Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming

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

Sun Wei; Huang, Guo H., E-mail: huang@iseis.org; Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan, S4S 0A2

2012-06-15

Highlights: Black-Right-Pointing-Pointer Inexact piecewise-linearization-based fuzzy flexible programming is proposed. Black-Right-Pointing-Pointer It's the first application to waste management under multiple complexities. Black-Right-Pointing-Pointer It tackles nonlinear economies-of-scale effects in interval-parameter constraints. Black-Right-Pointing-Pointer It estimates costs more accurately than the linear-regression-based model. Black-Right-Pointing-Pointer Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerancemore » intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3

Continuous piecewise-linear, reduced-order electrochemical model for lithium-ion batteries in real-time applications

NASA Astrophysics Data System (ADS)

Farag, Mohammed; Fleckenstein, Matthias; Habibi, Saeid

2017-02-01

Model-order reduction and minimization of the CPU run-time while maintaining the model accuracy are critical requirements for real-time implementation of lithium-ion electrochemical battery models. In this paper, an isothermal, continuous, piecewise-linear, electrode-average model is developed by using an optimal knot placement technique. The proposed model reduces the univariate nonlinear function of the electrode's open circuit potential dependence on the state of charge to continuous piecewise regions. The parameterization experiments were chosen to provide a trade-off between extensive experimental characterization techniques and purely identifying all parameters using optimization techniques. The model is then parameterized in each continuous, piecewise-linear, region. Applying the proposed technique cuts down the CPU run-time by around 20%, compared to the reduced-order, electrode-average model. Finally, the model validation against real-time driving profiles (FTP-72, WLTP) demonstrates the ability of the model to predict the cell voltage accurately with less than 2% error.

True orbit simulation of piecewise linear and linear fractional maps of arbitrary dimension using algebraic numbers

NASA Astrophysics Data System (ADS)

Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji

2015-06-01

We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.

Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens.

PubMed

Métris, Aline; George, Susie M; Ropers, Delphine

2017-01-02

Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available

Least Squares Approximation By G1 Piecewise Parametric Cubes

DTIC Science & Technology

1993-12-01

ADDRESS(ES) 10.SPONSORING/MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not...CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) Parametric piecewise cubic polynomials are used throughout...piecewise parametric cubic polynomial to a sequence of ordered points in the plane. Cubic Bdzier curves are used as a basis. The parameterization, the

A prototype piecewise-linear dynamic attenuator

NASA Astrophysics Data System (ADS)

Hsieh, Scott S.; Peng, Mark V.; May, Christopher A.; Shunhavanich, Picha; Fleischmann, Dominik; Pelc, Norbert J.

2016-07-01

The piecewise-linear dynamic attenuator has been proposed as a mechanism in CT scanning for personalizing the x-ray illumination on a patient- and application-specific basis. Previous simulations have shown benefits in image quality, scatter, and dose objectives. We report on the first prototype implementation. This prototype is reduced in scale and speed and is integrated into a tabletop CT system with a smaller field of view (25 cm) and longer scan time (42 s) compared to a clinical system. Stainless steel wedges were machined and affixed to linear actuators, which were in turn held secure by a frame built using rapid prototyping technologies. The actuators were computer-controlled, with characteristic noise of about 100 microns. Simulations suggest that in a clinical setting, the impact of actuator noise could lead to artifacts of only 1 HU. Ring artifacts were minimized by careful design of the wedges. A water beam hardening correction was applied and the scan was collimated to reduce scatter. We scanned a 16 cm water cylinder phantom as well as an anthropomorphic pediatric phantom. The artifacts present in reconstructed images are comparable to artifacts normally seen with this tabletop system. Compared to a flat-field reference scan, increased detectability at reduced dose is shown and streaking is reduced. Artifacts are modest in our images and further refinement is possible. Issues of mechanical speed and stability in the challenging clinical CT environment will be addressed in a future design.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

PubMed Central

Vazquez-Leal, H.; Jimenez-Fernandez, V. M.; Benhammouda, B.; Filobello-Nino, U.; Sarmiento-Reyes, A.; Ramirez-Pinero, A.; Marin-Hernandez, A.; Huerta-Chua, J.

2014-01-01

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation. PMID:25184157

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

The piecewise-linear dynamic attenuator reduces the impact of count rate loss with photon-counting detectors

NASA Astrophysics Data System (ADS)

Hsieh, Scott S.; Pelc, Norbert J.

