grassland ecosystems as compared to cropland (20 % underestimation) and woody savanna (40 % overestimation). Model inter-comparison suggested that ET differences between the models are robustly correlated with gA and associated roughness length estimation uncertainties which are intrinsically connected to TR uncertainties, vapor pressure deficit (DA), and vegetation cover. A consistent performance of STIC1.2 in a broad range of hydrological and biome categories, as well as the capacity to capture spatio-temporal ET signatures across an aridity gradient, points to the potential for this simplified analytical model for near-real-time ET mapping from regional to continental scales.

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

PubMed

Petrenko, Taras; Kossmann, Simone; Neese, Frank

2011-02-07

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.

Concentration gradient induced morphology evolution of silica nanostructure growth on photoresist-derived carbon micropatterns

NASA Astrophysics Data System (ADS)

Liu, Dan; Shi, Tielin; Xi, Shuang; Lai, Wuxing; Liu, Shiyuan; Li, Xiaoping; Tang, Zirong

2012-09-01

The evolution of silica nanostructure morphology induced by local Si vapor source concentration gradient has been investigated by a smart design of experiments. Silica nanostructure or their assemblies with different morphologies are obtained on photoresist-derived three-dimensional carbon microelectrode array. At a temperature of 1,000°C, rope-, feather-, and octopus-like nanowire assemblies can be obtained along with the Si vapor source concentration gradient flow. While at 950°C, stringlike assemblies, bamboo-like nanostructures with large joints, and hollow structures with smaller sizes can be obtained along with the Si vapor source concentration gradient flow. Both vapor-liquid-solid and vapor-quasiliquid-solid growth mechanisms have been applied to explain the diverse morphologies involving branching, connecting, and batch growth behaviors. The present approach offers a potential method for precise design and controlled synthesis of nanostructures with different features.

On the effect of velocity gradients on the depth of correlation in μPIV

NASA Astrophysics Data System (ADS)

Mustin, B.; Stoeber, B.

2016-03-01

The present work revisits the effect of velocity gradients on the depth of the measurement volume (depth of correlation) in microscopic particle image velocimetry (μPIV). General relations between the μPIV weighting functions and the local correlation function are derived from the original definition of the weighting functions. These relations are used to investigate under which circumstances the weighting functions are related to the curvature of the local correlation function. Furthermore, this work proposes a modified definition of the depth of correlation that leads to more realistic results than previous definitions for the case when flow gradients are taken into account. Dimensionless parameters suitable to describe the effect of velocity gradients on μPIV cross correlation are derived and visual interpretations of these parameters are proposed. We then investigate the effect of the dimensionless parameters on the weighting functions and the depth of correlation for different flow fields with spatially constant flow gradients and with spatially varying gradients. Finally this work demonstrates that the results and dimensionless parameters are not strictly bound to a certain model for particle image intensity distributions but are also meaningful when other models for particle images are used.

Adaptive spectral filtering of PIV cross correlations

NASA Astrophysics Data System (ADS)

Giarra, Matthew; Vlachos, Pavlos; Aether Lab Team

2016-11-01

Using cross correlations (CCs) in particle image velocimetry (PIV) assumes that tracer particles in interrogation regions (IRs) move with the same velocity. But this assumption is nearly always violated because real flows exhibit velocity gradients, which degrade the signal-to-noise ratio (SNR) of the CC and are a major driver of error in PIV. Iterative methods help reduce these errors, but even they can fail when gradients are large within individual IRs. We present an algorithm to mitigate the effects of velocity gradients on PIV measurements. Our algorithm is based on a model of the CC, which predicts a relationship between the PDF of particle displacements and the variation of the correlation's SNR across the Fourier spectrum. We give an algorithm to measure this SNR from the CC, and use this insight to create a filter that suppresses the low-SNR portions of the spectrum. Our algorithm extends to the ensemble correlation, where it accelerates the convergence of the measurement and also reveals the PDF of displacements of the ensemble (and therefore of statistical metrics like diffusion coefficient). Finally, our model provides theoretical foundations for a number of "rules of thumb" in PIV, like the quarter-window rule.

Hydro morphodynamic modelling in Mediterranean storms: errors and uncertainties under sharp gradients

NASA Astrophysics Data System (ADS)

Sánchez-Arcilla, A.; Gracia, V.; García, M.

2014-02-01

This paper deals with the limits in hydrodynamic and morphodynamic predictions for semi-enclosed coastal domains subject to sharp gradients (in bathymetry, topography, sediment transport and coastal damages). It starts with an overview of wave prediction limits (based on satellite images) in a restricted domain such as is the Mediterranean basin, followed by an in-depth analysis of the Catalan coast, one of the land boundaries of such a domain. The morphodynamic modeling for such gradient regions is next illustrated with the simulation of the largest recorded storm in the Catalan coast, whose morphological impact is a key element of the storm impact. The driving wave and surge conditions produce a morphodynamic response that is validated against the pre and post storm beach state, recovered from two LIDAR images. The quality of the fit is discussed in terms of the physical processes and the suitability of the employed modeling equations. Some remarks about the role of the numerical discretization and boundary conditions are also included in the analysis. From here an assessment of errors and uncertainties is presented, with the aim of establishing the prediction limits for coastal engineering flooding and erosion analyses.

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory

PubMed Central

Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM. PMID:29391864

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory.

PubMed

Yang, Haimin; Pan, Zhisong; Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM.

Nurses' Responses and Reactions to an Emergent Pediatric Simulation Exercise.

PubMed

Hoffman, Kenneth; von Sadovszky, Victoria

Pediatric nurses' responses and reactions in emergent simulations are understudied. Using authority gradient theory as a guide, the purpose of this study was to examine nurses' reactions during an emergency simulation exercise when directed to give an incorrect medication dose. Ten groups of noncritical care nurses were videotaped from the beginning of the simulation through debriefing. Although errors were made during the simulation event, all groups responded correctly during debriefing, indicating that authority gradient may play a role in clinical decision-making.

Toward more complete magnetic gradiometry with the Swarm mission

NASA Astrophysics Data System (ADS)

Kotsiaros, Stavros

2016-07-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (Geophys J Int 111(1):159-169, 1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into \\varvec{Γ }^{(1)} = {[\\varvec{nabla } {{B}}]_{rθ },[\\varvec{nabla } {{B}}]_{r\\varphi }} resp. \\varvec{Γ }^{(2)} = {[\\varvec{nabla } {{B}}]_{θ θ }-[\\varvec{nabla } {{B}}]_{\\varphi \\varphi }, 2[\\varvec{nabla } {{B}}]_{θ \\varphi }}. It is shown that the estimated combinations \\varvec{Γ }^{(1)} and \\varvec{Γ }^{(2)} produce similar signal content as the theoretical radial gradient \\varvec{Γ }^{(0)} = {[\\varvec{nabla } {{B}}]_{rr}}. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations \\varvec{Γ }^{(1)} and \\varvec{Γ }^{(2)} and compared with models derived from traditional vector and gradient data. The model resulting from \\varvec{Γ }^{(1)} leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e., a full set of vector, North-South and East-West gradients. This demonstrates the high information content of \\varvec{Γ }^{(1)}.

Errors from approximation of ODE systems with reduced order models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevska, Tanya

2016-12-30

This is a code to calculate the error from approximation of systems of ordinary differential equations (ODEs) by using Proper Orthogonal Decomposition (POD) Reduced Order Models (ROM) methods and to compare and analyze the errors for two POD ROM variants. The first variant is the standard POD ROM, the second variant is a modification of the method using the values of the time derivatives (a.k.a. time-derivative snapshots). The code compares the errors from the two variants under different conditions.

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

NASA Technical Reports Server (NTRS)

Kerr, R. A.

1983-01-01

In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

Wetting of flat gradient surfaces.

PubMed

Bormashenko, Edward

2018-04-01

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed. Copyright © 2018 Elsevier Inc. All rights reserved.

T1 mapping with the variable flip angle technique: A simple correction for insufficient spoiling of transverse magnetization.

PubMed

Baudrexel, Simon; Nöth, Ulrike; Schüre, Jan-Rüdiger; Deichmann, Ralf

2018-06-01

The variable flip angle method derives T 1 maps from radiofrequency-spoiled gradient-echo data sets, acquired with different flip angles α. Because the method assumes validity of the Ernst equation, insufficient spoiling of transverse magnetization yields errors in T 1 estimation, depending on the chosen radiofrequency-spoiling phase increment (Δϕ). This paper presents a versatile correction method that uses modified flip angles α' to restore the validity of the Ernst equation. Spoiled gradient-echo signals were simulated for three commonly used phase increments Δϕ (50°/117°/150°), different values of α, repetition time (TR), T 1 , and a T 2 of 85 ms. For each parameter combination, α' (for which the Ernst equation yielded the same signal) and a correction factor C Δϕ (α, TR, T 1 ) = α'/α were determined. C Δϕ was found to be independent of T 1 and fitted as polynomial C Δϕ (α, TR), allowing to calculate α' for any protocol using this Δϕ. The accuracy of the correction method for T 2 values deviating from 85 ms was also determined. The method was tested in vitro and in vivo for variable flip angle scans with different acquisition parameters. The technique considerably improved the accuracy of variable flip angle-based T 1 maps in vitro and in vivo. The proposed method allows for a simple correction of insufficient spoiling in gradient-echo data. The required polynomial parameters are supplied for three common Δϕ. Magn Reson Med 79:3082-3092, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

NASA Astrophysics Data System (ADS)

Coco, Armando; Russo, Giovanni

2018-05-01

In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

Steer-PROP: a GRASE-PROPELLER sequence with interecho steering gradient pulses.

PubMed

Srinivasan, Girish; Rangwala, Novena; Zhou, Xiaohong Joe

2018-05-01

This study demonstrates a novel PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction) pulse sequence, termed Steer-PROP, based on gradient and spin echo (GRASE), to reduce the imaging times and address phase errors inherent to GRASE. The study also illustrates the feasibility of using Steer-PROP as an alternative to single-shot echo planar imaging (SS-EPI) to produce distortion-free diffusion images in all imaging planes. Steer-PROP uses a series of blip gradient pulses to produce N (N = 3-5) adjacent k-space blades in each repetition time, where N is the number of gradient echoes in a GRASE sequence. This sampling strategy enables a phase correction algorithm to systematically address the GRASE phase errors as well as the motion-induced phase inconsistency. Steer-PROP was evaluated on phantoms and healthy human subjects at both 1.5T and 3.0T for T 2 - and diffusion-weighted imaging. Steer-PROP produced similar image quality as conventional PROPELLER based on fast spin echo (FSE), while taking only a fraction (e.g., 1/3) of the scan time. The robustness against motion in Steer-PROP was comparable to that of FSE-based PROPELLER. Using Steer-PROP, high quality and distortion-free diffusion images were obtained from human subjects in all imaging planes, demonstrating a considerable advantage over SS-EPI. The proposed Steer-PROP sequence can substantially reduce the scan times compared with FSE-based PROPELLER while achieving adequate image quality. The novel k-space sampling strategy in Steer-PROP not only enables an integrated phase correction method that addresses various sources of phase errors, but also minimizes the echo spacing compared with alternative sampling strategies. Steer-PROP can also be a viable alternative to SS-EPI to decrease image distortion in all imaging planes. Magn Reson Med 79:2533-2541, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Gradient ascent pulse engineering approach to CNOT gates in donor electron spin quantum computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, D.-B.; Goan, H.-S.

2008-11-07

In this paper, we demonstrate how gradient ascent pulse engineering (GRAPE) optimal control methods can be implemented on donor electron spin qubits in semiconductors with an architecture complementary to the original Kane's proposal. We focus on the high fidelity controlled-NOT (CNOT) gate and we explicitly find the digitized control sequences for a controlled-NOT gate by optimizing its fidelity using the effective, reduced donor electron spin Hamiltonian with external controls over the hyperfine A and exchange J interactions. We then simulate the CNOT-gate sequence with the full spin Hamiltonian and find that it has an error of 10{sup -6} that ismore » below the error threshold of 10{sup -4} required for fault-tolerant quantum computation. Also the CNOT gate operation time of 100 ns is 3 times faster than 297 ns of the proposed global control scheme.« less

Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Athenodorou, Andreas; Cichy, Krzysztof; Constantinou, Martha; Horkel, Derek P.; Jansen, Karl; Koutsou, Giannis; Larkin, Conor

2018-04-01

We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral-projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cutoff effects. This finally yields a much smaller total error in the spectral-projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.

Effects of myopic spectacle correction and radial refractive gradient spectacles on peripheral refraction.

PubMed

Tabernero, Juan; Vazquez, Daniel; Seidemann, Anne; Uttenweiler, Dietmar; Schaeffel, Frank

2009-08-01

The recent observation that central refractive development might be controlled by the refractive errors in the periphery, also in primates, revived the interest in the peripheral optics of the eye. We optimized an eccentric photorefractor to measure the peripheral refractive error in the vertical pupil meridian over the horizontal visual field (from -45 degrees to 45 degrees ), with and without myopic spectacle correction. Furthermore, a newly designed radial refractive gradient lens (RRG lens) that induces increasing myopia in all radial directions from the center was tested. We found that for the geometry of our measurement setup conventional spectacles induced significant relative hyperopia in the periphery, although its magnitude varied greatly among different spectacle designs and subjects. In contrast, the newly designed RRG lens induced relative peripheral myopia. These results are of interest to analyze the effect that different optical corrections might have on the emmetropization process.

Compressed sensing with gradient total variation for low-dose CBCT reconstruction

NASA Astrophysics Data System (ADS)

Seo, Chang-Woo; Cha, Bo Kyung; Jeon, Seongchae; Huh, Young; Park, Justin C.; Lee, Byeonghun; Baek, Junghee; Kim, Eunyoung

2015-06-01

This paper describes the improvement of convergence speed with gradient total variation (GTV) in compressed sensing (CS) for low-dose cone-beam computed tomography (CBCT) reconstruction. We derive a fast algorithm for the constrained total variation (TV)-based a minimum number of noisy projections. To achieve this task we combine the GTV with a TV-norm regularization term to promote an accelerated sparsity in the X-ray attenuation characteristics of the human body. The GTV is derived from a TV and enforces more efficient computationally and faster in convergence until a desired solution is achieved. The numerical algorithm is simple and derives relatively fast convergence. We apply a gradient projection algorithm that seeks a solution iteratively in the direction of the projected gradient while enforcing a non-negatively of the found solution. In comparison with the Feldkamp, Davis, and Kress (FDK) and conventional TV algorithms, the proposed GTV algorithm showed convergence in ≤18 iterations, whereas the original TV algorithm needs at least 34 iterations in reducing 50% of the projections compared with the FDK algorithm in order to reconstruct the chest phantom images. Future investigation includes improving imaging quality, particularly regarding X-ray cone-beam scatter, and motion artifacts of CBCT reconstruction.

Controls of nitrogen cycling evaluated along a well-characterized climate gradient.

PubMed

von Sperber, Christian; Chadwick, Oliver A; Casciotti, Karen L; Peay, Kabir G; Francis, Christopher A; Kim, Amy E; Vitousek, Peter M

2017-04-01

The supply of nitrogen (N) constrains primary productivity in many ecosystems, raising the question "what controls the availability and cycling of N"? As a step toward answering this question, we evaluated N cycling processes and aspects of their regulation on a climate gradient on Kohala Volcano, Hawaii, USA. The gradient extends from sites receiving <300 mm/yr of rain to those receiving >3,000 mm/yr, and the pedology and dynamics of rock-derived nutrients in soils on the gradient are well understood. In particular, there is a soil process domain at intermediate rainfall within which ongoing weathering and biological uplift have enriched total and available pools of rock-derived nutrients substantially; sites at higher rainfall than this domain are acid and infertile as a consequence of depletion of rock-derived nutrients, while sites at lower rainfall are unproductive and subject to wind erosion. We found elevated rates of potential net N mineralization in the domain where rock-derived nutrients are enriched. Higher-rainfall sites have low rates of potential net N mineralization and high rates of microbial N immobilization, despite relatively high rates of gross N mineralization. Lower-rainfall sites have moderately low potential net N mineralization, relatively low rates of gross N mineralization, and rates of microbial N immobilization sufficient to sequester almost all the mineral N produced. Bulk soil δ 15 N also varied along the gradient, from +4‰ at high rainfall sites to +14‰ at low rainfall sites, indicating differences in the sources and dynamics of soil N. Our analysis shows that there is a strong association between N cycling and soil process domains that are defined using soil characteristics independent of N along this gradient, and that short-term controls of N cycling can be understood in terms of the supply of and demand for N. © 2017 by the Ecological Society of America.

Sea surface velocities from visible and infrared multispectral atmospheric mapping sensor imagery

NASA Technical Reports Server (NTRS)

Pope, P. A.; Emery, W. J.; Radebaugh, M.

1992-01-01

High resolution (100 m), sequential Multispectral Atmospheric Mapping Sensor (MAMS) images were used in a study to calculate advective surface velocities using the Maximum Cross Correlation (MCC) technique. Radiance and brightness temperature gradient magnitude images were formed from visible (0.48 microns) and infrared (11.12 microns) image pairs, respectively, of Chandeleur Sound, which is a shallow body of water northeast of the Mississippi delta, at 145546 GMT and 170701 GMT on 30 Mar. 1989. The gradient magnitude images enhanced the surface water feature boundaries, and a lower cutoff on the gradient magnitudes calculated allowed the undesirable sunglare and backscatter gradients in the visible images, and the water vapor absorption gradients in the infrared images, to be reduced in strength. Requiring high (greater than 0.4) maximum cross correlation coefficients and spatial coherence of the vector field aided in the selection of an optimal template size of 10 x 10 pixels (first image) and search limit of 20 pixels (second image) to use in the MCC technique. Use of these optimum input parameters to the MCC algorithm, and high correlation and spatial coherence filtering of the resulting velocity field from the MCC calculation yielded a clustered velocity distribution over the visible and infrared gradient images. The velocity field calculated from the visible gradient image pair agreed well with a subjective analysis of the motion, but the velocity field from the infrared gradient image pair did not. This was attributed to the changing shapes of the gradient features, their nonuniqueness, and large displacements relative to the mean distance between them. These problems implied a lower repeat time for the imagery was needed in order to improve the velocity field derived from gradient imagery. Suggestions are given for optimizing the repeat time of sequential imagery when using the MCC method for motion studies. Applying the MCC method to the infrared brightness temperature imagery yielded a velocity field which did agree with the subjective analysis of the motion and that derived from the visible gradient imagery. Differences between the visible and infrared derived velocities were 14.9 cm/s in speed and 56.7 degrees in direction. Both of these velocity fields also agreed well with the motion expected from considerations of the ocean bottom topography and wind and tidal forcing in the study area during the 2.175 hour time interval.