2014-06-01

Photon counting x-ray detectors (PCXDs) offer several advantages compared to standard energy-integrating x-ray detectors, but also face significant challenges. One key challenge is the high count rates required in CT. At high count rates, PCXDs exhibit count rate loss and show reduced detective quantum efficiency in signal-rich (or high flux) measurements. In order to reduce count rate requirements, a dynamic beam-shaping filter can be used to redistribute flux incident on the patient. We study the piecewise-linear attenuator in conjunction with PCXDs without energy discrimination capabilities. We examined three detector models: the classic nonparalyzable and paralyzable detector models, and a ‘hybrid’ detector model which is a weighted average of the two which approximates an existing, real detector (Taguchi et al 2011 Med. Phys. 38 1089-102 ). We derive analytic expressions for the variance of the CT measurements for these detectors. These expressions are used with raw data estimated from DICOM image files of an abdomen and a thorax to estimate variance in reconstructed images for both the dynamic attenuator and a static beam-shaping (‘bowtie’) filter. By redistributing flux, the dynamic attenuator reduces dose by 40% without increasing peak variance for the ideal detector. For non-ideal PCXDs, the impact of count rate loss is also reduced. The nonparalyzable detector shows little impact from count rate loss, but with the paralyzable model, count rate loss leads to noise streaks that can be controlled with the dynamic attenuator. With the hybrid model, the characteristic count rates required before noise streaks dominate the reconstruction are reduced by a factor of 2 to 3. We conclude that the piecewise-linear attenuator can reduce the count rate requirements of the PCXD in addition to improving dose efficiency. The magnitude of this reduction depends on the detector, with paralyzable detectors showing much greater benefit than nonparalyzable detectors.

Resonant activation in piecewise linear asymmetric potentials.

PubMed

Fiasconaro, Alessandro; Spagnolo, Bernardo

2011-04-01

This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time τ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of τ; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments. ©2011 American Physical Society

Piecewise polynomial representations of genomic tracks.

PubMed

Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

2012-01-01

Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.

The application of the piecewise linear approximation to the spectral neighborhood of soil line for the analysis of the quality of normalization of remote sensing materials

NASA Astrophysics Data System (ADS)

Kulyanitsa, A. L.; Rukhovich, A. D.; Rukhovich, D. D.; Koroleva, P. V.; Rukhovich, D. I.; Simakova, M. S.

2017-04-01

The concept of soil line can be to describe the temporal distribution of spectral characteristics of the bare soil surface. In this case, the soil line can be referred to as the multi-temporal soil line, or simply temporal soil line (TSL). In order to create TSL for 8000 regular lattice points for the territory of three regions of Tula oblast, we used 34 Landsat images obtained in the period from 1985 to 2014 after their certain transformation. As Landsat images are the matrices of the values of spectral brightness, this transformation is the normalization of matrices. There are several methods of normalization that move, rotate, and scale the spectral plane. In our study, we applied the method of piecewise linear approximation to the spectral neighborhood of soil line in order to assess the quality of normalization mathematically. This approach allowed us to range normalization methods according to their quality as follows: classic normalization > successive application of the turn and shift > successive application of the atmospheric correction and shift > atmospheric correction > shift > turn > raw data. The normalized data allowed us to create the maps of the distribution of a and b coefficients of the TSL. The map of b coefficient is characterized by the high correlation with the ground-truth data obtained from 1899 soil pits described during the soil surveys performed by the local institute for land management (GIPROZEM).

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming.

PubMed

Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen

2012-06-01

To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities. Copyright © 2012 Elsevier Ltd. All rights reserved.

2D discontinuous piecewise linear map: Emergence of fashion cycles.

PubMed

Gardini, L; Sushko, I; Matsuyama, K

2018-05-01

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Hurst Estimation of Scale Invariant Processes with Stationary Increments and Piecewise Linear Drift

NASA Astrophysics Data System (ADS)

Modarresi, N.; Rezakhah, S.

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first, we determine the scale intervals, their linear drifts and eliminate them. Then, a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion (fBm).

Analytical modelling of Halbach linear generator incorporating pole shifting and piece-wise spring for ocean wave energy harvesting

NASA Astrophysics Data System (ADS)

Tan, Yimin; Lin, Kejian; Zu, Jean W.

2018-05-01

Halbach permanent magnet (PM) array has attracted tremendous research attention in the development of electromagnetic generators for its unique properties. This paper has proposed a generalized analytical model for linear generators. The slotted stator pole-shifting and implementation of Halbach array have been combined for the first time. Initially, the magnetization components of the Halbach array have been determined using Fourier decomposition. Then, based on the magnetic scalar potential method, the magnetic field distribution has been derived employing specially treated boundary conditions. FEM analysis has been conducted to verify the analytical model. A slotted linear PM generator with Halbach PM has been constructed to validate the model and further improved using piece-wise springs to trigger full range reciprocating motion. A dynamic model has been developed to characterize the dynamic behavior of the slider. This analytical method provides an effective tool in development and optimization of Halbach PM generator. The experimental results indicate that piece-wise springs can be employed to improve generator performance under low excitation frequency.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

PubMed

Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

2015-04-01

Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Development of a piecewise linear omnidirectional 3D image registration method

NASA Astrophysics Data System (ADS)

Bae, Hyunsoo; Kang, Wonjin; Lee, SukGyu; Kim, Youngwoo

2016-12-01

This paper proposes a new piecewise linear omnidirectional image registration method. The proposed method segments an image captured by multiple cameras into 2D segments defined by feature points of the image and then stitches each segment geometrically by considering the inclination of the segment in the 3D space. Depending on the intended use of image registration, the proposed method can be used to improve image registration accuracy or reduce the computation time in image registration because the trade-off between the computation time and image registration accuracy can be controlled for. In general, nonlinear image registration methods have been used in 3D omnidirectional image registration processes to reduce image distortion by camera lenses. The proposed method depends on a linear transformation process for omnidirectional image registration, and therefore it can enhance the effectiveness of the geometry recognition process, increase image registration accuracy by increasing the number of cameras or feature points of each image, increase the image registration speed by reducing the number of cameras or feature points of each image, and provide simultaneous information on shapes and colors of captured objects.

Tell a Piecewise Story

ERIC Educational Resources Information Center

Sinclair, Nathalie; Armstrong, Alayne

2011-01-01

Piecewise linear functions and story graphs are concepts usually associated with algebra, but in the authors' classroom, they found success teaching this topic in a distinctly geometrical manner. The focus of the approach was less on learning geometric concepts and more on using spatial and kinetic reasoning. It not only supports the learning of…

A generalized analog implementation of piecewise linear neuron models using CCII building blocks.

PubMed

Soleimani, Hamid; Ahmadi, Arash; Bavandpour, Mohammad; Sharifipoor, Ozra

2014-03-01

This paper presents a set of reconfigurable analog implementations of piecewise linear spiking neuron models using second generation current conveyor (CCII) building blocks. With the same topology and circuit elements, without W/L modification which is impossible after circuit fabrication, these circuits can produce different behaviors, similar to the biological neurons, both for a single neuron as well as a network of neurons just by tuning reference current and voltage sources. The models are investigated, in terms of analog implementation feasibility and costs, targeting large scale hardware implementations. Results show that, in order to gain the best performance, area and accuracy; these models can be compromised. Simulation results are presented for different neuron behaviors with CMOS 350 nm technology. Copyright © 2013 Elsevier Ltd. All rights reserved.

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

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

Rajpathak, Bhooshan, E-mail: bhooshan@ee.iitb.ac.in; Pillai, Harish K., E-mail: hp@ee.iitb.ac.in; Bandyopadhyay, Santanu, E-mail: santanu@me.iitb.ac.in

2015-10-15

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.

Linear Approximation SAR Azimuth Processing Study

NASA Technical Reports Server (NTRS)

Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

1979-01-01

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

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

Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.

2016-02-23

Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examinemore » the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/T 3, but we formulate and test a slight extension for opacities ~ 1/T 3.5, where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.« less

Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness

NASA Astrophysics Data System (ADS)

Shui, Xin; Wang, Shimin

2018-02-01

The design and characterization of a mechanical vibration absorber are addressed. A distinctive feature of the absorber is its tunable piecewise-linear stiffness, which is realized by means of a slider with two stop-blocks installed constraining the bilateral deflections of the elastic support. A new analytical approach named as the equivalent stiffness technique (EST) is introduced and then employed to obtain the analytical relations of the frequency, amplitude and phase with a view to exhibit a more comprehensive characterization of the absorber. Experiments are conducted to demonstrate the feasibility of the design. The experimental data show good agreement with the analytical results. The final results indicate that the tunable stiffness absorber (TSA) possesses a typical nonlinear characteristic at each given position of the slider, and its stiffness can be tuned in real time over a wide range by adjusting the slider position. Hence the TSA has a large optimum vibration-absorption range together with a wide suppression band around each optimal position, which contributes to its excellent capacity of vibration absorption.