Differences in the accommodation stimulus response curves of adult myopes and emmetropes: a summary and update.

PubMed

Schmid, Katrina L; Strang, Niall C

2015-11-01

To provide a summary of the classic paper "Differences in the accommodation stimulus response curves of adult myopes and emmetropes" published in Ophthalmic and Physiological Optics in 1998 and to provide an update on the topic of accommodation errors in myopia. The accommodation responses of 33 participants (10 emmetropes, 11 early onset myopes and 12 late onset myopes) aged 18-31 years were measured using the Canon Autoref R-1 free space autorefractor using three methods to vary the accommodation demand: decreasing distance (4 m to 0.25 cm), negative lenses (0 to -4 D at 4 m) and positive lenses (+4 to 0 D at 0.25 m). We observed that the greatest accommodation errors occurred for the negative lens method whereas minimal errors were observed using positive lenses. Adult progressing myopes had greater lags of accommodation than stable myopes at higher demands induced by negative lenses. Progressing myopes had shallower response gradients than the emmetropes and stable myopes; however the reduced gradient was much less than that observed in children using similar methods. This paper has been often cited as evidence that accommodation responses at near may be primarily reduced in adults with progressing myopia and not in stable myopes and/or that challenging accommodation stimuli (negative lenses with monocular viewing) are required to generate larger accommodation errors. As an analogy, animals reared with hyperopic errors develop axial elongation and myopia. Retinal defocus signals are presumably passed to the retinal pigment epithelium and choroid and then ultimately the sclera to modify eye length. A number of lens treatments that act to slow myopia progression may partially work through reducing accommodation errors. © 2015 The Authors Ophthalmic & Physiological Optics © 2015 The College of Optometrists.

Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

PubMed

He, Wangli; Qian, Feng; Han, Qing-Long; Cao, Jinde

2012-10-01

This paper investigates the problem of master-slave synchronization of two delayed Lur'e systems in the presence of parameter mismatches. First, by analyzing the corresponding synchronization error system, synchronization with an error level, which is referred to as quasi-synchronization, is established. Some delay-dependent quasi-synchronization criteria are derived. An estimation of the synchronization error bound is given, and an explicit expression of error levels is obtained. Second, sufficient conditions on the existence of feedback controllers under a predetermined error level are provided. The controller gains are obtained by solving a set of linear matrix inequalities. Finally, a delayed Chua's circuit is chosen to illustrate the effectiveness of the derived results.

Microfluidic liquid-air dual-gradient chip for synergic effect bio-evaluation of air pollutant.

PubMed

Liu, Xian-Jun; Hu, Shan-Wen; Xu, Bi-Yi; Zhao, Ge; Li, Xiang; Xie, Fu-Wei; Xu, Jing-Juan; Chen, Hong-Yuan

2018-05-15

In this paper, a novel prototype liquid-air dual gradient chip is introduced, which has paved the way for effective synergic effect bio-evaluation of air pollutant. The chip is composed of an array of the agarose liquid-air interfaces, top air gradient layer and bottom liquid gradient layer. The novel agarose liquid-air interface allows for non-biased exposure of cells to all the substances in the air and diffusive interactions with the liquid phase; while the dual liquid-air gradient provides powerful screening abilities, which well reduced errors, saved time and cost from repeated experiment. Coupling the two functions, the chip subsequently facilitates synergic effect evaluation of both liquid and air factors on cells. Here cigarette smoke was taken as the model air pollutant, and its strong synergic effects with inflammatory level of A549 lung cancer cells on their fate were successfully quantified for the first time. These results well testified that the proposed dual-gradient chip is powerful and indispensable for bio-evaluation of air pollutant. Copyright © 2018 Elsevier B.V. All rights reserved.

Monitoring Streambed Scour/Deposition Under Nonideal Temperature Signal and Flood Conditions

NASA Astrophysics Data System (ADS)

DeWeese, Timothy; Tonina, Daniele; Luce, Charles

2017-12-01

Streambed erosion and deposition are fundamental geomorphic processes in riverbeds, and monitoring their evolution is important for ecological system management and in-stream infrastructure stability. Previous research showed proof of concept that analysis of paired temperature signals of stream and pore waters can simultaneously provide monitoring scour and deposition, stream sediment thermal regime, and seepage velocity information. However, it did not address challenges often associated with natural systems, including nonideal temperature variations (low-amplitude, nonsinusoidal signal, and vertical thermal gradients) and natural flooding conditions on monitoring scour and deposition processes over time. Here we addressed this knowledge gap by testing the proposed thermal scour-deposition chain (TSDC) methodology, with laboratory experiments to test the impact of nonideal temperature signals under a range of seepage velocities and with a field application during a pulse flood. Both analyses showed excellent match between surveyed and temperature-derived bed elevation changes even under very low temperature signal amplitudes (less than 1°C), nonideal signal shape (sawtooth shape), and strong and changing vertical thermal gradients (4°C/m). Root-mean-square errors on predicting the change in streambed elevations were comparable with the median grain size of the streambed sediment. Future research should focus on improved techniques for temperature signal phase and amplitude extractions, as well as TSDC applications over long periods spanning entire hydrographs.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

NASA Astrophysics Data System (ADS)

Ba, Yan; Liu, Haihu; Li, Qing; Kang, Qinjun; Sun, Jinju

2016-08-01

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

Instabilities in mimetic matter perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Firouzjahi, Hassan; Gorji, Mohammad Ali; Mansoori, Seyed Ali Hosseini, E-mail: firouz@ipm.ir, E-mail: gorji@ipm.ir, E-mail: shosseini@shahroodut.ac.ir, E-mail: shossein@ipm.ir

2017-07-01

We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilitiesmore » such as the Ostrogradsky ghost.« less

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation A2 term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

The q-G method : A q-version of the Steepest Descent method for global optimization.

PubMed

Soterroni, Aline C; Galski, Roberto L; Scarabello, Marluce C; Ramos, Fernando M

2015-01-01

In this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a generalization of the classical gradient vector based on the concept of Jackson's derivative from the q-calculus. Its use provides the algorithm an effective mechanism for escaping from local minima. The q-G method reduces to the Steepest Descent method when the parameter q tends to 1. The algorithm has three free parameters and it is implemented so that the search process gradually shifts from global exploration in the beginning to local exploitation in the end. We evaluated the q-G method on 34 test functions, and compared its performance with 34 optimization algorithms, including derivative-free algorithms and the Steepest Descent method. Our results show that the q-G method is competitive and has a great potential for solving multimodal optimization problems.

Investigation into the limitations of straightness interferometers using a multisensor-based error separation method

NASA Astrophysics Data System (ADS)

Weichert, Christoph; Köchert, Paul; Schötka, Eugen; Flügge, Jens; Manske, Eberhard

2018-06-01

The uncertainty of a straightness interferometer is independent of the component used to introduce the divergence angle between the two probing beams, and is limited by three main error sources, which are linked to each other: their resolution, the influence of refractive index gradients and the topography of the straightness reflector. To identify the configuration with minimal uncertainties under laboratory conditions, a fully fibre-coupled heterodyne interferometer was successively equipped with three different wedge prisms, resulting in three different divergence angles (4°, 8° and 20°). To separate the error sources an independent reference with a smaller reproducibility is needed. Therefore, the straightness measurement capability of the Nanometer Comparator, based on a multisensor error separation method, was improved to provide measurements with a reproducibility of 0.2 nm. The comparison results revealed that the influence of the refractive index gradients of air did not increase with interspaces between the probing beams of more than 11.3 mm. Therefore, over a movement range of 220 mm, the lowest uncertainty was achieved with the largest divergence angle. The dominant uncertainty contribution arose from the mirror topography, which was additionally determined with a Fizeau interferometer. The measured topography agreed within  ±1.3 nm with the systematic deviations revealed in the straightness comparison, resulting in an uncertainty contribution of 2.6 nm for the straightness interferometer.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

PubMed

Davids, Mathias; Schad, Lothar R; Wald, Lawrence L; Guérin, Bastien

2016-10-01

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Minimum maximum temperature gradient coil design.

PubMed

While, Peter T; Poole, Michael S; Forbes, Larry K; Crozier, Stuart

2013-08-01

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting "fish-eye" spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit. © 2012 Wiley Periodicals, Inc.

Solving the optimal attention allocation problem in manual control

NASA Technical Reports Server (NTRS)

Kleinman, D. L.

1976-01-01

Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods.

PubMed

Tripathi, Ashish; McNulty, Ian; Shpyrko, Oleg G

2014-01-27

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.

Influence of eddy current, Maxwell and gradient field corrections on 3D flow visualization of 3D CINE PC-MRI data.

PubMed

Lorenz, Ramona; Bock, Jelena; Snyder, Jeff; Korvink, Jan G; Jung, Bernd A; Markl, Michael

2014-07-01

The measurement of velocities based on phase contrast MRI can be subject to different phase offset errors which can affect the accuracy of velocity data. The purpose of this study was to determine the impact of these inaccuracies and to evaluate different correction strategies on three-dimensional visualization. Phase contrast MRI was performed on a 3 T system (Siemens Trio) for in vitro (curved/straight tube models; venc: 0.3 m/s) and in vivo (aorta/intracranial vasculature; venc: 1.5/0.4 m/s) data. For comparison of the impact of different magnetic field gradient designs, in vitro data was additionally acquired on a wide bore 1.5 T system (Siemens Espree). Different correction methods were applied to correct for eddy currents, Maxwell terms, and gradient field inhomogeneities. The application of phase offset correction methods lead to an improvement of three-dimensional particle trace visualization and count. The most pronounced differences were found for in vivo/in vitro data (68%/82% more particle traces) acquired with a low venc (0.3 m/s/0.4 m/s, respectively). In vivo data acquired with high venc (1.5 m/s) showed noticeable but only minor improvement. This study suggests that the correction of phase offset errors can be important for a more reliable visualization of particle traces but is strongly dependent on the velocity sensitivity, object geometry, and gradient coil design. Copyright © 2013 Wiley Periodicals, Inc.

Influence of Eddy Current, Maxwell and Gradient Field Corrections on 3D Flow Visualization of 3D CINE PC-MRI Data

PubMed Central

Lorenz, R.; Bock, J.; Snyder, J.; Korvink, J.G.; Jung, B.A.; Markl, M.

2013-01-01

Purpose The measurement of velocities based on PC-MRI can be subject to different phase offset errors which can affect the accuracy of velocity data. The purpose of this study was to determine the impact of these inaccuracies and to evaluate different correction strategies on 3D visualization. Methods PC-MRI was performed on a 3 T system (Siemens Trio) for in vitro (curved/straight tube models; venc: 0.3 m/s) and in vivo (aorta/intracranial vasculature; venc: 1.5/0.4 m/s) data. For comparison of the impact of different magnetic field gradient designs, in vitro data was additionally acquired on a wide bore 1.5 T system (Siemens Espree). Different correction methods were applied to correct for eddy currents, Maxwell terms and gradient field inhomogeneities. Results The application of phase offset correction methods lead to an improvement of 3D particle trace visualization and count. The most pronounced differences were found for in vivo/in vitro data (68%/82% more particle traces) acquired with a low venc (0.3 m/s/0.4 m/s, respectively). In vivo data acquired with high venc (1.5 m/s) showed noticeable but only minor improvement. Conclusion This study suggests that the correction of phase offset errors can be important for a more reliable visualization of particle traces but is strongly dependent on the velocity sensitivity, object geometry, and gradient coil design. PMID:24006013

SDSS-IV MaNGA: Spatially resolved star formation histories in galaxies as a function of galaxy mass and type

NASA Astrophysics Data System (ADS)

Goddard, D.; Thomas, D.; Maraston, C.; Westfall, K.; Etherington, J.; Riffel, R.; Mallmann, N. D.; Zheng, Z.; Argudo-Fernández, M.; Lian, J.; Bershady, M.; Bundy, K.; Drory, N.; Law, D.; Yan, R.; Wake, D.; Weijmans, A.; Bizyaev, D.; Brownstein, J.; Lane, R. R.; Maiolino, R.; Masters, K.; Merrifield, M.; Nitschelm, C.; Pan, K.; Roman-Lopes, A.; Storchi-Bergmann, T.; Schneider, D. P.

2017-04-01

We study the internal gradients of stellar population properties within 1.5 Re for a representative sample of 721 galaxies, with stellar masses ranging between 109 M⊙ and 1011.5 M⊙ from the SDSS-IV MaNGA Integral-Field-Unit survey. Through the use of our full spectral fitting code firefly, we derive light- and mass-weighted stellar population properties and their radial gradients, as well as full star formation and metal enrichment histories. We also quantify the impact that different stellar population models and full spectral fitting routines have on the derived stellar population properties and the radial gradient measurements. In our analysis, we find that age gradients tend to be shallow for both early-type and late-type galaxies. Mass-weighted age gradients of early-types arepositive (˜0.09 dex/Re) pointing to 'outside-in' progression of star formation, while late-type galaxies have negative light-weighted age gradients (˜-0.11 dex/Re), suggesting an 'inside-out' formation of discs. We detect negative metallicity gradients in both early- and late-type galaxies, but these are significantly steeper in late-types, suggesting that the radial dependence of chemical enrichment processes and the effect of gas inflow and metal transport are far more pronounced in discs. Metallicity gradients of both morphological classes correlate with galaxy mass, with negative metallicity gradients becoming steeper with increasing galaxy mass. The correlation with mass is stronger for late-type galaxies, with a slope of d(∇[Z/H])/d(log M) ˜ -0.2 ± 0.05 , compared to d(∇[Z/H])/d(log M) ˜ -0.05 ± 0.05 for early-types. This result suggests that the merger history plays a relatively small role in shaping metallicity gradients of galaxies.

A z-gradient array for simultaneous multi-slice excitation with a single-band RF pulse.

PubMed

Ertan, Koray; Taraghinia, Soheil; Sadeghi, Alireza; Atalar, Ergin

2018-07-01

Multi-slice radiofrequency (RF) pulses have higher specific absorption rates, more peak RF power, and longer pulse durations than single-slice RF pulses. Gradient field design techniques using a z-gradient array are investigated for exciting multiple slices with a single-band RF pulse. Two different field design methods are formulated to solve for the required current values of the gradient array elements for the given slice locations. The method requirements are specified, optimization problems are formulated for the minimum current norm and an analytical solution is provided. A 9-channel z-gradient coil array driven by independent, custom-designed gradient amplifiers is used to validate the theory. Performance measures such as normalized slice thickness error, gradient strength per unit norm current, power dissipation, and maximum amplitude of the magnetic field are provided for various slice locations and numbers of slices. Two and 3 slices are excited by a single-band RF pulse in simulations and phantom experiments. The possibility of multi-slice excitation with a single-band RF pulse using a z-gradient array is validated in simulations and phantom experiments. Magn Reson Med 80:400-412, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Sub-diurnal Variation of SST Gradients in Infrared Satellite Data

NASA Astrophysics Data System (ADS)

Salter, J. P.; Cornillon, P. C.; Clayson, C. A.

2016-02-01

Ocean fronts are known to influence many physical, biological, and chemical processes including ocean mixing, air-sea interaction, cloud and wind patterns, and marine productivity. Satellite-derived Sea Surface Temperature (SST) measurements are an invaluable tool in studying ocean fronts because of the large spatial and temporal coverage of satellite data, extending back as far as the early 1980s. One of the limitations to satellite-derived ocean fronts is that they provide no information about the underlying vertical structure; furthermore, the dynamics on sub-diurnal time scales for ocean fronts are poorly understood. In this poster we examine the daily signal of SST gradient magnitudes for the eastern Mediterranean sea as the first step in quantifying a subset of ocean fronts globally and how they vary on sub-diurnal time scales. We find that mean gradient magnitude in summer months increases and peaks around 2-4 PM Local Sun Time (LST). We find that the peak in summer months results from an increase in the magnitude of weaker gradients while the magnitude of the strongest gradients decrease; however, the weaker gradients contribute more strongly to the mean signal, resulting in the increase. The mid-afternoon peak in SST gradient magnitude disappears in winter with only a suggestion of a peak earlier in the day although the paucity of cloud free data in winter precludes making a statistically significant statement in this regard.

Estimating pixel variances in the scenes of staring sensors

DOEpatents

Simonson, Katherine M [Cedar Crest, NM; Ma, Tian J [Albuquerque, NM

2012-01-24

A technique for detecting changes in a scene perceived by a staring sensor is disclosed. The technique includes acquiring a reference image frame and a current image frame of a scene with the staring sensor. A raw difference frame is generated based upon differences between the reference image frame and the current image frame. Pixel error estimates are generated for each pixel in the raw difference frame based at least in part upon spatial error estimates related to spatial intensity gradients in the scene. The pixel error estimates are used to mitigate effects of camera jitter in the scene between the current image frame and the reference image frame.

Errors in finite-difference computations on curvilinear coordinate systems

NASA Technical Reports Server (NTRS)

Mastin, C. W.; Thompson, J. F.

1980-01-01

Curvilinear coordinate systems were used extensively to solve partial differential equations on arbitrary regions. An analysis of truncation error in the computation of derivatives revealed why numerical results may be erroneous. A more accurate method of computing derivatives is presented.

Advances in adaptive control theory: Gradient- and derivative-free approaches

NASA Astrophysics Data System (ADS)

Yucelen, Tansel

In this dissertation, we present new approaches to improve standard designs in adaptive control theory, and novel adaptive control architectures. We first present a novel Kalman filter based approach for approximately enforcing a linear constraint in standard adaptive control design. One application is that this leads to alternative forms for well known modification terms such as e-modification. In addition, it leads to smaller tracking errors without incurring significant oscillations in the system response and without requiring high modification gain. We derive alternative forms of e- and adaptive loop recovery (ALR-) modifications. Next, we show how to use Kalman filter optimization to derive a novel adaptation law. This results in an optimization-based time-varying adaptation gain that reduces the need for adaptation gain tuning. A second major contribution of this dissertation is the development of a novel derivative-free, delayed weight update law for adaptive control. The assumption of constant unknown ideal weights is relaxed to the existence of time-varying weights, such that fast and possibly discontinuous variation in weights are allowed. This approach is particulary advantageous for applications to systems that can undergo a sudden change in dynamics, such as might be due to reconfiguration, deployment of a payload, docking, or structural damage, and for rejection of external disturbance processes. As a third and final contribution, we develop a novel approach for extending all the methods developed in this dissertation to the case of output feedback. The approach is developed only for the case of derivative-free adaptive control, and the extension of the other approaches developed previously for the state feedback case to output feedback is left as a future research topic. The proposed approaches of this dissertation are illustrated in both simulation and flight test.

Bidirectional composition on lie groups for gradient-based image alignment.