A refraction-corrected tomographic algorithm for immersion laser-ultrasonic imaging of solids with piecewise linear surface profile

NASA Astrophysics Data System (ADS)

Zarubin, V.; Bychkov, A.; Simonova, V.; Zhigarkov, V.; Karabutov, A.; Cherepetskaya, E.

2018-05-01

In this paper, a technique for reflection mode immersion 2D laser-ultrasound tomography of solid objects with piecewise linear 2D surface profiles is presented. Pulsed laser radiation was used for generation of short ultrasonic probe pulses, providing high spatial resolution. A piezofilm sensor array was used for detection of the waves reflected by the surface and internal inhomogeneities of the object. The original ultrasonic image reconstruction algorithm accounting for refraction of acoustic waves at the liquid-solid interface provided longitudinal resolution better than 100 μm in the polymethyl methacrylate sample object.

Weak-noise limit of a piecewise-smooth stochastic differential equation.

PubMed

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

A new framework for modeling decisions about changing information: The Piecewise Linear Ballistic Accumulator model

PubMed Central

Heathcote, Andrew

2016-01-01

In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We use a random-dot motion paradigm along with cognitive modeling to investigate how the decision process is updated when a stimulus changes. Participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. To further investigate the underlying changes in the decision process, we developed a Piecewise Linear Ballistic Accumulator model (PLBA). The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modeling framework using a non-parametric approximate Bayesian algorithm. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Thus, the perceptual decision process was slow to react to, and underestimated, new contrary motion information. PMID:26760448

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Rationale choosing interval of a piecewise-constant approximation of input rate of non-stationary queue system

NASA Astrophysics Data System (ADS)

Korelin, Ivan A.; Porshnev, Sergey V.

2018-01-01

The paper demonstrates the possibility of calculating the characteristics of the flow of visitors to objects carrying out mass events passing through checkpoints. The mathematical model is based on the non-stationary queuing system (NQS) where dependence of requests input rate from time is described by the function. This function was chosen in such way that its properties were similar to the real dependencies of speed of visitors arrival on football matches to the stadium. A piecewise-constant approximation of the function is used when statistical modeling of NQS performing. Authors calculated the dependencies of the queue length and waiting time for visitors to service (time in queue) on time for different laws. Time required to service the entire queue and the number of visitors entering the stadium at the beginning of the match were calculated too. We found the dependence for macroscopic quantitative characteristics of NQS from the number of averaging sections of the input rate.

A megahertz-frequency tunable piecewise-linear electromechanical resonator realized via nonlinear feedback

NASA Astrophysics Data System (ADS)

Bajaj, Nikhil; Chiu, George T.-C.; Rhoads, Jeffrey F.

2018-07-01

Vibration-based sensing modalities traditionally have relied upon monitoring small shifts in natural frequency in order to detect structural changes (such as those in mass or stiffness). In contrast, bifurcation-based sensing schemes rely on the detection of a qualitative change in the behavior of a system as a parameter is varied. This can produce easy-to-detect changes in response amplitude with high sensitivity to structural change, but requires resonant devices with specific dynamic behavior which is not always easily reproduced. Desirable behavior for such devices can be produced reliably via nonlinear feedback circuitry, but has in past efforts been largely limited to sub-MHz operation, partially due to the time delay limitations present in certain nonlinear feedback circuits, such as multipliers. This work demonstrates the design and implementation of a piecewise-linear resonator realized via diode- and integrated circuit-based feedback electronics and a quartz crystal resonator. The proposed system is fabricated and characterized, and the creation and selective placement of the bifurcation points of the overall electromechanical system is demonstrated by tuning the circuit gains. The demonstrated circuit operates at 16 MHz. Preliminary modeling and analysis is presented that qualitatively agrees with the experimentally-observed behavior.