PubMed

Mégret, Rémi; Authesserre, Jean-Baptiste; Berthoumieu, Yannick

2010-09-01

In this paper, a new formulation based on bidirectional composition on Lie groups (BCL) for parametric gradient-based image alignment is presented. Contrary to the conventional approaches, the BCL method takes advantage of the gradients of both template and current image without combining them a priori. Based on this bidirectional formulation, two methods are proposed and their relationship with state-of-the-art gradient based approaches is fully discussed. The first one, i.e., the BCL method, relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector. The second one, the projected BCL (PBCL), corresponds to a close approximation of the BCL approach. A comparative study is carried out dealing with computational complexity, convergence rate and frequence of convergence. Numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise, which is also discussed from a theoretical point of view.

Zero- to low-field MRI with averaging of concomitant gradient fields.

PubMed

Meriles, Carlos A; Sakellariou, Dimitris; Trabesinger, Andreas H; Demas, Vasiliki; Pines, Alexander

2005-02-08

Magnetic resonance imaging (MRI) encounters fundamental limits in circumstances in which the static magnetic field is not sufficiently strong to truncate unwanted, so-called concomitant components of the gradient field. This limitation affects the attainable optimal image fidelity and resolution most prominently in low-field imaging. In this article, we introduce the use of pulsed magnetic-field averaging toward relaxing these constraints. It is found that the image of an object can be retrieved by pulsed low fields in the presence of the full spatial variation of the imaging encoding gradient field even in the absence of the typical uniform high-field time-independent contribution. In addition, error-compensation schemes can be introduced through the application of symmetrized pulse sequences. Such schemes substantially mitigate artifacts related to evolution in strong magnetic-field gradients, magnetic fields that vary in direction and orientation, and imperfections of the applied field pulses.

Stability of Gradient Field Corrections for Quantitative Diffusion MRI.

PubMed

Rogers, Baxter P; Blaber, Justin; Welch, E Brian; Ding, Zhaohua; Anderson, Adam W; Landman, Bennett A

2017-02-11

In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fields, we predicted the obtained b-values and applied gradient directions throughout a typical field of view for brain imaging for a typical 32-direction diffusion imaging sequence. We measured the stability of these predictions over time. At 80 mm from scanner isocenter, predicted b-value was 1-6% different than intended due to gradient nonlinearity, and predicted gradient directions were in error by up to 1 degree. Over the course of one month the change in these quantities due to calibration-related factors such as scanner drift and variation in phantom placement was <0.5% for b-values, and <0.5 degrees for angular deviation. The proposed calibration procedure allows the estimation of gradient nonlinearity to correct b-values and gradient directions ahead of advanced diffusion image processing for high angular resolution data, and requires only a five-minute phantom scan that can be included in a weekly or monthly quality assurance protocol.

Application of gradient elasticity to benchmark problems of beam vibrations

NASA Astrophysics Data System (ADS)

Kateb, K. M.; Almitani, K. H.; Alnefaie, K. A.; Abu-Hamdeh, N. H.; Papadopoulos, P.; Askes, H.; Aifantis, E. C.

2016-04-01

The gradient approach, specifically gradient elasticity theory, is adopted to revisit certain typical configurations on mechanical vibrations. New results on size effects and scale-dependent behavior not captured by classical elasticity are derived, aiming at illustrating the usefulness of this approach to applications in advanced technologies. In particular, elastic prismatic straight beams in bending are discussed using two different governing equations: the gradient elasticity bending moment equation (fourth order) and the gradient elasticity deflection equation (sixth order). Different boundary/support conditions are examined. One problem considers the free vibrations of a cantilever beam loaded by an end force. A second problem is concerned with a simply supported beam disturbed by a concentrated force in the middle of the beam. Both problems are solved analytically. Exact free vibration frequencies and mode shapes are derived and presented. The difference between the gradient elasticity solution and its classical counterpart is revealed. The size ratio c/L (c denotes internal length and L is the length of the beam) induces significant effects on vibration frequencies. For both beam configurations, it turns out that as the ratio c/L increases, the vibration frequencies decrease, a fact which implies lower beam stiffness. Numerical examples show this behavior explicitly and recover the classical vibration behavior for vanishing size ratio c/L.

Performance of cellular frequency-hopped spread-spectrum radio networks

NASA Astrophysics Data System (ADS)

Gluck, Jeffrey W.; Geraniotis, Evaggelos

1989-10-01

Multiple access interference is characterized for cellular mobile networks, in which users are assumed to be Poisson-distributed in the plane and employ frequency-hopped spread-spectrum signaling with transmitter-oriented assignment of frequency-hopping patterns. Exact expressions for the bit error probabilities are derived for binary coherently demodulated systems without coding. Approximations for the packet error probability are derived for coherent and noncoherent systems and these approximations are applied when forward-error-control coding is employed. In all cases, the effects of varying interference power are accurately taken into account according to some propagation law. Numerical results are given in terms of bit error probability for the exact case and throughput for the approximate analyses. Comparisons are made with previously derived bounds and it is shown that these tend to be very pessimistic.

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

Model reduction of dynamical systems by proper orthogonal decomposition: Error bounds and comparison of methods using snapshots from the solution and the time derivatives [Proper orthogonal decomposition model reduction of dynamical systems: error bounds and comparison of methods using snapshots from the solution and the time derivatives

DOE PAGES

Kostova-Vassilevska, Tanya; Oxberry, Geoffrey M.

2017-09-17

In this study, we consider two proper orthogonal decomposition (POD) methods for dimension reduction of dynamical systems. The first method (M1) uses only time snapshots of the solution, while the second method (M2) augments the snapshot set with time-derivative snapshots. The goal of the paper is to analyze and compare the approximation errors resulting from the two methods by using error bounds. We derive several new bounds of the error from POD model reduction by each of the two methods. The new error bounds involve a multiplicative factor depending on the time steps between the snapshots. For method M1 themore » factor depends on the second power of the time step, while for method 2 the dependence is on the fourth power of the time step, suggesting that method M2 can be more accurate for small between-snapshot intervals. However, three other factors also affect the size of the error bounds. These include (i) the norm of the second (for M1) and fourth derivatives (M2); (ii) the first neglected singular value and (iii) the spectral properties of the projection of the system’s Jacobian in the reduced space. Because of the interplay of these factors neither method is more accurate than the other in all cases. Finally, we present numerical examples demonstrating that when the number of collected snapshots is small and the first neglected singular value has a value of zero, method M2 results in a better approximation.« less

Model reduction of dynamical systems by proper orthogonal decomposition: Error bounds and comparison of methods using snapshots from the solution and the time derivatives [Proper orthogonal decomposition model reduction of dynamical systems: error bounds and comparison of methods using snapshots from the solution and the time derivatives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kostova-Vassilevska, Tanya; Oxberry, Geoffrey M.

In this study, we consider two proper orthogonal decomposition (POD) methods for dimension reduction of dynamical systems. The first method (M1) uses only time snapshots of the solution, while the second method (M2) augments the snapshot set with time-derivative snapshots. The goal of the paper is to analyze and compare the approximation errors resulting from the two methods by using error bounds. We derive several new bounds of the error from POD model reduction by each of the two methods. The new error bounds involve a multiplicative factor depending on the time steps between the snapshots. For method M1 themore » factor depends on the second power of the time step, while for method 2 the dependence is on the fourth power of the time step, suggesting that method M2 can be more accurate for small between-snapshot intervals. However, three other factors also affect the size of the error bounds. These include (i) the norm of the second (for M1) and fourth derivatives (M2); (ii) the first neglected singular value and (iii) the spectral properties of the projection of the system’s Jacobian in the reduced space. Because of the interplay of these factors neither method is more accurate than the other in all cases. Finally, we present numerical examples demonstrating that when the number of collected snapshots is small and the first neglected singular value has a value of zero, method M2 results in a better approximation.« less

A pipeline leakage locating method based on the gradient descent algorithm

NASA Astrophysics Data System (ADS)

Li, Yulong; Yang, Fan; Ni, Na

2018-04-01

A pipeline leakage locating method based on the gradient descent algorithm is proposed in this paper. The method has low computing complexity, which is suitable for practical application. We have built experimental environment in real underground pipeline network. A lot of real data has been gathered in the past three months. Every leak point has been certificated by excavation. Results show that positioning error is within 0.4 meter. Rate of false alarm and missing alarm are both under 20%. The calculating time is not above 5 seconds.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Systems biology derived source-sink mechanism of BMP gradient formation

PubMed Central

Zinski, Joseph; Bu, Ye; Wang, Xu; Dou, Wei

2017-01-01

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development. PMID:28826472

Systems biology derived source-sink mechanism of BMP gradient formation.

PubMed

Zinski, Joseph; Bu, Ye; Wang, Xu; Dou, Wei; Umulis, David; Mullins, Mary C

2017-08-09

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

PubMed

Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru-Guzik, Alán

2018-05-23

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult , a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree–Fock

PubMed Central

2018-01-01

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult, a Hartree–Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

Evaluation of gravitational gradients generated by Earth's crustal structures

NASA Astrophysics Data System (ADS)

Novák, Pavel; Tenzer, Robert; Eshagh, Mehdi; Bagherbandi, Mohammad

2013-02-01

Spectral formulas for the evaluation of gravitational gradients generated by upper Earth's mass components are presented in the manuscript. The spectral approach allows for numerical evaluation of global gravitational gradient fields that can be used to constrain gravitational gradients either synthesised from global gravitational models or directly measured by the spaceborne gradiometer on board of the GOCE satellite mission. Gravitational gradients generated by static atmospheric, topographic and continental ice masses are evaluated numerically based on available global models of Earth's topography, bathymetry and continental ice sheets. CRUST2.0 data are then applied for the numerical evaluation of gravitational gradients generated by mass density contrasts within soft and hard sediments, upper, middle and lower crust layers. Combined gravitational gradients are compared to disturbing gravitational gradients derived from a global gravitational model and an idealised Earth's model represented by the geocentric homogeneous biaxial ellipsoid GRS80. The methodology could be used for improved modelling of the Earth's inner structure.

A contemporary view of the ventricular gradient of Wilson.

PubMed

Plonsey, R

1979-10-01

We have derived quantitative expressions for QRS, T, and QRST areas of the scalar electrocardiogram. The QRST area, or ventricular gradient, is seen to be essentially independent of the activation sequence and to reflect recovery properties of the tissue as weighted by the vector lead field of a given lead. The results are derived for uniform isotropic conditions and under the assumption that the temporal waveforms everywhere are identical except for possible variations in the duration of the plateau. However, it is noted that the results are, probably, valid under anisotropic conditions as well. The examination of ventricular gradients from epicardial and intramural leads should reflect local recovery properties and be a useful tool in study of the physiology of recovery, as well as the study of arrhythmias.

Multicolour CCD surface photometry for E and S0 galaxies in 10 clusters

NASA Astrophysics Data System (ADS)

Jorgensen, Inger; Franx, Marijn; Kjaergaard, Per

1995-04-01

CCD surface photometry for 232 E and S0 galaxies is presented. The galaxies are observed in Gunn r and Johnson B, or Gunn r and g. For 48 of the galaxies surface photometry in Johnson U is also presented. Aperture magnitudes in Gunn nu are derived for half of the galaxies. Galaxies in the following clusters have been observed: Abell 194, Abell 539, Abell 3381, Abell 3574, Abell S639, Abell S753, HydraI (Abell 1060), DC2345-28, Doradus and Grm15. The data are part of our ongoing study of the large-scale motions in the Universe and the physical background for the fundamental plane. We use a full model fitting technique for analysing the CCD images. This gives radial profiles of local surface brightness, colour, ellipticity and position angle. The residuals relative to the elliptical isophotes are described quantitatively by Fourier expansions. Effective radius, mean surface brightness and total magnitude are derived by fitting a de Vaucouleurs r^¼ growth curve. We have derived a characteristic radius r_n similar to the diameter D_n introduced by Dressler et al. The derivation of the effective parameters and of r_n takes the seeing into account. We confirm the results by Saglia et al. that the effects of the seeing can be substantial. Seeing-corrected values of the effective parameters and r_n are also presented for 147 E and S0 galaxies in the Coma cluster. Colours, colour gradients and geometrical parameters are derived. The photometry is internally consistent within 0.016 mag. Comparison with the photoelectric aperture photometry from Burstein et al. shows a mean offset of 0.010 mag with an rms scatter of 0.034 mag. The global photometric parameters are compared with data from Faber et al., Lucey et al. and Lucey & Carter. These comparisons imply that the typical rms errors are as follows - log r_n:+/-0.015 log r_e:+/-0.045 m_T:+/-0.09 mag; _e:+/-0.16 mag. The rms error on the combination log r_e-0.35_e which enters the fundamental plane is +/-0.020. Also, comparisons with data from Saglia et al. are presented. The accuracy of the absolute photometry, as well as the derived parameters, makes the data suitable for our investigations of the fundamental plane and of the large-scale motions in the Universe.

Prospects for UT1 Measurements from VLBI Intensive Sessions

NASA Technical Reports Server (NTRS)

Boehm, Johannes; Nilsson, Tobias; Schuh, Harald

2010-01-01

Very Long Baseline Interferometry (VLBI) Intensives are one-hour single baseline sessions to provide Universal Time (UT1) in near real-time up to a delay of three days if a site is not e-transferring the observational data. Due to the importance of UT1 estimates for the prediction of Earth orientation parameters, as well as any kind of navigation on Earth or in space, there is not only the need to improve the timeliness of the results but also their accuracy. We identify the asymmetry of the tropospheric delays as the major error source, and we provide two strategies to improve the results, in particular of those Intensives which include the station Tsukuba in Japan with its large tropospheric variation. We find an improvement when (1) using ray-traced delays from a numerical weather model, and (2) when estimating tropospheric gradients within the analysis of Intensive sessions. The improvement is shown in terms of reduction of rms of length-of-day estimates w.r.t. those derived from Global Positioning System observations

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

Low-level water vapor fields from the VISSR atmospheric sounder (VAS) split window channels at 11 and 12 microns. [visible infrared spin scan radiometer

NASA Technical Reports Server (NTRS)

Chesters, D.; Uccellini, L.; Robinson, W.

1982-01-01

A series of high-resolution water vapor fields were derived from the 11 and 12 micron channels of the VISSR Atmospheric Sounder (VAS) on GOES-5. The low-level tropospheric moisture content was separated from the surface and atmospheric radiances by using the differential adsorption across the 'split window' along with the average air temperature from imbedded radiosondes. Fields of precipitable water are presented in a time sequence of five false color images taken over the United States at 3-hour intervals. Vivid subsynoptic and mesoscale patterns evolve at 15 km horizontal resolution over the 12-hour observing period. Convective cloud formations develop from several areas of enhanced low-level water vapor, especially where the vertical water vapor gradient relatively strong. Independent verification at radiosonde sites indicates fairly good absolute accuracy, and the spatial and temporal continuity of the water vapor features indicates very good relative accuracy. Residual errors are dominated by radiometer noise and unresolved clouds.

Contour Tracking with a Spatio-Temporal Intensity Moment.

PubMed

Demi, Marcello

2016-06-01

Standard edge detection operators such as the Laplacian of Gaussian and the gradient of Gaussian can be used to track contours in image sequences. When using edge operators, a contour, which is determined on a frame of the sequence, is simply used as a starting contour to locate the nearest contour on the subsequent frame. However, the strategy used to look for the nearest edge points may not work when tracking contours of non isolated gray level discontinuities. In these cases, strategies derived from the optical flow equation, which look for similar gray level distributions, appear to be more appropriate since these can work with a lower frame rate than that needed for strategies based on pure edge detection operators. However, an optical flow strategy tends to propagate the localization errors through the sequence and an additional edge detection procedure is essential to compensate for such a drawback. In this paper a spatio-temporal intensity moment is proposed which integrates the two basic functions of edge detection and tracking.

Detecting and isolating abrupt changes in linear switching systems

NASA Astrophysics Data System (ADS)

Nazari, Sohail; Zhao, Qing; Huang, Biao

2015-04-01

In this paper, a novel fault detection and isolation (FDI) method for switching linear systems is developed. All input and output signals are assumed to be corrupted with measurement noises. In the proposed method, a 'lifted' linear model named as stochastic hybrid decoupling polynomial (SHDP) is introduced. The SHDP model governs the dynamics of the switching linear system with all different modes, and is independent of the switching sequence. The error-in-variable (EIV) representation of SHDP is derived, and is used for the fault residual generation and isolation following the well-adopted local approach. The proposed FDI method can detect and isolate the fault-induced abrupt changes in switching models' parameters without estimating the switching modes. Furthermore, in this paper, the analytical expressions of the gradient vector and Hessian matrix are obtained based on the EIV SHDP formulation, so that they can be used to implement the online fault detection scheme. The performance of the proposed method is then illustrated by simulation examples.

Statistical Hypothesis Testing using CNN Features for Synthesis of Adversarial Counterexamples to Human and Object Detection Vision Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raj, Sunny; Jha, Sumit Kumar; Pullum, Laura L.

Validating the correctness of human detection vision systems is crucial for safety applications such as pedestrian collision avoidance in autonomous vehicles. The enormous space of possible inputs to such an intelligent system makes it difficult to design test cases for such systems. In this report, we present our tool MAYA that uses an error model derived from a convolutional neural network (CNN) to explore the space of images similar to a given input image, and then tests the correctness of a given human or object detection system on such perturbed images. We demonstrate the capability of our tool on themore » pre-trained Histogram-of-Oriented-Gradients (HOG) human detection algorithm implemented in the popular OpenCV toolset and the Caffe object detection system pre-trained on the ImageNet benchmark. Our tool may serve as a testing resource for the designers of intelligent human and object detection systems.« less

Electronic properties of copper aluminate examined by three theoretical approaches

NASA Astrophysics Data System (ADS)

Christensen, Niels; Svane, Axel

2010-03-01

Electronic properties of 3R.CuAlO2 are derived vs. pressure from ab initio band structure calculations within the local-density approximation (LDA), LDA+U scheme as well as the quasiparticle self-consistent GW approximation (QSGW, van Schilfgaarde, Kotani, and Falaev). The LDA underestimates the gap and places the Cu-3d states at too high energies. An effective U value, 8.2 eV, can be selected so that LDA+U lowers the 3d states to match XPS data and such that the lowest gap agrees rather well with optical absorption experiments. The electrical field gradient (EFG) on Cu is in error when calculated within the LDA. The agreement with experiment can be improved by LDA+U, but a larger U, 13.5 eV, is needed for full adjustment. QSGW yields correct Cu-EFG and, when electron-hole correlations are included, also correct band gaps. The QSGW and LDA band gap deformation potential values differ significantly.

Long-range corrected density functional through the density matrix expansion based semilocal exchange hole.

PubMed

Patra, Bikash; Jana, Subrata; Samal, Prasanjit

2018-03-28

The exchange hole, which is one of the principal constituents of the density functional formalism, can be used to design accurate range-separated hybrid functionals in association with appropriate correlation. In this regard, the exchange hole derived from the density matrix expansion has gained attention due to its fulfillment of some of the desired exact constraints. Thus, the new long-range corrected density functional proposed here combines the meta generalized gradient approximation level exchange functional designed from the density matrix expansion based exchange hole coupled with the ab initio Hartree-Fock exchange through the range separation of the Coulomb interaction operator using the standard error function technique. Then, in association with the Lee-Yang-Parr correlation functional, the assessment and benchmarking of the above newly constructed range-separated functional with various well-known test sets shows its reasonable performance for a broad range of molecular properties, such as thermochemistry, non-covalent interaction and barrier heights of the chemical reactions.

Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations.

PubMed

Jana, Subrata; Samal, Prasanjit

2017-06-29

Semilocal density functionals for the exchange-correlation energy of electrons are extensively used as they produce realistic and accurate results for finite and extended systems. The choice of techniques plays a crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semilocal exchange energy functional in two dimensions is constructed by making use of the corresponding hole which is derived based on the density matrix expansion. The exchange hole involved is localized under the generalized coordinate transformation and satisfies all the relevant constraints. Comprehensive testing and excellent performance of the functional is demonstrated versus exact exchange results. The accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems. The underlying principles involved in the functional construction are physically appealing and hold promise for developing range separated and nonlocal exchange functionals in two dimensions.

FSMRank: feature selection algorithm for learning to rank.

PubMed

Lai, Han-Jiang; Pan, Yan; Tang, Yong; Yu, Rong

2013-06-01

In recent years, there has been growing interest in learning to rank. The introduction of feature selection into different learning problems has been proven effective. These facts motivate us to investigate the problem of feature selection for learning to rank. We propose a joint convex optimization formulation which minimizes ranking errors while simultaneously conducting feature selection. This optimization formulation provides a flexible framework in which we can easily incorporate various importance measures and similarity measures of the features. To solve this optimization problem, we use the Nesterov's approach to derive an accelerated gradient algorithm with a fast convergence rate O(1/T(2)). We further develop a generalization bound for the proposed optimization problem using the Rademacher complexities. Extensive experimental evaluations are conducted on the public LETOR benchmark datasets. The results demonstrate that the proposed method shows: 1) significant ranking performance gain compared to several feature selection baselines for ranking, and 2) very competitive performance compared to several state-of-the-art learning-to-rank algorithms.

Rules and mechanisms for efficient two-stage learning in neural circuits.

PubMed

Teşileanu, Tiberiu; Ölveczky, Bence; Balasubramanian, Vijay

2017-04-04

Trial-and-error learning requires evaluating variable actions and reinforcing successful variants. In songbirds, vocal exploration is induced by LMAN, the output of a basal ganglia-related circuit that also contributes a corrective bias to the vocal output. This bias is gradually consolidated in RA, a motor cortex analogue downstream of LMAN. We develop a new model of such two-stage learning. Using stochastic gradient descent, we derive how the activity in 'tutor' circuits ( e.g., LMAN) should match plasticity mechanisms in 'student' circuits ( e.g., RA) to achieve efficient learning. We further describe a reinforcement learning framework through which the tutor can build its teaching signal. We show that mismatches between the tutor signal and the plasticity mechanism can impair learning. Applied to birdsong, our results predict the temporal structure of the corrective bias from LMAN given a plasticity rule in RA. Our framework can be applied predictively to other paired brain areas showing two-stage learning.

Grid sensitivity for aerodynamic optimization and flow analysis

NASA Technical Reports Server (NTRS)

Sadrehaghighi, I.; Tiwari, S. N.

1993-01-01

After reviewing relevant literature, it is apparent that one aspect of aerodynamic sensitivity analysis, namely grid sensitivity, has not been investigated extensively. The grid sensitivity algorithms in most of these studies are based on structural design models. Such models, although sufficient for preliminary or conceptional design, are not acceptable for detailed design analysis. Careless grid sensitivity evaluations, would introduce gradient errors within the sensitivity module, therefore, infecting the overall optimization process. Development of an efficient and reliable grid sensitivity module with special emphasis on aerodynamic applications appear essential. The organization of this study is as follows. The physical and geometric representations of a typical model are derived in chapter 2. The grid generation algorithm and boundary grid distribution are developed in chapter 3. Chapter 4 discusses the theoretical formulation and aerodynamic sensitivity equation. The method of solution is provided in chapter 5. The results are presented and discussed in chapter 6. Finally, some concluding remarks are provided in chapter 7.

Asymmetric Uncertainty Expression for High Gradient Aerodynamics

NASA Technical Reports Server (NTRS)

Pinier, Jeremy T

2012-01-01

When the physics of the flow around an aircraft changes very abruptly either in time or space (e.g., flow separation/reattachment, boundary layer transition, unsteadiness, shocks, etc), the measurements that are performed in a simulated environment like a wind tunnel test or a computational simulation will most likely incorrectly predict the exact location of where (or when) the change in physics happens. There are many reasons for this, includ- ing the error introduced by simulating a real system at a smaller scale and at non-ideal conditions, or the error due to turbulence models in a computational simulation. The un- certainty analysis principles that have been developed and are being implemented today do not fully account for uncertainty in the knowledge of the location of abrupt physics changes or sharp gradients, leading to a potentially underestimated uncertainty in those areas. To address this problem, a new asymmetric aerodynamic uncertainty expression containing an extra term to account for a phase-uncertainty, the magnitude of which is emphasized in the high-gradient aerodynamic regions is proposed in this paper. Additionally, based on previous work, a method for dispersing aerodynamic data within asymmetric uncer- tainty bounds in a more realistic way has been developed for use within Monte Carlo-type analyses.

Regional gravity field modelling from GOCE observables

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Novák, Pavel; Tenzer, Robert

2017-01-01

In this article we discuss a regional recovery of gravity disturbances at the mean geocentric sphere approximating the Earth over the area of Central Europe from satellite gravitational gradients. For this purpose, we derive integral formulas which allow converting the gravity disturbances onto the disturbing gravitational gradients in the local north-oriented frame (LNOF). The derived formulas are free of singularities in case of r ≠ R . We then investigate three numerical approaches for solving their inverses. In the initial approach, the integral formulas are firstly modified for solving individually the near- and distant-zone contributions. While the effect of the near-zone gravitational gradients is solved as an inverse problem, the effect of the distant-zone gravitational gradients is computed by numerical integration from the global gravitational model (GGM) TIM-r4. In the second approach, we further elaborate the first scenario by reducing measured gravitational gradients for gravitational effects of topographic masses. In the third approach, we apply additional modification by reducing gravitational gradients for the reference GGM. In all approaches we determine the gravity disturbances from each of the four accurately measured gravitational gradients separately as well as from their combination. Our regional gravitational field solutions are based on the GOCE EGG_TRF_2 gravitational gradients collected within the period from November 1 2009 until January 11 2010. Obtained results are compared with EGM2008, DIR-r1, TIM-r1 and SPW-r1. The best fit, in terms of RMS (2.9 mGal), is achieved for EGM2008 while using the third approach which combine all four well-measured gravitational gradients. This is explained by the fact that a-priori information about the Earth's gravitational field up to the degree and order 180 was used.

Thomas Young's investigations in gradient-index optics.

PubMed

Atchison, David A; Charman, W Neil

2011-05-01

James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some 50 years earlier, Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young's contributions. We attempted to derive Young's equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. We did not confirm Young's equation for the axial gradient to provide aberration-free optics but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index toward the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Young's theoretical work in gradient-index optics received no acknowledgment from either his contemporaries or later authors. Although his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young's work deserves wider recognition.

Reference tissue quantification of DCE-MRI data without a contrast agent calibration

NASA Astrophysics Data System (ADS)

Walker-Samuel, Simon; Leach, Martin O.; Collins, David J.

2007-02-01

The quantification of dynamic contrast-enhanced (DCE) MRI data conventionally requires a conversion from signal intensity to contrast agent concentration by measuring a change in the tissue longitudinal relaxation rate, R1. In this paper, it is shown that the use of a spoiled gradient-echo acquisition sequence (optimized so that signal intensity scales linearly with contrast agent concentration) in conjunction with a reference tissue-derived vascular input function (VIF), avoids the need for the conversion to Gd-DTPA concentration. This study evaluates how to optimize such sequences and which dynamic time-series parameters are most suitable for this type of analysis. It is shown that signal difference and relative enhancement provide useful alternatives when full contrast agent quantification cannot be achieved, but that pharmacokinetic parameters derived from both contain sources of error (such as those caused by differences between reference tissue and region of interest proton density and native T1 values). It is shown in a rectal cancer study that these sources of uncertainty are smaller when using signal difference, compared with relative enhancement (15 ± 4% compared with 33 ± 4%). Both of these uncertainties are of the order of those associated with the conversion to Gd-DTPA concentration, according to literature estimates.

Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

USGS Publications Warehouse

Cox, T.J.; Runkel, R.L.

2008-01-01

Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

Stable modeling based control methods using a new RBF network.

PubMed

Beyhan, Selami; Alci, Musa

2010-10-01

This paper presents a novel model with radial basis functions (RBFs), which is applied successively for online stable identification and control of nonlinear discrete-time systems. First, the proposed model is utilized for direct inverse modeling of the plant to generate the control input where it is assumed that inverse plant dynamics exist. Second, it is employed for system identification to generate a sliding-mode control input. Finally, the network is employed to tune PID (proportional + integrative + derivative) controller parameters automatically. The adaptive learning rate (ALR), which is employed in the gradient descent (GD) method, provides the global convergence of the modeling errors. Using the Lyapunov stability approach, the boundedness of the tracking errors and the system parameters are shown both theoretically and in real time. To show the superiority of the new model with RBFs, its tracking results are compared with the results of a conventional sigmoidal multi-layer perceptron (MLP) neural network and the new model with sigmoid activation functions. To see the real-time capability of the new model, the proposed network is employed for online identification and control of a cascaded parallel two-tank liquid-level system. Even though there exist large disturbances, the proposed model with RBFs generates a suitable control input to track the reference signal better than other methods in both simulations and real time. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Generalization in Adaptation to Stable and Unstable Dynamics

PubMed Central

Kadiallah, Abdelhamid; Franklin, David W.; Burdet, Etienne

2012-01-01

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. PMID:23056191

Direct measurements of local bed shear stress in the presence of pressure gradients

NASA Astrophysics Data System (ADS)

Pujara, Nimish; Liu, Philip L.-F.

2014-07-01

This paper describes the development of a shear plate sensor capable of directly measuring the local mean bed shear stress in small-scale and large-scale laboratory flumes. The sensor is capable of measuring bed shear stress in the range 200 Pa with an accuracy up to 1 %. Its size, 43 mm in the flow direction, is designed to be small enough to give spatially local measurements, and its bandwidth, 75 Hz, is high enough to resolve time-varying forcing. Typically, shear plate sensors are restricted to use in zero pressure gradient flows because secondary forces on the edge of the shear plate caused by pressure gradients can introduce large errors. However, by analysis of the pressure distribution at the edges of the shear plate in mild pressure gradients, we introduce a new methodology for correcting for the pressure gradient force. The developed sensor includes pressure tappings to measure the pressure gradient in the flow, and the methodology for correction is applied to obtain accurate measurements of bed shear stress under solitary waves in a small-scale wave flume. The sensor is also validated by measurements in a turbulent flat plate boundary layer in open channel flow.

Determining the mean hydraulic gradient of ground water affected by tidal fluctuations

USGS Publications Warehouse

Serfes, Michael E.

1991-01-01

Tidal fluctuations in surface-water bodies produce progressive pressure waves in adjacent aquifers. As these pressure waves propagate inland, ground-water levels and hydraulic gradients continuously fluctuate, creating a situation where a single set of water-level measurements cannot be used to accurately characterize ground-water flow. For example, a time series of water levels measured in a confined aquifer in Atlantic City, New Jersey, showed that the hydraulic gradient ranged from .01 to .001 with a 22-degree change in direction during a tidal day of approximately 25 hours. At any point where ground water tidally fluctuates, the magnitude and direction of the hydraulic gradient fluctuates about the mean or regional hydraulic gradient. The net effect of these fluctuations on ground-water flow can be determined using the mean hydraulic gradient, which can be calculated by comparing mean ground- and surface-water elevations. Filtering methods traditionally used to determine daily mean sea level can be similarly applied to ground water to determine mean levels. Method (1) uses 71 consecutive hourly water-level observations to accurately determine the mean level. Method (2) approximates the mean level using only 25 consecutive hourly observations; however, there is a small error associated with this method.

CO2 Flux Estimation Errors Associated with Moist Atmospheric Processes

NASA Technical Reports Server (NTRS)

Parazoo, N. C.; Denning, A. S.; Kawa, S. R.; Pawson, S.; Lokupitiya, R.

2012-01-01

Vertical transport by moist sub-grid scale processes such as deep convection is a well-known source of uncertainty in CO2 source/sink inversion. However, a dynamical link between vertical transport, satellite based retrievals of column mole fractions of CO2, and source/sink inversion has not yet been established. By using the same offline transport model with meteorological fields from slightly different data assimilation systems, we examine sensitivity of frontal CO2 transport and retrieved fluxes to different parameterizations of sub-grid vertical transport. We find that frontal transport feeds off background vertical CO2 gradients, which are modulated by sub-grid vertical transport. The implication for source/sink estimation is two-fold. First, CO2 variations contained in moist poleward moving air masses are systematically different from variations in dry equatorward moving air. Moist poleward transport is hidden from orbital sensors on satellites, causing a sampling bias, which leads directly to small but systematic flux retrieval errors in northern mid-latitudes. Second, differences in the representation of moist sub-grid vertical transport in GEOS-4 and GEOS-5 meteorological fields cause differences in vertical gradients of CO2, which leads to systematic differences in moist poleward and dry equatorward CO2 transport and therefore the fraction of CO2 variations hidden in moist air from satellites. As a result, sampling biases are amplified and regional scale flux errors enhanced, most notably in Europe (0.43+/-0.35 PgC /yr). These results, cast from the perspective of moist frontal transport processes, support previous arguments that the vertical gradient of CO2 is a major source of uncertainty in source/sink inversion.

Gradient-Induced Voltages on 12-Lead ECGs during High Duty-Cycle MRI Sequences and a Method for Their Removal considering Linear and Concomitant Gradient Terms

PubMed Central

Zhang, Shelley HuaLei; Ho Tse, Zion Tsz; Dumoulin, Charles L.; Kwong, Raymond Y.; Stevenson, William G.; Watkins, Ronald; Ward, Jay; Wang, Wei; Schmidt, Ehud J.

2015-01-01

Purpose To restore 12-lead ECG signal fidelity inside MRI by removing magnetic-field gradient induced-voltages during high gradient-duty-cycle sequences. Theory and Methods A theoretical equation was derived, providing first- and second-order electrical fields induced at individual ECG electrode as a function of gradient fields. Experiments were performed at 3T on healthy volunteers, using a customized acquisition system which captured full amplitude and frequency response of ECGs, or a commercial recording system. The 19 equation coefficients were derived by linear regression of data from accelerated sequences, and used to compute induced-voltages in real-time during full-resolution sequences to remove ECG artifacts. Restored traces were evaluated relative to ones acquired without imaging. Results Measured induced-voltages were 0.7V peak-to-peak during balanced Steady-State Free Precession (bSSFP) with heart at the isocenter. Applying the equation during gradient echo sequencing, three-dimensional fast spin echo and multi-slice bSSFP imaging restored nonsaturated traces and second-order concomitant terms showed larger contributions in electrodes farther from the magnet isocenter. Equation coefficients are evaluated with high repeatability (ρ = 0.996) and are subject, sequence, and slice-orientation dependent. Conclusion Close agreement between theoretical and measured gradient-induced voltages allowed for real-time removal. Prospective estimation of sequence-periods where large induced-voltages occur may allow hardware removal of these signals. PMID:26101951

ACCELERATED FITTING OF STELLAR SPECTRA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ting, Yuan-Sen; Conroy, Charlie; Rix, Hans-Walter

2016-07-20

Stellar spectra are often modeled and fitted by interpolating within a rectilinear grid of synthetic spectra to derive the stars’ labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and self-consistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach—Convex Hull Adaptive Tessellation (chat)—which includes several new ideas for inexpensively generating amore » sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock data sets demonstrate that chat can reduce the number of required synthetic model calculations by three orders of magnitude in an eight-dimensional label space. The reduction will be even larger for higher dimensional label spaces. In chat the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in the label space an approximate synthetic spectrum can be generated through linear expansion using a set of “gradient spectra” that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15–30 labels simultaneously.« less

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

PubMed

Temel, Burcin; Mills, Greg; Metiu, Horia

2008-03-27

We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

NASA Astrophysics Data System (ADS)

Atkinson, Callum; Coudert, Sebastien; Foucaut, Jean-Marc; Stanislas, Michel; Soria, Julio

2011-04-01

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Reθ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume "fat" light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.

Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters.

PubMed

Chung, SungWon; Lu, Ying; Henry, Roland G

2006-11-01

Bootstrap is an empirical non-parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor MRI (DTI) parameters, useful in tractography and in assessing DTI methods. The current bootstrap method (repetition bootstrap) used for DTI analysis performs resampling within the data sharing common diffusion gradients, requiring multiple acquisitions for each diffusion gradient. Recently, wild bootstrap was proposed that can be applied without multiple acquisitions. In this paper, two new approaches are introduced called residual bootstrap and repetition bootknife. We show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and, therefore, better estimates the standard errors. Like wild bootstrap, residual bootstrap is applicable to single acquisition scheme, and both are based on regression residuals (called model-based resampling). Residual bootstrap is based on the assumption that non-constant variance of measured diffusion-attenuated signals can be modeled, which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor. The performances of these bootstrap approaches were compared in terms of bias, variance, and overall error of bootstrap-estimated standard error by Monte Carlo simulation. We demonstrate that residual bootstrap has smaller biases and overall errors, which enables estimation of uncertainties with higher accuracy. Understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on DTI parameters, probabilistic fiber tracking, and optimizing DTI methods.

An error analysis of tropical cyclone divergence and vorticity fields derived from satellite cloud winds on the Atmospheric and Oceanographic Information Processing System (AOIPS)

NASA Technical Reports Server (NTRS)

Hasler, A. F.; Rodgers, E. B.

1977-01-01

An advanced Man-Interactive image and data processing system (AOIPS) was developed to extract basic meteorological parameters from satellite data and to perform further analyses. The errors in the satellite derived cloud wind fields for tropical cyclones are investigated. The propagation of these errors through the AOIPS system and their effects on the analysis of horizontal divergence and relative vorticity are evaluated.

The lateral variation of P n velocity gradient under Eurasia

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaoning

We report that mantle lid P wave velocity gradient, or P n velocity gradient, reflects the depth and lateral variations of thermal and rheological state of the uppermost mantle. Mapping the P n velocity gradient and its lateral variation helps us gain insight into the temperature, composition, and dynamics of the uppermost mantle. In addition, because P n velocity gradient has profound influence on P n propagation behavior, an accurate mapping of P n velocity gradient also improves the modeling and prediction of P n travel times and amplitudes. In this study, I used measured P n travel times tomore » derive path-specific P n velocity gradients. I then inverted these velocity gradients for two-dimensional (2-D) P n velocity-gradient models for Eurasia based on the assumption that a path-specific Pn velocity gradient is the mean of laterally varying P n velocity gradients along the P n path. Result from a Monte Carlo simulation indicates that the assumption is appropriate. The 2-D velocity-gradient models show that most of Eurasia has positive velocity gradients. High velocity gradients exist mainly in tectonically active regions. Most tectonically stable regions show low and more uniform velocity gradients. In conclusion, strong velocity-gradient variations occur largely along convergent plate boundaries, particularly under overriding plates.« less

The lateral variation of P n velocity gradient under Eurasia

DOE PAGES

Yang, Xiaoning

2017-05-03

We report that mantle lid P wave velocity gradient, or P n velocity gradient, reflects the depth and lateral variations of thermal and rheological state of the uppermost mantle. Mapping the P n velocity gradient and its lateral variation helps us gain insight into the temperature, composition, and dynamics of the uppermost mantle. In addition, because P n velocity gradient has profound influence on P n propagation behavior, an accurate mapping of P n velocity gradient also improves the modeling and prediction of P n travel times and amplitudes. In this study, I used measured P n travel times tomore » derive path-specific P n velocity gradients. I then inverted these velocity gradients for two-dimensional (2-D) P n velocity-gradient models for Eurasia based on the assumption that a path-specific Pn velocity gradient is the mean of laterally varying P n velocity gradients along the P n path. Result from a Monte Carlo simulation indicates that the assumption is appropriate. The 2-D velocity-gradient models show that most of Eurasia has positive velocity gradients. High velocity gradients exist mainly in tectonically active regions. Most tectonically stable regions show low and more uniform velocity gradients. In conclusion, strong velocity-gradient variations occur largely along convergent plate boundaries, particularly under overriding plates.« less

A new assessment method of pHEMT models by comparing relative errors of drain current and its derivatives up to the third order

NASA Astrophysics Data System (ADS)

Dobeš, Josef; Grábner, Martin; Puričer, Pavel; Vejražka, František; Míchal, Jan; Popp, Jakub

2017-05-01

Nowadays, there exist relatively precise pHEMT models available for computer-aided design, and they are frequently compared to each other. However, such comparisons are mostly based on absolute errors of drain-current equations and their derivatives. In the paper, a novel method is suggested based on relative root-mean-square errors of both drain current and its derivatives up to the third order. Moreover, the relative errors are subsequently relativized to the best model in each category to further clarify obtained accuracies of both drain current and its derivatives. Furthermore, one our older and two newly suggested models are also included in comparison with the traditionally precise Ahmed, TOM-2 and Materka ones. The assessment is performed using measured characteristics of a pHEMT operating up to 110 GHz. Finally, a usability of the proposed models including the higher-order derivatives is illustrated using s-parameters analysis and measurement at more operating points as well as computation and measurement of IP3 points of a low-noise amplifier of a multi-constellation satellite navigation receiver with ATF-54143 pHEMT.

A wet/wet differential pressure sensor for measuring vertical hydraulic gradient.

PubMed

Fritz, Brad G; Mackley, Rob D

2010-01-01

Vertical hydraulic gradient is commonly measured in rivers, lakes, and streams for studies of groundwater-surface water interaction. While a number of methods with subtle differences have been applied, these methods can generally be separated into two categories; measuring surface water elevation and pressure in the subsurface separately or making direct measurements of the head difference with a manometer. Making separate head measurements allows for the use of electronic pressure sensors, providing large datasets that are particularly useful when the vertical hydraulic gradient fluctuates over time. On the other hand, using a manometer-based method provides an easier and more rapid measurement with a simpler computation to calculate the vertical hydraulic gradient. In this study, we evaluated a wet/wet differential pressure sensor for use in measuring vertical hydraulic gradient. This approach combines the advantage of high-temporal frequency measurements obtained with instrumented piezometers with the simplicity and reduced potential for human-induced error obtained with a manometer board method. Our results showed that the wet/wet differential pressure sensor provided results comparable to more traditional methods, making it an acceptable method for future use.

Improved convection compensating pulsed field gradient spin-echo and stimulated-echo methods.

PubMed

Sørland, G H; Seland, J G; Krane, J; Anthonsen, H W

2000-02-01

The need for convection compensating methods in NMR has been manifested through an increasing number of publications related to the subject over the past few years (J. Magn. Reson. 125, 372 (1997); 132, 13 (1998); 131, 126 (1998); 118, 50 (1996); 133, 379 (1998)). When performing measurements at elevated temperature, small convection currents may give rise to erroneous values of the diffusion coefficient. In work with high resolution NMR spectroscopy, the application of magnetic field gradients also introduces an eddy-current magnetic field which may result in errors in phase and baseline in the FFT-spectra. The eddy current field has been greatly suppressed by the application of bipolar magnetic field gradients. However, when introducing bipolar magnetic field gradients, the pulse sequence is lengthened significantly. This has recently been pointed out as a major drawback because of the loss of coherence and of NMR-signal due to transverse relaxation processes. Here we present modified convection compensating pulsed field gradient double spin echo and double stimulated echo sequences which suppress the eddy-current magnetic field without increasing the duration of the pulse sequences. Copyright 2000 Academic Press.

Improved UTE-based attenuation correction for cranial PET-MR using dynamic magnetic field monitoring

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aitken, A. P.; Giese, D.; Tsoumpas, C.

2014-01-15

Purpose: Ultrashort echo time (UTE) MRI has been proposed as a way to produce segmented attenuation maps for PET, as it provides contrast between bone, air, and soft tissue. However, UTE sequences require samples to be acquired during rapidly changing gradient fields, which makes the resulting images prone to eddy current artifacts. In this work it is demonstrated that this can lead to misclassification of tissues in segmented attenuation maps (AC maps) and that these effects can be corrected for by measuring the true k-space trajectories using a magnetic field camera. Methods: The k-space trajectories during a dual echo UTEmore » sequence were measured using a dynamic magnetic field camera. UTE images were reconstructed using nominal trajectories and again using the measured trajectories. A numerical phantom was used to demonstrate the effect of reconstructing with incorrect trajectories. Images of an ovine leg phantom were reconstructed and segmented and the resulting attenuation maps were compared to a segmented map derived from a CT scan of the same phantom, using the Dice similarity measure. The feasibility of the proposed method was demonstrated inin vivo cranial imaging in five healthy volunteers. Simulated PET data were generated for one volunteer to show the impact of misclassifications on the PET reconstruction. Results: Images of the numerical phantom exhibited blurring and edge artifacts on the bone–tissue and air–tissue interfaces when nominal k-space trajectories were used, leading to misclassification of soft tissue as bone and misclassification of bone as air. Images of the tissue phantom and thein vivo cranial images exhibited the same artifacts. The artifacts were greatly reduced when the measured trajectories were used. For the tissue phantom, the Dice coefficient for bone in MR relative to CT was 0.616 using the nominal trajectories and 0.814 using the measured trajectories. The Dice coefficients for soft tissue were 0.933 and 0.934 for the nominal and measured cases, respectively. For air the corresponding figures were 0.991 and 0.993. Compared to an unattenuated reference image, the mean error in simulated PET uptake in the brain was 9.16% when AC maps derived from nominal trajectories was used, with errors in the SUV{sub max} for simulated lesions in the range of 7.17%–12.19%. Corresponding figures when AC maps derived from measured trajectories were used were 0.34% (mean error) and −0.21% to +1.81% (lesions). Conclusions: Eddy current artifacts in UTE imaging can be corrected for by measuring the true k-space trajectories during a calibration scan and using them in subsequent image reconstructions. This improves the accuracy of segmented PET attenuation maps derived from UTE sequences and subsequent PET reconstruction.« less

Evaluation of the impact of ionospheric disturbances on air navigation augmentation system using multi-point GPS receivers

NASA Astrophysics Data System (ADS)

Omatsu, N.; Otsuka, Y.; Shiokawa, K.; Saito, S.

2013-12-01

In recent years, GPS has been utilized for navigation system for airplanes. Propagation delays in the ionosphere due to total electron content (TEC) between GPS satellite and receiver cause large positioning errors. In precision measurement using GPS, the ionospheric delay correction is generally conducted using both GPS L1 and L2 frequencies. However, L2 frequency is not internationally accepted as air navigation band, so it is not available for positioning directly in air navigation. In air navigation, not only positioning accuracy but safety is important, so augmentation systems are required to ensure the safety. Augmentation systems such as the satellite-based augmentation system (SBAS) or the ground-based augmentation system (GBAS) are being developed and some of them are already in operation. GBAS is available in a relatively narrow area around airports. In general, it corrects for the combined effects of multiple sources of positioning errors simultaneously, including satellite clock and orbital information errors, ionospheric delay errors, and tropospheric delay errors, using the differential corrections broadcast by GBAS ground station. However, if the spatial ionospheric delay gradient exists in the area, correction errors remain even after correction by GBAS. It must be a threat to GBAS. In this study, we use the GPS data provided by the Geographical Survey Institute in Japan. From the GPS data, TEC is obtained every 30 seconds. We select 4 observation points from 24.4 to 35.6 degrees north latitude in Japan, and analyze TEC data of these points from 2001 to 2011. Then we reveal dependences of Rate of TEC change Index (ROTI) on latitude, season, and solar activity statistically. ROTI is the root-mean-square deviation of time subtraction of TEC within 5 minutes. In the result, it is the midnight of the spring and the summer of the solar maximum in the point of 26.4 degrees north latitude that the value of ROTI becomes the largest. We think it is caused by plasma bubbles, and the maximum value of ROTI is about 6 TECU/min. Since it is thought that ROTI is an index representing the spatial ionospheric delay gradient, we can evaluate the effect of spatial ionospheric delay gradient to GBAS. In addition, we will discuss azimuth angle dependence of ROTI. We have found that ROTI tends to be high when the GPS satellites are seen westward. Initial analysis results in Indonesia show a similar feature. This feature could arise from the westward tilt of the plasma bubbles with altitude. More detailed results will be reported in this presentation.

Nonuniformity correction for an infrared focal plane array based on diamond search block matching.

PubMed

Sheng-Hui, Rong; Hui-Xin, Zhou; Han-Lin, Qin; Rui, Lai; Kun, Qian

2016-05-01

In scene-based nonuniformity correction algorithms, artificial ghosting and image blurring degrade the correction quality severely. In this paper, an improved algorithm based on the diamond search block matching algorithm and the adaptive learning rate is proposed. First, accurate transform pairs between two adjacent frames are estimated by the diamond search block matching algorithm. Then, based on the error between the corresponding transform pairs, the gradient descent algorithm is applied to update correction parameters. During the process of gradient descent, the local standard deviation and a threshold are utilized to control the learning rate to avoid the accumulation of matching error. Finally, the nonuniformity correction would be realized by a linear model with updated correction parameters. The performance of the proposed algorithm is thoroughly studied with four real infrared image sequences. Experimental results indicate that the proposed algorithm can reduce the nonuniformity with less ghosting artifacts in moving areas and can also overcome the problem of image blurring in static areas.

Efficient boundary hunting via vector quantization

NASA Astrophysics Data System (ADS)

Diamantini, Claudia; Panti, Maurizio

2001-03-01

A great amount of information about a classification problem is contained in those instances falling near the decision boundary. This intuition dates back to the earliest studies in pattern recognition, and in the more recent adaptive approaches to the so called boundary hunting, such as the work of Aha et alii on Instance Based Learning and the work of Vapnik et alii on Support Vector Machines. The last work is of particular interest, since theoretical and experimental results ensure the accuracy of boundary reconstruction. However, its optimization approach has heavy computational and memory requirements, which limits its application on huge amounts of data. In the paper we describe an alternative approach to boundary hunting based on adaptive labeled quantization architectures. The adaptation is performed by a stochastic gradient algorithm for the minimization of the error probability. Error probability minimization guarantees the accurate approximation of the optimal decision boundary, while the use of a stochastic gradient algorithm defines an efficient method to reach such approximation. In the paper comparisons to Support Vector Machines are considered.

Automatic knee cartilage delineation using inheritable segmentation

NASA Astrophysics Data System (ADS)

Dries, Sebastian P. M.; Pekar, Vladimir; Bystrov, Daniel; Heese, Harald S.; Blaffert, Thomas; Bos, Clemens; van Muiswinkel, Arianne M. C.

2008-03-01

We present a fully automatic method for segmentation of knee joint cartilage from fat suppressed MRI. The method first applies 3-D model-based segmentation technology, which allows to reliably segment the femur, patella, and tibia by iterative adaptation of the model according to image gradients. Thin plate spline interpolation is used in the next step to position deformable cartilage models for each of the three bones with reference to the segmented bone models. After initialization, the cartilage models are fine adjusted by automatic iterative adaptation to image data based on gray value gradients. The method has been validated on a collection of 8 (3 left, 5 right) fat suppressed datasets and demonstrated the sensitivity of 83+/-6% compared to manual segmentation on a per voxel basis as primary endpoint. Gross cartilage volume measurement yielded an average error of 9+/-7% as secondary endpoint. For cartilage being a thin structure, already small deviations in distance result in large errors on a per voxel basis, rendering the primary endpoint a hard criterion.

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

NASA Astrophysics Data System (ADS)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

Dynamically corrected gates for singlet-triplet spin qubits with control-dependent errors

NASA Astrophysics Data System (ADS)

Jacobson, N. Tobias; Witzel, Wayne M.; Nielsen, Erik; Carroll, Malcolm S.

2013-03-01

Magnetic field inhomogeneity due to random polarization of quasi-static local magnetic impurities is a major source of environmentally induced error for singlet-triplet double quantum dot (DQD) spin qubits. Moreover, for singlet-triplet qubits this error may depend on the applied controls. This effect is significant when a static magnetic field gradient is applied to enable full qubit control. Through a configuration interaction analysis, we observe that the dependence of the field inhomogeneity-induced error on the DQD bias voltage can vary systematically as a function of the controls for certain experimentally relevant operating regimes. To account for this effect, we have developed a straightforward prescription for adapting dynamically corrected gate sequences that assume control-independent errors into sequences that compensate for systematic control-dependent errors. We show that accounting for such errors may lead to a substantial increase in gate fidelities. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Error simulation of paired-comparison-based scaling methods

NASA Astrophysics Data System (ADS)

Cui, Chengwu

2000-12-01

Subjective image quality measurement usually resorts to psycho physical scaling. However, it is difficult to evaluate the inherent precision of these scaling methods. Without knowing the potential errors of the measurement, subsequent use of the data can be misleading. In this paper, the errors on scaled values derived form paired comparison based scaling methods are simulated with randomly introduced proportion of choice errors that follow the binomial distribution. Simulation results are given for various combinations of the number of stimuli and the sampling size. The errors are presented in the form of average standard deviation of the scaled values and can be fitted reasonably well with an empirical equation that can be sued for scaling error estimation and measurement design. The simulation proves paired comparison based scaling methods can have large errors on the derived scaled values when the sampling size and the number of stimuli are small. Examples are also given to show the potential errors on actually scaled values of color image prints as measured by the method of paired comparison.

Gravity and isostatic anomaly maps of Greece produced

NASA Astrophysics Data System (ADS)

Lagios, E.; Chailas, S.; Hipkin, R. G.

A gravity anomaly map of Greece was first compiled in the early 1970s [Makris and Stavrou, 1984] from all available gravity data collected by different Hellenic institutions. However, to compose this map the data had to be smoothed to the point that many of the smaller-wavelength gravity anomalies were lost. New work begun in 1987 has resulted in the publication of an updated map [Lagios et al., 1994] and an isostatic anomaly map derived from it.The gravity data cover the area between east longitudes 19° and 27° and north latitudes 32° and 42°, organized in files of 100-km squares and grouped in 10-km squares using UTM zone 34 coordinates. Most of the data on land come from the gravity observations of Makris and Stavrou [1984] with additional data from the Institute of Geology and Mining Exploration, the Public Oil Corporation of Greece, and Athens University. These data were checked using techniques similar to those used in compiling the gravity anomaly map of the United States, but the horizontal gradient was used as a check rather than the gravity difference. Marine data were digitized from the maps of Morelli et al. [1975a, 1975b]. All gravity anomaly values are referred to the IGSN-71 system, reduced with the standard Bouger density of 2.67 Mg/m3. We estimate the errors of the anomalies in the continental part of Greece to be ±0.9 mGal; this is expected to be smaller over fairly flat regions. For stations whose height has been determined by leveling, the error is only ±0.3 mGal. For the marine areas, the errors are about ±5 mGal [Morelli, 1990].

Gradients and Non-Adiabatic Derivative Coupling Terms for Spin-Orbit Wavefunctions

DTIC Science & Technology

2011-06-01

derivative, symmetric to the first time derivative. Solutions to the Dirac equation simultaneously satisfy the simple relativistic wave equation, the...For Pooki vi Acknowledgments I would like to thank the members of my committee for their time and...Theorem..............................................................................191 Appendix J. The Symmetric Group

Implementation of neural network for color properties of polycarbonates

NASA Astrophysics Data System (ADS)

Saeed, U.; Ahmad, S.; Alsadi, J.; Ross, D.; Rizvi, G.

2014-05-01

In present paper, the applicability of artificial neural networks (ANN) is investigated for color properties of plastics. The neural networks toolbox of Matlab 6.5 is used to develop and test the ANN model on a personal computer. An optimal design is completed for 10, 12, 14,16,18 & 20 hidden neurons on single hidden layer with five different algorithms: batch gradient descent (GD), batch variable learning rate (GDX), resilient back-propagation (RP), scaled conjugate gradient (SCG), levenberg-marquardt (LM) in the feed forward back-propagation neural network model. The training data for ANN is obtained from experimental measurements. There were twenty two inputs including resins, additives & pigments while three tristimulus color values L*, a* and b* were used as output layer. Statistical analysis in terms of Root-Mean-Squared (RMS), absolute fraction of variance (R squared), as well as mean square error is used to investigate the performance of ANN. LM algorithm with fourteen neurons on hidden layer in Feed Forward Back-Propagation of ANN model has shown best result in the present study. The degree of accuracy of the ANN model in reduction of errors is proven acceptable in all statistical analysis and shown in results. However, it was concluded that ANN provides a feasible method in error reduction in specific color tristimulus values.

Flow tilt angle measurements using lidar anemometry

NASA Astrophysics Data System (ADS)

Dellwik, Ebba; Mann, Jakob

2010-05-01

A new way of estimating near-surface mean flow tilt angles from ground based Doppler lidar measurements is presented. The results are compared with traditional mast based in-situ sonic anemometry. The tilt angle assessed with the lidar is based on 10 or 30 minute mean values of the velocity field from a conically scanning lidar. In this mode of measurement, the lidar beam is rotated in a circle by a prism with a fixed angle to the vertical at varying focus distances. By fitting a trigonometric function to the scans, the mean vertical velocity can be estimated. Lidar measurements from (1) a fetch-limited beech forest site taken at 48-175m above ground level, (2) a reference site in flat agricultural terrain and (3) a second reference site in very complex terrain are presented. The method to derive flow tilt angles and mean vertical velocities from lidar has several advantages compared to sonic anemometry; there is no flow distortion caused by the instrument itself, there are no temperature effects and the instrument misalignment can be corrected for by comparing tilt estimates at various heights. Contrary to mast-based instruments, the lidar measures the wind field with the exact same alignment error at a multitude of heights. Disadvantages with estimating vertical velocities from a lidar compared to mast-based measurements are slightly increased levels of statistical errors due to limited sampling time, because the sampling is disjunct and a requirement for homogeneous flow. The estimated mean vertical velocity is biased if the flow over the scanned circle is not homogeneous. However, the error on the mean vertical velocity due to flow inhomogeneity can be approximated by a function of the angle of the lidar beam to the vertical, the measurement height and the vertical gradient of the mean vertical velocity, whereas the error due to flow inhomogeneity on the horizontal mean wind speed is independent of the lidar beam angle. For the presented measurements over forest, it is evaluated that the systematic error due to the inhomogeneity of the flow is less than 0.2 degrees. Other possibilities for utilizing lidars for flow tilt angle and mean vertical velocities are discussed.

Reciprocal subsidies and food web pathways leading to chum salmon fry in a temperate marine-terrestrial ecotone.

PubMed

Romanuk, Tamara N; Levings, Colin D

2010-04-08

Stable isotope analysis was used to determine the relative proportions of terrestrial and marine subsidies of carbon to invertebrates along a tidal gradient (low-intertidal, mid-intertidal, high-intertidal, supralittoral) and to determine the relative importance of terrestrial carbon in food web pathways leading to chum salmon fry Oncorhynchus keta (Walbaum) in Howe Sound, British Columbia. We found a clear gradient in the proportion of terrestrially derived carbon along the tidal gradient ranging from 68% across all invertebrate taxa in the supralittoral to 25% in the high-intertidal, 20% in the mid-intertidal, and 12% in the low-intertidal. Stable isotope values of chum salmon fry indicated carbon contributions from both terrestrial and marine sources, with terrestrially derived carbon ranging from 12.8 to 61.5% in the muscle tissue of chum salmon fry (mean 30%). Our results provide evidence for reciprocal subsidies of marine and terrestrially derived carbon on beaches in the estuary and suggest that the vegetated supralittoral is an important trophic link in supplying terrestrial carbon to nearshore food webs.

Osteochondral tissue formation through adipose-derived stromal cell differentiation on biomimetic polycaprolactone nanofibrous scaffolds with graded insulin and Beta-glycerophosphate concentrations.

PubMed

Erisken, Cevat; Kalyon, Dilhan M; Wang, Hongjun; Ornek-Ballanco, Ceren; Xu, Jiahua

2011-05-01

The ability to fabricate tissue engineering scaffolds containing systematic gradients in the distributions of stimulators provides additional means for the mimicking of the important gradients observed in native tissues. Here the concentration distributions of two bioactive agents were varied concomitantly for the first time (one increasing, whereas the other decreasing monotonically) in between the two sides of a nanofibrous scaffold. This was achieved via the application of a new processing method, that is, the twin-screw extrusion and electrospinning method, to generate gradients of insulin, a stimulator of chondrogenic differentiation, and β-glycerophosphate (β-GP), for mineralization. The graded poly(ɛ-caprolactone) mesh was seeded with human adipose-derived stromal cells and cultured over 8 weeks. The resulting tissue constructs were analyzed for and revealed indications of selective differentiation of human adipose-derived stromal cells toward chondrogenic lineage and mineralization as functions of position as a result of the corresponding concentrations of insulin and β-GP. Chondrogenic differentiation of the stem cells increased at insulin-rich locations and mineralization increased at β-GP-rich locations.

Retrieval Assimilation and Modeling of Atmospheric Water Vapor from Ground- and Space-Based GPS Networks: Investigation of the Global and Regional Hydrological Cycles

NASA Technical Reports Server (NTRS)

Dickey, Jean O.

1999-01-01

Uncertainty over the response of the atmospheric hydrological cycle (particularly the distribution of water vapor and cloudiness) to anthropogenic forcing is a primary source of doubt in current estimates of global climate sensitivity, which raises severe difficulties in evaluating its likely societal impact. Fortunately, a variety of advanced techniques and sensors are beginning to shed new light on the atmospheric hydrological cycle. One of the most promising makes use of the sensitivity of the Global Positioning System (GPS) to the thermodynamic state, and in particular the water vapor content, of the atmosphere through which the radio signals propagate. Our strategy to derive the maximum benefit for hydrological studies from the rapidly increasing GPS data stream will proceed in three stages: (1) systematically analyze and archive quality-controlled retrievals using state-of-the-art techniques; (2) employ both currently available and innovative assimilation procedures to incorporate these determinations into advanced regional and global atmospheric models and assess their effects; and (3) apply the results to investigate selected scientific issues of relevance to regional and global hydrological studies. An archive of GPS-based estimation of total zenith delay (TZD) data and water vapor where applicable has been established with expanded automated quality control. The accuracy of the GPS estimates is being monitored; the investigation of systematic errors is ongoing using comparisons with water vapor radiometers. Meteorological packages have been implemented. The accuracy and utilization of the TZD estimates has been improved by implementing a troposphere gradient model. GPS-based gradients have been validated as real atmospheric moisture gradients, establishing a link between the estimated gradients and the passage of weather fronts. We have developed a generalized ray tracing inversion scheme that can be used to analyze occultation data acquired from space- or land-based receivers. The National Center for Atmospheric Research mesoscale model (version MM5) has been adapted for Southern California, and assimilation studies are underway. Additional information is contained in the original.

GOCE and Future Gravity Missions for Geothermal Energy Exploitation

NASA Astrophysics Data System (ADS)

Pastorutti, Alberto; Braitenberg, Carla; Pivetta, Tommaso; Mariani, Patrizia

2016-08-01

Geothermal energy is a valuable renewable energy source the exploitation of which contributes to the worldwide reduction of consumption of fossil fuels oil and gas. The exploitation of geothermal energy is facilitated where the thermal gradient is higher than average leading to increased surface heat flow. Apart from the hydrologic circulation properties which depend on rock fractures and are important due to the heat transportation from the hotter layers to the surface, essential properties that increase the thermal gradient are crustal thinning and radiogenic heat producing rocks. Crustal thickness and rock composition form the link to the exploration with the satellite derived gravity field, because both induce subsurface mass changes that generate observable gravity anomalies. The recognition of gravity as a useful investigation tool for geothermal energy lead to a cooperation with ESA and the International Renewable Energy Agency (IRENA) that included the GOCE derived gravity field in the online geothermal energy investigation tool of the IRENA database. The relation between the gravity field products as the free air gravity anomaly, the Bouguer and isostatic anomalies and the heat flow values is though not straightforward and has not a unique relationship. It is complicated by the fact that it depends on the geodynamical context, on the geologic context and the age of the crustal rocks. Globally the geological context and geodynamical history of an area is known close to everywhere, so that a specific known relationship between gravity and geothermal potential can be applied. In this study we show the results of a systematic analysis of the problem, including some simulations of the key factors. The study relies on the data of GOCE and the resolution and accuracy of this satellite. We also give conclusions on the improved exploration power of a gravity mission with higher spatial resolution and reduced data error, as could be achieved in principle by flying an atom interferometer sensor on board a satellite.

An approach to the analysis of performance of quasi-optimum digital phase-locked loops.

NASA Technical Reports Server (NTRS)

Polk, D. R.; Gupta, S. C.

1973-01-01

An approach to the analysis of performance of quasi-optimum digital phase-locked loops (DPLL's) is presented. An expression for the characteristic function of the prior error in the state estimate is derived, and from this expression an infinite dimensional equation for the prior error variance is obtained. The prior error-variance equation is a function of the communication system model and the DPLL gain and is independent of the method used to derive the DPLL gain. Two approximations are discussed for reducing the prior error-variance equation to finite dimension. The effectiveness of one approximation in analyzing DPLL performance is studied.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ba, Yan; Liu, Haihu; Li, Qing

2016-08-15

In this paper, we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multi-relaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a new form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulatedmore » with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike/bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.« less

Sensitivity Analysis of Nuclide Importance to One-Group Neutron Cross Sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sekimoto, Hiroshi; Nemoto, Atsushi; Yoshimura, Yoshikane

The importance of nuclides is useful when investigating nuclide characteristics in a given neutron spectrum. However, it is derived using one-group microscopic cross sections, which may contain large errors or uncertainties. The sensitivity coefficient shows the effect of these errors or uncertainties on the importance.The equations for calculating sensitivity coefficients of importance to one-group nuclear constants are derived using the perturbation method. Numerical values are also evaluated for some important cases for fast and thermal reactor systems.Many characteristics of the sensitivity coefficients are derived from the derived equations and numerical results. The matrix of sensitivity coefficients seems diagonally dominant. However,more » it is not always satisfied in a detailed structure. The detailed structure of the matrix and the characteristics of coefficients are given.By using the obtained sensitivity coefficients, some demonstration calculations have been performed. The effects of error and uncertainty of nuclear data and of the change of one-group cross-section input caused by fuel design changes through the neutron spectrum are investigated. These calculations show that the sensitivity coefficient is useful when evaluating error or uncertainty of nuclide importance caused by the cross-section data error or uncertainty and when checking effectiveness of fuel cell or core design change for improving neutron economy.« less

The Development of MST Test Information for the Prediction of Test Performances

ERIC Educational Resources Information Center

Park, Ryoungsun; Kim, Jiseon; Chung, Hyewon; Dodd, Barbara G.

2017-01-01

The current study proposes novel methods to predict multistage testing (MST) performance without conducting simulations. This method, called MST test information, is based on analytic derivation of standard errors of ability estimates across theta levels. We compared standard errors derived analytically to the simulation results to demonstrate the…

Does the Budyko curve reflect a maximum power state of hydrological systems? A backward analysis

NASA Astrophysics Data System (ADS)

Westhoff, M.; Zehe, E.; Archambeau, P.; Dewals, B.

2015-08-01

Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving runoff and evaporation for a simple one-box model. We did this in such a way that when the conductances are optimized with the maximum power principle, the steady state behaviour of the model leads exactly to a point on the Budyko curve. Subsequently we derived gradients that, under constant forcing, resulted in a Budyko curve following the asymptotes closely. With these gradients we explored the sensitivity of dry spells and dynamics in actual evaporation. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves derived with dynamics in rainfall and evaporation. This indicates that the maximum power principle may be used (i) to derive the Budyko curve and (ii) to move away from the empiricism in free parameters present in many Budyko functions. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-01

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-21

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Refinements in the short-circuit technique and its application to active potassium transport across the cecropia midgut.

PubMed

Wood, J L; Moreton, R B

1978-12-01

1. The conventional, two-electrode method for measuring potential difference across an epithelium is subject to error due to potential gradients caused by current flow in the bathing medium. Mathematical analysis shows that the error in measuring short-circuit current is proportional to the resistivity of the bathing medium and to the separation of the two recording electrodes. It is particularly serious for the insect larval midgut, where the resistivity of the medium is high, and that of the tissue is low. 2. A system has been devised, which uses a third recording electrode to monitor directly the potential gradient in the bathing medium. By suitable electrical connexions, the gradient can be automatically compensated, leaving a residual error which depends on the thickness of the tissue, but not on the electrode separation. Because the thicknesses of most epithelia are smaller than the smallest practical electrode spacing, this error is smaller than that inherent in a two-electrode system. 3. Since voltage-gradients are automatically compensated, it is possible to obtain continuous readings of potential and current. A 'voltage-clamp' circuit is described, which allows the time-course of the short-circuit current to be studied. 4.The three-electrode system has been used to study the larval midgut of Hyalophora cecropia. The average results from five experiments were: initial potential difference (open-circuit): 98+/-11 mV (S.E.M.); short-circuit current at time 60 min: 498+/-160 microA cm=2; 'steady-state' resistance at 60 min: 150+/-26 omega cm2. The current is equivalent to a net potassium transport of 18.6 mu-equiv cm-2 h-1. 5. The electrical parameters of the midgut change rapidly with time. The potential difference decays with a half-time of about 158 min, the resistance increases with a half-time of about 16 min, and the short-circuit current decays as the sum of two exponential terms, with half-times of about 16 and 158 min respectively. In addition, potential and short-circuit current show transient responses to step changes. 6. The properties of the midgut are compared with those of other transporting epithelia, and their dependence on the degree of folding of the preparation is discussed. Their time-dependence is discussed in the context of changes in potassium content of the tissue, and the implications for measurements depending on the assumption of a steady state are outlined.

Characterization of the startup transient electrokinetic flow in rectangular channels of arbitrary dimensions, zeta potential distribution, and time-varying pressure gradient.

PubMed

Miller, Andrew; Villegas, Arturo; Diez, F Javier

2015-03-01

The solution to the startup transient EOF in an arbitrary rectangular microchannel is derived analytically and validated experimentally. This full 2D transient solution describes the evolution of the flow through five distinct periods until reaching a final steady state. The derived analytical velocity solution is validated experimentally for different channel sizes and aspect ratios under time-varying pressure gradients. The experiments used a time resolved micro particle image velocimetry technique to calculate the startup transient velocity profiles. The measurements captured the effect of time-varying pressure gradient fields derived in the analytical solutions. This is tested by using small reservoirs at both ends of the channel which allowed a time-varying pressure gradient to develop with a time scale on the order of the transient EOF. Results showed that under these common conditions, the effect of the pressure build up in the reservoirs on the temporal development of the transient startup EOF in the channels cannot be neglected. The measurements also captured the analytical predictions for channel walls made of different materials (i.e., zeta potentials). This was tested in channels that had three PDMS and one quartz wall, resulting in a flow with an asymmetric velocity profile due to variations in the zeta potential between the walls. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Modularization of gradient-index optical design using wavefront matching enabled optimization.

PubMed

Nagar, Jogender; Brocker, Donovan E; Campbell, Sawyer D; Easum, John A; Werner, Douglas H

2016-05-02

This paper proposes a new design paradigm which allows for a modular approach to replacing a homogeneous optical lens system with a higher-performance GRadient-INdex (GRIN) lens system using a WaveFront Matching (WFM) method. In multi-lens GRIN systems, a full-system-optimization approach can be challenging due to the large number of design variables. The proposed WFM design paradigm enables optimization of each component independently by explicitly matching the WaveFront Error (WFE) of the original homogeneous component at the exit pupil, resulting in an efficient design procedure for complex multi-lens systems.

Radiation-induced refraction artifacts in the optical CT readout of polymer gel dosimeters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campbell, Warren G.; Jirasek, Andrew, E-mail: jirasek@uvic.ca; Wells, Derek M.

2014-11-01

Purpose: The objective of this work is to demonstrate imaging artifacts that can occur during the optical computed tomography (CT) scanning of polymer gel dosimeters due to radiation-induced refractive index (RI) changes in polyacrylamide gels. Methods: A 1 L cylindrical polyacrylamide gel dosimeter was irradiated with 3 × 3 cm{sup 2} square beams of 6 MV photons. A prototype fan-beam optical CT scanner was used to image the dosimeter. Investigative optical CT scans were performed to examine two types of rayline bending: (i) bending within the plane of the fan-beam and (ii) bending out the plane of the fan-beam. Tomore » address structured errors, an iterative Savitzky–Golay (ISG) filtering routine was designed to filter 2D projections in sinogram space. For comparison, 2D projections were alternatively filtered using an adaptive-mean (AM) filter. Results: In-plane rayline bending was most notably observed in optical CT projections where rays of the fan-beam confronted a sustained dose gradient that was perpendicular to their trajectory but within the fan-beam plane. These errors caused distinct streaking artifacts in image reconstructions due to the refraction of higher intensity rays toward more opaque regions of the dosimeter. Out-of-plane rayline bending was observed in slices of the dosimeter that featured dose gradients perpendicular to the plane of the fan-beam. These errors caused widespread, severe overestimations of dose in image reconstructions due to the higher-than-actual opacity that is perceived by the scanner when light is bent off of the detector array. The ISG filtering routine outperformed AM filtering for both in-plane and out-of-plane rayline errors caused by radiation-induced RI changes. For in-plane rayline errors, streaks in an irradiated region (>7 Gy) were as high as 49% for unfiltered data, 14% for AM, and 6% for ISG. For out-of-plane rayline errors, overestimations of dose in a low-dose region (∼50 cGy) were as high as 13 Gy for unfiltered data, 10 Gy for AM, and 3.1 Gy for ISG. The ISG routine also addressed unrelated artifacts that previously needed to be manually removed in sinogram space. However, the ISG routine blurred reconstructions, causing losses in spatial resolution of ∼5 mm in the plane of the fan-beam and ∼8 mm perpendicular to the fan-beam. Conclusions: This paper reveals a new category of imaging artifacts that can affect the optical CT readout of polyacrylamide gel dosimeters. Investigative scans show that radiation-induced RI changes can cause significant rayline errors when rays confront a prolonged dose gradient that runs perpendicular to their trajectory. In fan-beam optical CT, these errors manifested in two ways: (1) distinct streaking artifacts caused by in-plane rayline bending and (2) severe overestimations of opacity caused by rays bending out of the fan-beam plane and missing the detector array. Although the ISG filtering routine mitigated these errors better than an adaptive-mean filtering routine, it caused unacceptable losses in spatial resolution.« less

Radiation-induced refraction artifacts in the optical CT readout of polymer gel dosimeters.

PubMed

Campbell, Warren G; Wells, Derek M; Jirasek, Andrew

2014-11-01

The objective of this work is to demonstrate imaging artifacts that can occur during the optical computed tomography (CT) scanning of polymer gel dosimeters due to radiation-induced refractive index (RI) changes in polyacrylamide gels. A 1 L cylindrical polyacrylamide gel dosimeter was irradiated with 3 × 3 cm(2) square beams of 6 MV photons. A prototype fan-beam optical CT scanner was used to image the dosimeter. Investigative optical CT scans were performed to examine two types of rayline bending: (i) bending within the plane of the fan-beam and (ii) bending out the plane of the fan-beam. To address structured errors, an iterative Savitzky-Golay (ISG) filtering routine was designed to filter 2D projections in sinogram space. For comparison, 2D projections were alternatively filtered using an adaptive-mean (AM) filter. In-plane rayline bending was most notably observed in optical CT projections where rays of the fan-beam confronted a sustained dose gradient that was perpendicular to their trajectory but within the fan-beam plane. These errors caused distinct streaking artifacts in image reconstructions due to the refraction of higher intensity rays toward more opaque regions of the dosimeter. Out-of-plane rayline bending was observed in slices of the dosimeter that featured dose gradients perpendicular to the plane of the fan-beam. These errors caused widespread, severe overestimations of dose in image reconstructions due to the higher-than-actual opacity that is perceived by the scanner when light is bent off of the detector array. The ISG filtering routine outperformed AM filtering for both in-plane and out-of-plane rayline errors caused by radiation-induced RI changes. For in-plane rayline errors, streaks in an irradiated region (>7 Gy) were as high as 49% for unfiltered data, 14% for AM, and 6% for ISG. For out-of-plane rayline errors, overestimations of dose in a low-dose region (∼50 cGy) were as high as 13 Gy for unfiltered data, 10 Gy for AM, and 3.1 Gy for ISG. The ISG routine also addressed unrelated artifacts that previously needed to be manually removed in sinogram space. However, the ISG routine blurred reconstructions, causing losses in spatial resolution of ∼5 mm in the plane of the fan-beam and ∼8 mm perpendicular to the fan-beam. This paper reveals a new category of imaging artifacts that can affect the optical CT readout of polyacrylamide gel dosimeters. Investigative scans show that radiation-induced RI changes can cause significant rayline errors when rays confront a prolonged dose gradient that runs perpendicular to their trajectory. In fan-beam optical CT, these errors manifested in two ways: (1) distinct streaking artifacts caused by in-plane rayline bending and (2) severe overestimations of opacity caused by rays bending out of the fan-beam plane and missing the detector array. Although the ISG filtering routine mitigated these errors better than an adaptive-mean filtering routine, it caused unacceptable losses in spatial resolution.

Note on the Effect of Horizontal Gradients for Nadir-Viewing Microwave and Infrared Sounders

NASA Technical Reports Server (NTRS)

Joiner, J.; Poli, P.

2004-01-01

Passive microwave and infrared nadir sounders such as the Advanced Microwave Sounding Unit A (AMSU-A) and the Atmospheric InfraRed Sounder (AIRS), both flying on NASA s EOS Aqua satellite, provide information about vertical temperature and humidity structure that is used in data assimilation systems for numerical weather prediction and climate applications. These instruments scan cross track so that at the satellite swath edges, the satellite zenith angles can reach approx. 60 deg. The emission path through the atmosphere as observed by the satellite is therefore slanted with respect to the satellite footprint s zenith. Although radiative transfer codes currently in use at operational centers use the appropriate satellite zenith angle to compute brightness temperature, the input atmospheric fields are those from the vertical profile above the center of the satellite footprint. If horizontal gradients are present in the atmospheric fields, the use of a vertical atmospheric profile may produce an error. This note attempts to quantify the effects of horizontal gradients on AIRS and AMSU-A channels by computing brightness temperatures with accurate slanted atmospheric profiles. We use slanted temperature, water vapor, and ozone fields from data assimilation systems. We compare the calculated slanted and vertical brightness temperatures with AIRS and AMSU-A observations. We show that the effects of horizontal gradients on these sounders are generally small and below instrument noise. However, there are cases where the effects are greater than the instrument noise and may produce erroneous increments in an assimilation system. The majority of the affected channels have weighting functions that peak in the upper troposphere (water vapor sensitive channels) and above (temperature sensitive channels) and are unlikely t o significantly impact tropospheric numerical weather prediction. However, the errors could be significant for other applications such as stratospheric analysis. Gradients in ozone and tropospheric temperature appear to be well captured by the analyses. In contrast, gradients in upper stratospheric and mesospheric temperature as well as upper tropospheric humidity are less well captured. This is likely due in part to a lack of data to specify these fields accurately in the analyses. Advanced new sounders, like AIRS, may help to better specify these fields in the future.

Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging.

PubMed

Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Tryggestad, Erik J; Gunter, Jeffrey L; McGee, Kiaran P; Litwiller, Daniel V; Hwang, Ken-Pin; Bernstein, Matt A

2017-05-01

Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI. A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections. Copyright © 2016 Elsevier Inc. All rights reserved.

Scale matters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L. G.

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Scale matters

DOE PAGES

Margolin, L. G.

2018-03-19

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Induced electric currents in the Alaska oil pipeline measured by gradient, fluxgate, and SQUID magnetometers

NASA Technical Reports Server (NTRS)

Campbell, W. H.; Zimmerman, J. E.

1979-01-01

The field gradient method for observing the electric currents in the Alaska pipeline provided consistent values for both the fluxgate and SQUID method of observation. These currents were linearly related to the regularly measured electric and magnetic field changes. Determinations of pipeline current were consistent with values obtained by a direct connection, current shunt technique at a pipeline site about 9.6 km away. The gradient method has the distinct advantage of portability and buried- pipe capability. Field gradients due to the pipe magnetization, geological features, or ionospheric source currents do not seem to contribute a measurable error to such pipe current determination. The SQUID gradiometer is inherently sensitive enough to detect very small currents in a linear conductor at 10 meters, or conversely, to detect small currents of one amphere or more at relatively great distances. It is fairly straightforward to achieve imbalance less than one part in ten thousand, and with extreme care, one part in one million or better.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Comparison of Alcator C data with the Rebut-Lallia-Watkins critical gradient scaling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, I.H.

The critical temperature gradient model of Rebut, Lallia and Watkins is compared with data from Alcator C. The predicted central electron temperature is derived from the model, and a simple analytic formula is given. It is found to be in quite good agreement with the observed temperatures on Alcator C under ohmic heating conditions. However, the thermal diffusivity postulated in the model for gradients that exceed the critical is not consistent with the observed electron heating by Lower Hybrid waves.

Method and means for a spatial and temporal probe for laser-generated plumes based on density gradients

DOEpatents

Yeung, Edward S.; Chen, Guoying

1990-05-01

A method and means for a spatial and temporal probe for laser generated plumes based on density gradients includes generation of a plume of vaporized material from a surface by an energy source. The probe laser beam is positioned so that the plume passes through the probe laser beam. Movement of the probe laser beam caused by refraction from the density gradient of the plume is monitored. Spatial and temporal information, correlated to one another, is then derived.

Primer vector theory and applications

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1975-01-01

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.

Improved alternating gradient transport and focusing of neutral molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalnins, Juris; Lambertson, Glen; Gould, Harvey

2001-12-02

Polar molecules, in strong-field seeking states, can be transported and focused by an alternating sequence of electric field gradients that focus in one transverse direction while defocusing in the other. We show by calculation and numerical simulation, how one may greatly improve the alternating gradient transport and focusing of molecules. We use a new optimized multipole lens design, a FODO lattice beam transport line, and lenses to match the beam transport line to the beam source and the final focus. We derive analytic expressions for the potentials, fields, and gradients that may be used to design these lenses. We describemore » a simple lens optimization procedure and derive the equations of motion for tracking molecules through a beam transport line. As an example, we model a straight beamline that transports a 560 m/s jet-source beam of methyl fluoride molecules 15 m from its source and focuses it to 2 mm diameter. We calculate the beam transport line acceptance and transmission, for a beam with velocity spread, and estimate the transmitted intensity for specified source conditions. Possible applications are discussed.« less

Monoplane 3D-2D registration of cerebral angiograms based on multi-objective stratified optimization

NASA Astrophysics Data System (ADS)

Aksoy, T.; Špiclin, Ž.; Pernuš, F.; Unal, G.

2017-12-01

Registration of 3D pre-interventional to 2D intra-interventional medical images has an increasingly important role in surgical planning, navigation and treatment, because it enables the physician to co-locate depth information given by pre-interventional 3D images with the live information in intra-interventional 2D images such as x-ray. Most tasks during image-guided interventions are carried out under a monoplane x-ray, which is a highly ill-posed problem for state-of-the-art 3D to 2D registration methods. To address the problem of rigid 3D-2D monoplane registration we propose a novel multi-objective stratified parameter optimization, wherein a small set of high-magnitude intensity gradients are matched between the 3D and 2D images. The stratified parameter optimization matches rotation templates to depth templates, first sampled from projected 3D gradients and second from the 2D image gradients, so as to recover 3D rigid-body rotations and out-of-plane translation. The objective for matching was the gradient magnitude correlation coefficient, which is invariant to in-plane translation. The in-plane translations are then found by locating the maximum of the gradient phase correlation between the best matching pair of rotation and depth templates. On twenty pairs of 3D and 2D images of ten patients undergoing cerebral endovascular image-guided intervention the 3D to monoplane 2D registration experiments were setup with a rather high range of initial mean target registration error from 0 to 100 mm. The proposed method effectively reduced the registration error to below 2 mm, which was further refined by a fast iterative method and resulted in a high final registration accuracy (0.40 mm) and high success rate (> 96%). Taking into account a fast execution time below 10 s, the observed performance of the proposed method shows a high potential for application into clinical image-guidance systems.

SDSS-IV MaNGA: The Spatially Resolved Stellar Initial Mass Function in ˜400 Early-Type Galaxies

NASA Astrophysics Data System (ADS)

Parikh, Taniya; Thomas, Daniel; Maraston, Claudia; Westfall, Kyle B.; Goddard, Daniel; Lian, Jianhui; Meneses-Goytia, Sofia; Jones, Amy; Vaughan, Sam; Andrews, Brett H.; Bershady, Matthew; Bizyaev, Dmitry; Brinkmann, Jonathan; Brownstein, Joel R.; Bundy, Kevin; Drory, Niv; Emsellem, Eric; Law, David R.; Newman, Jeffrey A.; Roman-Lopes, Alexandre; Wake, David; Yan, Renbin; Zheng, Zheng

2018-03-01

MaNGA provides the opportunity to make precise spatially resolved measurements of the IMF slope in galaxies owing to its unique combination of spatial resolution, wavelength coverage and sample size. We derive radial gradients in age, element abundances and IMF slope analysing optical and near-infrared absorption features from stacked spectra out to the half-light radius of 366 early-type galaxies with masses 9.9 - 10.8 log M/M⊙. We find flat gradients in age and [α/Fe] ratio, as well as negative gradients in metallicity, consistent with the literature. We further derive significant negative gradients in the [Na/Fe] ratio with galaxy centres being well enhanced in Na abundance by up to 0.5 dex. Finally, we find a gradient in IMF slope with a bottom-heavy IMF in the centre (typical mass excess factor of 1.5) and a Milky Way-type IMF at the half-light radius. This pattern is mass-dependent with the lowest mass galaxies in our sample featuring only a shallow gradient around a Milky Way IMF. Our results imply the local IMF-σ relation within galaxies to be even steeper than the global relation and hint towards the local metallicity being the dominating factor behind the IMF variations. We also employ different stellar population models in our analysis and show that a radial IMF gradient is found independently of the stellar population model used. A similar analysis of the Wing-Ford band provides inconsistent results and further evidence of the difficulty in measuring and modelling this particular feature.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

Analysis of bacterial migration; 1: Numerical solution of balance equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frymier, P.D.; Ford, R.M.; Cummings, P.T.

1994-04-01

Chemotaxis describes the ability of motile bacteria to bias their motion in the direction of increasing gradients of chemicals, usually energy sources, known as attractants. In experimental studies of the migration of chemotactic bacteria, 1-D phenomenological cell balance equations have been used to quantitatively analyze experimental observations. While attractive for their simplicity and the ease of solution, they are limited in the strict mathematical sense to the situation in which individual bacteria are confined to motion in one dimension and respond to attractant gradients in one dimension only. Recently, Ford and Cummings (1992) reduced the general 3-D cell balance equationmore » of Alt (1980) to obtain an equation describing the migration of a bacterial population in response to a 1-D attractant gradient. Solutions of this equation for single gradients of attractants are compared to those of 1-D balance equations, results from cellular dynamics simulations, and experimental data from the authors' laboratory for E. coli responding to [alpha]-methylaspartate. The authors also investigate two aspects of the experimentally derived expression for the tumbling probability: the effect of different models for the down-gradient swimming behavior of the bacteria and the validity of ignoring the temporal derivative of the attractant concentration.« less

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Predicting longshore gradients in longshore transport: the CERC formula compared to Delft3D

USGS Publications Warehouse

List, Jeffrey H.; Hanes, Daniel M.; Ruggiero, Peter

2007-01-01

The prediction of longshore transport gradients is critical for forecasting shoreline change. We employ simple test cases consisting of shoreface pits at varying distances from the shoreline to compare the longshore transport gradients predicted by the CERC formula against results derived from the process-based model Delft3D. Results show that while in some cases the two approaches give very similar results, in many cases the results diverge greatly. Although neither approach is validated with field data here, the Delft3D-based transport gradients provide much more consistent predictions of erosional and accretionary zones as the pit location varies across the shoreface.

Gradient estimates on the weighted p-Laplace heat equation

NASA Astrophysics Data System (ADS)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Regional recovery of the disturbing gravitational potential by inverting satellite gravitational gradients

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Hamáčková, Eliška; Novák, Pavel

2016-04-01

Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m2 s-2.

Standard Errors and Confidence Intervals of Norm Statistics for Educational and Psychological Tests.

PubMed

Oosterhuis, Hannah E M; van der Ark, L Andries; Sijtsma, Klaas

2016-11-14

Norm statistics allow for the interpretation of scores on psychological and educational tests, by relating the test score of an individual test taker to the test scores of individuals belonging to the same gender, age, or education groups, et cetera. Given the uncertainty due to sampling error, one would expect researchers to report standard errors for norm statistics. In practice, standard errors are seldom reported; they are either unavailable or derived under strong distributional assumptions that may not be realistic for test scores. We derived standard errors for four norm statistics (standard deviation, percentile ranks, stanine boundaries and Z-scores) under the mild assumption that the test scores are multinomially distributed. A simulation study showed that the standard errors were unbiased and that corresponding Wald-based confidence intervals had good coverage. Finally, we discuss the possibilities for applying the standard errors in practical test use in education and psychology. The procedure is provided via the R function check.norms, which is available in the mokken package.

Introductory Linear Regression Programs in Undergraduate Chemistry.

ERIC Educational Resources Information Center

Gale, Robert J.

1982-01-01

Presented are simple programs in BASIC and FORTRAN to apply the method of least squares. They calculate gradients and intercepts and express errors as standard deviations. An introduction of undergraduate students to such programs in a chemistry class is reviewed, and issues instructors should be aware of are noted. (MP)

Research on particle swarm optimization algorithm based on optimal movement probability

NASA Astrophysics Data System (ADS)

Ma, Jianhong; Zhang, Han; He, Baofeng

2017-01-01

The particle swarm optimization algorithm to improve the control precision, and has great application value training neural network and fuzzy system control fields etc.The traditional particle swarm algorithm is used for the training of feed forward neural networks,the search efficiency is low, and easy to fall into local convergence.An improved particle swarm optimization algorithm is proposed based on error back propagation gradient descent. Particle swarm optimization for Solving Least Squares Problems to meme group, the particles in the fitness ranking, optimization problem of the overall consideration, the error back propagation gradient descent training BP neural network, particle to update the velocity and position according to their individual optimal and global optimization, make the particles more to the social optimal learning and less to its optimal learning, it can avoid the particles fall into local optimum, by using gradient information can accelerate the PSO local search ability, improve the multi beam particle swarm depth zero less trajectory information search efficiency, the realization of improved particle swarm optimization algorithm. Simulation results show that the algorithm in the initial stage of rapid convergence to the global optimal solution can be near to the global optimal solution and keep close to the trend, the algorithm has faster convergence speed and search performance in the same running time, it can improve the convergence speed of the algorithm, especially the later search efficiency.

A fast referenceless PRFS-based MR thermometry by phase finite difference

NASA Astrophysics Data System (ADS)

Zou, Chao; Shen, Huan; He, Mengyue; Tie, Changjun; Chung, Yiu-Cho; Liu, Xin

2013-08-01

Proton resonance frequency shift-based MR thermometry is a promising temperature monitoring approach for thermotherapy but its accuracy is vulnerable to inter-scan motion. Model-based referenceless thermometry has been proposed to address this problem but phase unwrapping is usually needed before the model fitting process. In this paper, a referenceless MR thermometry method using phase finite difference that avoids the time consuming phase unwrapping procedure is proposed. Unlike the previously proposed phase gradient technique, the use of finite difference in the new method reduces the fitting error resulting from the ringing artifacts associated with phase discontinuity in the calculation of the phase gradient image. The new method takes into account the values at the perimeter of the region of interest because of their direct relevance to the extrapolated baseline phase of the region of interest (where temperature increase takes place). In simulation study, in vivo and ex vivo experiments, the new method has a root-mean-square temperature error of 0.35 °C, 1.02 °C and 1.73 °C compared to 0.83 °C, 2.81 °C, and 3.76 °C from the phase gradient method, respectively. The method also demonstrated a slightly higher, albeit small, temperature accuracy than the original referenceless MR thermometry method. The proposed method is computationally efficient (∼0.1 s per image), making it very suitable for the real time temperature monitoring.

An Adaptive Orientation Estimation Method for Magnetic and Inertial Sensors in the Presence of Magnetic Disturbances

PubMed Central

Fan, Bingfei; Li, Qingguo; Wang, Chao; Liu, Tao

2017-01-01

Magnetic and inertial sensors have been widely used to estimate the orientation of human segments due to their low cost, compact size and light weight. However, the accuracy of the estimated orientation is easily affected by external factors, especially when the sensor is used in an environment with magnetic disturbances. In this paper, we propose an adaptive method to improve the accuracy of orientation estimations in the presence of magnetic disturbances. The method is based on existing gradient descent algorithms, and it is performed prior to sensor fusion algorithms. The proposed method includes stationary state detection and magnetic disturbance severity determination. The stationary state detection makes this method immune to magnetic disturbances in stationary state, while the magnetic disturbance severity determination helps to determine the credibility of magnetometer data under dynamic conditions, so as to mitigate the negative effect of the magnetic disturbances. The proposed method was validated through experiments performed on a customized three-axis instrumented gimbal with known orientations. The error of the proposed method and the original gradient descent algorithms were calculated and compared. Experimental results demonstrate that in stationary state, the proposed method is completely immune to magnetic disturbances, and in dynamic conditions, the error caused by magnetic disturbance is reduced by 51.2% compared with original MIMU gradient descent algorithm. PMID:28534858

Deriving Color-Color Transformations for VRI Photometry

NASA Astrophysics Data System (ADS)

Taylor, B. J.; Joner, M. D.

2006-12-01

In this paper, transformations between Cousins R-I and other indices are considered. New transformations to Cousins V-R and Johnson V-K are derived, a published transformation involving T1-T2 on the Washington system is rederived, and the basis for a transformation involving b-y is considered. In addition, a statistically rigorous procedure for deriving such transformations is presented and discussed in detail. Highlights of the discussion include (1) the need for statistical analysis when least-squares relations are determined and interpreted, (2) the permitted forms and best forms for such relations, (3) the essential role played by accidental errors, (4) the decision process for selecting terms to appear in the relations, (5) the use of plots of residuals, (6) detection of influential data, (7) a protocol for assessing systematic effects from absorption features and other sources, (8) the reasons for avoiding extrapolation of the relations, (9) a protocol for ensuring uniformity in data used to determine the relations, and (10) the derivation and testing of the accidental errors of those data. To put the last of these subjects in perspective, it is shown that rms errors for VRI photometry have been as small as 6 mmag for more than three decades and that standard errors for quantities derived from such photometry can be as small as 1 mmag or less.

A novel measure of reliability in Diffusion Tensor Imaging after data rejections due to subject motion.

PubMed

Sairanen, V; Kuusela, L; Sipilä, O; Savolainen, S; Vanhatalo, S

2017-02-15

Diffusion Tensor Imaging (DTI) is commonly challenged by subject motion during data acquisition, which often leads to corrupted image data. Currently used procedure in DTI analysis is to correct or completely reject such data before tensor estimations, however assessing the reliability and accuracy of the estimated tensor in such situations has evaded previous studies. This work aims to define the loss of data accuracy with increasing image rejections, and to define a robust method for assessing reliability of the result at voxel level. We carried out simulations of every possible sub-scheme (N=1,073,567,387) of Jones30 gradient scheme, followed by confirming the idea with MRI data from four newborn and three adult subjects. We assessed the relative error of the most commonly used tensor estimates for DTI and tractography studies, fractional anisotropy (FA) and the major orientation vector (V1), respectively. The error was estimated using two measures, the widely used electric potential (EP) criteria as well as the rotationally variant condition number (CN). Our results show that CN and EP are comparable in situations with very few rejections, but CN becomes clearly more sensitive to depicting errors when more gradient vectors and images were rejected. The error in FA and V1 was also found depend on the actual FA level in the given voxel; low actual FA levels were related to high relative errors in the FA and V1 estimates. Finally, the results were confirmed with clinical MRI data. This showed that the errors after rejections are, indeed, inhomogeneous across brain regions. The FA and V1 errors become progressively larger when moving from the thick white matter bundles towards more superficial subcortical structures. Our findings suggest that i) CN is a useful estimator of data reliability at voxel level, and ii) DTI preprocessing with data rejections leads to major challenges when assessing brain tissue with lower FA levels, such as all newborn brain, as well as the adult superficial, subcortical areas commonly traced in precise connectivity analyses between cortical regions. Copyright © 2016 Elsevier Inc. All rights reserved.

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

The Swarm Initial Field Model for the 2014 Geomagnetic Field

NASA Technical Reports Server (NTRS)

Olsen, Nils; Hulot, Gauthier; Lesur, Vincent; Finlay, Christopher C.; Beggan, Ciaran; Chulliat, Arnaud; Sabaka, Terence J.; Floberghagen, Rune; Friis-Christensen, Eigil; Haagmans, Roger

2015-01-01

Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites, explicit advantage is taken of the constellation aspect by including east-west magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the north-south gradient. The SIFM static field shows excellent agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for east-west intensity differences between the lower satellite pair being only 0.12 nT.

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

Variation of haemoglobin extinction coefficients can cause errors in the determination of haemoglobin concentration measured by near-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Kim, J. G.; Liu, H.

2007-10-01

Near-infrared spectroscopy or imaging has been extensively applied to various biomedical applications since it can detect the concentrations of oxyhaemoglobin (HbO2), deoxyhaemoglobin (Hb) and total haemoglobin (Hbtotal) from deep tissues. To quantify concentrations of these haemoglobin derivatives, the extinction coefficient values of HbO2 and Hb have to be employed. However, it was not well recognized among researchers that small differences in extinction coefficients could cause significant errors in quantifying the concentrations of haemoglobin derivatives. In this study, we derived equations to estimate errors of haemoglobin derivatives caused by the variation of haemoglobin extinction coefficients. To prove our error analysis, we performed experiments using liquid-tissue phantoms containing 1% Intralipid in a phosphate-buffered saline solution. The gas intervention of pure oxygen was given in the solution to examine the oxygenation changes in the phantom, and 3 mL of human blood was added twice to show the changes in [Hbtotal]. The error calculation has shown that even a small variation (0.01 cm-1 mM-1) in extinction coefficients can produce appreciable relative errors in quantification of Δ[HbO2], Δ[Hb] and Δ[Hbtotal]. We have also observed that the error of Δ[Hbtotal] is not always larger than those of Δ[HbO2] and Δ[Hb]. This study concludes that we need to be aware of any variation in haemoglobin extinction coefficients, which could result from changes in temperature, and to utilize corresponding animal's haemoglobin extinction coefficients for the animal experiments, in order to obtain more accurate values of Δ[HbO2], Δ[Hb] and Δ[Hbtotal] from in vivo tissue measurements.

Evaluation of Magnetic Resonance Imaging-Compatible Needles and Interactive Sequences for Musculoskeletal Interventions Using an Open High-Field Magnetic Resonance Imaging Scanner

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wonneberger, Uta, E-mail: uta.wonneberger@charite.d; Schnackenburg, Bernhard, E-mail: bernhard.schnackenburg@philips.co; Streitparth, Florian, E-mail: florian.streitparth@charite.de

2010-04-15

In this article, we study in vitro evaluation of needle artefacts and image quality for musculoskeletal laser-interventions in an open high-field magnetic resonance imaging (MRI) scanner at 1.0T with vertical field orientation. Five commercially available MRI-compatible puncture needles were assessed based on artefact characteristics in a CuSO4 phantom (0.1%) and in human cadaveric lumbar spines. First, six different interventional sequences were evaluated with varying needle orientation to the main magnetic field B0 (0{sup o} to 90{sup o}) in a sequence test. Artefact width, needle-tip error, and contrast-to-noise ratio (CNR) were calculated. Second, a gradient-echo sequence used for thermometric monitoring wasmore » assessed and in varying echo times, artefact width, tip error, and signal-to-noise ratio (SNR) were measured. Artefact width and needle-tip error correlated with needle material, instrument orientation to B0, and sequence type. Fast spin-echo sequences produced the smallest needle artefacts for all needles, except for the carbon fibre needle (width <3.5 mm, tip error <2 mm) at 45{sup o} to B0. Overall, the proton density-weighted spin-echo sequences had the best CNR (CNR{sub Muscle/Needle} >16.8). Concerning the thermometric gradient echo sequence, artefacts remained <5 mm, and the SNR reached its maximum at an echo time of 15 ms. If needle materials and sequences are accordingly combined, guidance and monitoring of musculoskeletal laser interventions may be feasible in a vertical magnetic field at 1.0T.« less

Restoration of the ASCA Source Position Accuracy

NASA Astrophysics Data System (ADS)

Gotthelf, E. V.; Ueda, Y.; Fujimoto, R.; Kii, T.; Yamaoka, K.

2000-11-01

We present a calibration of the absolute pointing accuracy of the Advanced Satellite for Cosmology and Astrophysics (ASCA) which allows us to compensate for a large error (up to 1') in the derived source coordinates. We parameterize a temperature dependent deviation of the attitude solution which is responsible for this error. By analyzing ASCA coordinates of 100 bright active galactic nuclei, we show that it is possible to reduce the uncertainty in the sky position for any given observation by a factor of 4. The revised 90% error circle radius is then 12", consistent with preflight specifications, effectively restoring the full ASCA pointing accuracy. Herein, we derive an algorithm which compensates for this attitude error and present an internet-based table to be used to correct post facto the coordinate of all ASCA observations. While the above error circle is strictly applicable to data taken with the on-board Solid-state Imaging Spectrometers (SISs), similar coordinate corrections are derived for data obtained with the Gas Imaging Spectrometers (GISs), which, however, have additional instrumental uncertainties. The 90% error circle radius for the central 20' diameter of the GIS is 24". The large reduction in the error circle area for the two instruments offers the opportunity to greatly enhance the search for X-ray counterparts at other wavelengths. This has important implications for current and future ASCA source catalogs and surveys.

Realization of preconditioned Lanczos and conjugate gradient algorithms on optical linear algebra processors.

PubMed

Ghosh, A

1988-08-01

Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.

Optimal wavefront control for adaptive segmented mirrors

NASA Technical Reports Server (NTRS)

Downie, John D.; Goodman, Joseph W.

1989-01-01

A ground-based astronomical telescope with a segmented primary mirror will suffer image-degrading wavefront aberrations from at least two sources: (1) atmospheric turbulence and (2) segment misalignment or figure errors of the mirror itself. This paper describes the derivation of a mirror control feedback matrix that assumes the presence of both types of aberration and is optimum in the sense that it minimizes the mean-squared residual wavefront error. Assumptions of the statistical nature of the wavefront measurement errors, atmospheric phase aberrations, and segment misalignment errors are made in the process of derivation. Examples of the degree of correlation are presented for three different types of wavefront measurement data and compared to results of simple corrections.

Procedures and computer program for deriving the Ferguson plot from electrophoresis in a single pore gradient gel: application to agarose gel and a polystyrene particle.

PubMed

Tietz, D; Gombocz, E; Chrambach, A

1991-10-01

This study presents a computerized evaluation of pore gradient gel electrophoretograms to arrive at estimates for both the particle-free mobility and retardation coefficient, which is related to particle size. Agarose pore gradient gels ranging from 0.2 to 1.1% agarose were formed. Gel gradients were stabilized during their formation by a density gradient of 0-20% 5-(N-2,3-dihydroxypropylacetamido)- 2,4,6-triiodo-N,N'bis-(2,3-dihydroxypropyl)-isophthalamide (Nycodenz). Densitometry of gelled-in Bromophenol Blue showed that these pore gradients exhibited a linear central segment and were reproducible. Migration distances of polystyrene sulfate microspheres (36.5 nm radius) in agarose pore gradient gel electrophoresis were determined by time-lapse photography at several durations of electrophoresis. These migration distances were evaluated as a function of migration time as previously reported (D. Tietz, Adv. Electrophoresis 1988, 2, 109-169). Although this is not necessarily required, the mathematical approach used in this study assumed linearity of both the pore gradient and the Ferguson plot for reasons of simplicity. The data evaluation on the basis of the extended Ogston model is incorporated in a user-friendly program, GRADFIT, which is designed for personal computers (Macintosh). The results obtained are compared with (1) conventional electrophoresis using several gels of single concentration with and without Nycodenz, and (ii) a different mathematical approach for the analysis of gradient gels (Rodbard et al., Anal. Biochem. 1971, 40, 135-157). Moreover, a simple procedure for evaluating linear pore gradient gels using linear regression analysis is presented. It is concluded that the values of particle-free mobility and retardation coefficient derived from pore gradient gel electrophoresis using the different mathematical methods are statistically indistinguishable from each other. However, these values are different, albeit close, to those obtained from conventional Ferguson plots. One of the possible reasons for this relatively minor discrepancy is that the particle-free mobility changed slightly during electrophoresis, which has a different effect on electrophoresis in homogeneous gels (single time measurement) and pore gradient gels (multiple time measurements). The characterization of particles according to size and charge by pore gradient electrophoresis provides a significant operational simplification and sample economy compared to that requiring the use of several gel concentrations, although at the price of increased requirements of instrumentation.

Reappraisal of quantitative evaluation of pulmonary regurgitation and estimation of pulmonary artery pressure by continuous wave Doppler echocardiography.

PubMed

Lei, M H; Chen, J J; Ko, Y L; Cheng, J J; Kuan, P; Lien, W P

1995-01-01

This study assessed the usefulness of continuous wave Doppler echocardiography and color flow mapping in evaluating pulmonary regurgitation (PR) and estimating pulmonary artery (PA) pressure. Forty-three patients were examined, and high quality Doppler spectral recordings of PR were obtained in 32. All patients underwent cardiac catheterization, and simultaneous PA and right ventricular (RV) pressures were recorded in 17. Four Doppler regurgitant flow velocity patterns were observed: pandiastolic plateau, biphasic, peak and plateau, and early diastolic triangular types. The peak diastolic and end-diastolic PA-to-RV pressure gradients derived from the Doppler flow profiles correlated well with the catheter measurements (r = 0.95 and r = 0.95, respectively). As PA pressure increased, the PR flow velocity became higher; a linear relationship between either systolic or mean PA pressure and Doppler-derived peak diastolic pressure gradient was noted (r = 0.90 and 0.94, respectively). Based on peak diastolic gradients of < 15, 15-30 or > 30 mm Hg, patients could be separated as those with mild, moderate or severe pulmonary hypertension, respectively (p < 0.05). A correlation was also observed between PA diastolic pressure and Doppler-derived end-diastolic pressure gradient (r = 0.91). Moreover, the Doppler velocity decay slope of PR closely correlated with that derived from the catheter method (r = 0.98). The decay slope tended to be steeper with the increment in regurgitant jet area and length obtained from color flow mapping. In conclusion, continuous wave Doppler evaluation of PR is a useful means for noninvasive estimation of PA pressure, and the Doppler velocity decay slope seems to reflect the severity of PR.

Cardiomyopathy in children: Can we rely on echocardiographic tricuspid regurgitation gradient estimates of right ventricular and pulmonary arterial pressure?

PubMed

Lee, Simon; Lytrivi, Irene D; Roytman, Zhanna; Ko, Hyun-Sook Helen; Vinograd, Cheryl; Srivastava, Shubhika

2016-10-01

Introduction Agreement between echocardiography and right heart catheterisation-derived right ventricular systolic pressure is modest in the adult heart failure population, but is unknown in the paediatric cardiomyopathy population. All patients at a single centre from 2001 to 2012 with a diagnosis of cardiomyopathy who underwent echocardiography and catheterisation within 30 days were included in this study. The correlation between tricuspid regurgitation gradient and catheterisation-derived right ventricular systolic pressure and mean pulmonary artery pressure was determined. Agreement between echocardiography and catheterisation-derived right ventricular systolic pressure was assessed using Bland-Altman plots. Analysis was repeated for patients who underwent both procedures within 7 days. Haemodynamic data from those with poor agreement and good agreement between echocardiography and catheterisation were compared. A total of 37 patients who underwent 48 catheterisation procedures were included in our study. The median age was 11.8 (0.1-20.6 years) with 22 males (58% total). There was a modest correlation (r=0.65) between echocardiography and catheterisation-derived right ventricular systolic pressure, but agreement was poor. Agreement between tricuspid regurgitation gradient and right ventricular systolic pressure showed wide 95% limits of agreement. There was a modest correlation between the tricuspid regurgitation gradient and mean pulmonary artery pressure (r=0.6). Shorter time interval between the two studies did not improve agreement. Those with poor agreement between echocardiography and catheterisation had higher right heart pressures, but this difference became insignificant after accounting for right atrial pressure. Transthoracic echocardiography estimation of right ventricular systolic pressure shows modest correlation with right heart pressures, but has limited agreement and may underestimate the degree of pulmonary hypertension in paediatric cardiomyopathy patients.

Perceptual Bias in Speech Error Data Collection: Insights from Spanish Speech Errors

ERIC Educational Resources Information Center

Perez, Elvira; Santiago, Julio; Palma, Alfonso; O'Seaghdha, Padraig G.

2007-01-01

This paper studies the reliability and validity of naturalistic speech errors as a tool for language production research. Possible biases when collecting naturalistic speech errors are identified and specific predictions derived. These patterns are then contrasted with published reports from Germanic languages (English, German and Dutch) and one…

A preliminary estimate of geoid-induced variations in repeat orbit satellite altimeter observations

NASA Technical Reports Server (NTRS)

Brenner, Anita C.; Beckley, B. D.; Koblinsky, C. J.

1990-01-01

Altimeter satellites are often maintained in a repeating orbit to facilitate the separation of sea-height variations from the geoid. However, atmospheric drag and solar radiation pressure cause a satellite orbit to drift. For Geosat this drift causes the ground track to vary by + or - 1 km about the nominal repeat path. This misalignment leads to an error in the estimates of sea surface height variations because of the local slope in the geoid. This error has been estimated globally for the Geosat Exact Repeat Mission using a mean sea surface constructed from Geos 3 and Seasat altimeter data. Over most of the ocean the geoid gradient is small, and the repeat-track misalignment leads to errors of only 1 to 2 cm. However, in the vicinity of trenches, continental shelves, islands, and seamounts, errors can exceed 20 cm. The estimated error is compared with direct estimates from Geosat altimetry, and a strong correlation is found in the vicinity of the Tonga and Aleutian trenches. This correlation increases as the orbit error is reduced because of the increased signal-to-noise ratio.

Permanence analysis of a concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.; Kasami, T.

1983-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however, the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.

Probability of undetected error after decoding for a concatenated coding scheme

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.

1984-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Atmospheric refraction effects on baseline error in satellite laser ranging systems

NASA Technical Reports Server (NTRS)

Im, K. E.; Gardner, C. S.

1982-01-01

Because of the mathematical complexities involved in exact analyses of baseline errors, it is not easy to isolate atmospheric refraction effects; however, by making certain simplifying assumptions about the ranging system geometry, relatively simple expressions can be derived which relate the baseline errors directly to the refraction errors. The results indicate that even in the absence of other errors, the baseline error for intercontinental baselines can be more than an order of magnitude larger than the refraction error.

Shifts in allochthonous input and autochthonous production in streams along an agricultural land-use gradient

Treesearch

Elizabeth Hagen; Matthew McTammany; Jackson Webster; Ernest Benfield

2010-01-01

Relative contributions of allochthonous inputs and autochthonous production vary depending on terrestrial land use and biome. Terrestrially derived organic matter and in-stream primary production were measured in 12 headwater streams along an agricultural land-use gradient. Streams were examined to see how carbon (C) supply shifts from forested streams receiving...

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.