Hierarchical structure in sharply divided phase space for the piecewise linear map

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ˜t-2 , the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

NASA Astrophysics Data System (ADS)

Suresh, R.; Srinivasan, K.; Senthilkumar, D. V.; Raja Mohamed, I.; Murali, K.; Lakshmanan, M.; Kurths, J.

2013-07-01

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central unit (relay unit) and at least one of the outer units, ZLS occurs in the two outer units whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger

Testing approximations for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

NASA Astrophysics Data System (ADS)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are

Piecewise multivariate modelling of sequential metabolic profiling data.

PubMed

Rantalainen, Mattias; Cloarec, Olivier; Ebbels, Timothy M D; Lundstedt, Torbjörn; Nicholson, Jeremy K; Holmes, Elaine; Trygg, Johan

2008-02-19

Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints. A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS) models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted. The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA) for modelling and analysis of short time-series data.

[Biometric identification method for ECG based on the piecewise linear representation (PLR) and dynamic time warping (DTW)].

PubMed

Yang, Licai; Shen, Jun; Bao, Shudi; Wei, Shoushui

2013-10-01

To treat the problem of identification performance and the complexity of the algorithm, we proposed a piecewise linear representation and dynamic time warping (PLR-DTW) method for ECG biometric identification. Firstly we detected R peaks to get the heartbeats after denoising preprocessing. Then we used the PLR method to keep important information of an ECG signal segment while reducing the data dimension at the same time. The improved DTW method was used for similarity measurements between the test data and the templates. The performance evaluation was carried out on the two ECG databases: PTB and MIT-BIH. The analystic results showed that compared to the discrete wavelet transform method, the proposed PLR-DTW method achieved a higher accuracy rate which is nearly 8% of rising, and saved about 30% operation time, and this demonstrated that the proposed method could provide a better performance.

Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Detection of kinetic change points in piece-wise linear single molecule motion

NASA Astrophysics Data System (ADS)

Hill, Flynn R.; van Oijen, Antoine M.; Duderstadt, Karl E.

2018-03-01

Single-molecule approaches present a powerful way to obtain detailed kinetic information at the molecular level. However, the identification of small rate changes is often hindered by the considerable noise present in such single-molecule kinetic data. We present a general method to detect such kinetic change points in trajectories of motion of processive single molecules having Gaussian noise, with a minimum number of parameters and without the need of an assumed kinetic model beyond piece-wise linearity of motion. Kinetic change points are detected using a likelihood ratio test in which the probability of no change is compared to the probability of a change occurring, given the experimental noise. A predetermined confidence interval minimizes the occurrence of false detections. Applying the method recursively to all sub-regions of a single molecule trajectory ensures that all kinetic change points are located. The algorithm presented allows rigorous and quantitative determination of kinetic change points in noisy single molecule observations without the need for filtering or binning, which reduce temporal resolution and obscure dynamics. The statistical framework for the approach and implementation details are discussed. The detection power of the algorithm is assessed using simulations with both single kinetic changes and multiple kinetic changes that typically arise in observations of single-molecule DNA-replication reactions. Implementations of the algorithm are provided in ImageJ plugin format written in Java and in the Julia language for numeric computing, with accompanying Jupyter Notebooks to allow reproduction of the analysis presented here.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Near constant-time optimal piecewise LDR to HDR inverse tone mapping

NASA Astrophysics Data System (ADS)

Chen, Qian; Su, Guan-Ming; Yin, Peng

2015-02-01

In a backward compatible HDR image/video compression, it is a general approach to reconstruct HDR from compressed LDR as a prediction to original HDR, which is referred to as inverse tone mapping. Experimental results show that 2- piecewise 2nd order polynomial has the best mapping accuracy than 1 piece high order or 2-piecewise linear, but it is also the most time-consuming method because to find the optimal pivot point to split LDR range to 2 pieces requires exhaustive search. In this paper, we propose a fast algorithm that completes optimal 2-piecewise 2nd order polynomial inverse tone mapping in near constant time without quality degradation. We observe that in least square solution, each entry in the intermediate matrix can be written as the sum of some basic terms, which can be pre-calculated into look-up tables. Since solving the matrix becomes looking up values in tables, computation time barely differs regardless of the number of points searched. Hence, we can carry out the most thorough pivot point search to find the optimal pivot that minimizes MSE in near constant time. Experiment shows that our proposed method achieves the same PSNR performance while saving 60 times computation time compared to the traditional exhaustive search in 2-piecewise 2nd order polynomial inverse tone mapping with continuous constraint.

Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing

2015-05-01

This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3(n) locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements.

PubMed

Durstewitz, Daniel

2017-06-01

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects

Determination of pKa values of alendronate sodium in aqueous solution by piecewise linear regression based on acid-base potentiometric titration.

PubMed

Ke, Jing; Dou, Hanfei; Zhang, Ximin; Uhagaze, Dushimabararezi Serge; Ding, Xiali; Dong, Yuming

2016-12-01

As a mono-sodium salt form of alendronic acid, alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups. The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and pH value based on acid-base potentiometric titration reaction. The distribution curves of alendronate sodium were drawn according to the determined pKa values. There were 4 dissociation constants (pKa 1 =2.43, pKa 2 =7.55, pKa 3 =10.80, pKa 4 =11.99, respectively) of alendronate sodium, and 12 existing forms, of which 4 could be ignored, existing in different pH environments.

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

PubMed

Luque-Fernandez, Miguel Angel; Belot, Aurélien; Quaresma, Manuela; Maringe, Camille; Coleman, Michel P; Rachet, Bernard

2016-10-01

In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.

The Linear Mixing Approximation for Planetary Ices

NASA Astrophysics Data System (ADS)

Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.

2017-12-01

We investigate the validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices, which are thought to dominate the interior of the ice giant planets Uranus and Neptune. For that purpose we perform density functional theory molecular dynamics simulations using the VASP code.[1] In particular, we compute 1:1 binary mixtures of water, ammonia, and methane, as well as their 2:1:4 ternary mixture at pressure-temperature conditions typical for the interior of Uranus and Neptune.[2,3] In addition, a new ab initio EOS for methane is presented. The linear mixing approximation is verified for the conditions present inside Uranus ranging up to 10 Mbar based on the comprehensive EOS data set. We also calculate the diffusion coefficients for the ternary mixture along different Uranus interior profiles and compare them to the values of the pure compounds. We find that deviations of the linear mixing approximation from the real mixture are generally small; for the EOS they fall within about 4% uncertainty while the diffusion coefficients deviate up to 20% . The EOS of planetary ices are applied to adiabatic models of Uranus. It turns out that a deep interior of almost pure ices is consistent with the gravity field data, in which case the planet becomes rather cold (T core ˜ 4000 K). [1] G. Kresse and J. Hafner, Physical Review B 47, 558 (1993). [2] R. Redmer, T.R. Mattsson, N. Nettelmann and M. French, Icarus 211, 798 (2011). [3] N. Nettelmann, K. Wang, J. J. Fortney, S. Hamel, S. Yellamilli, M. Bethkenhagen and R. Redmer, Icarus 275, 107 (2016).

Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2015-11-01

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

PubMed Central

Zhao, Rui; Catalano, Paul; DeGruttola, Victor G.; Michor, Franziska

2017-01-01

The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data. PMID:28723910

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Mechanical System Reliability and Cost Integration Using a Sequential Linear Approximation Method

NASA Technical Reports Server (NTRS)

Kowal, Michael T.

1997-01-01

The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1994-01-01

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

An approximate generalized linear model with random effects for informative missing data.

PubMed

Follmann, D; Wu, M

1995-03-01

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

RATE OF APPROXIMATION OF PIECEWISE-ANALYTIC FUNCTIONS BY RATIONAL FRACTIONS IN THE L_p-METRICS, 0 < p\\leq\\infty

NASA Astrophysics Data System (ADS)

Vjačeslavov, N. S.

1980-02-01

In this paper estimates are found for L_pR_n(f) - the least deviation in the L_p-metric, 0 < p\\leq\\infty, of a piecewise analytic function f from the rational functions of degree at most n. It is shown that these estimates are sharp in a well-defined sense.Bibliography: 12 titles.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.

The dynamics of two linearly coupled Goodwin oscillators

NASA Astrophysics Data System (ADS)

Antonova, A. O.; Reznik, S. N.; Todorov, M. D.

2017-10-01

In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Wall, Johnm W.

2011-01-01

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

2017-01-01

Scheme III (piecewise linear) and V (piecewise parabolic) of Van Leer are shown to yield identical solutions provided the initial conditions are chosen in an appropriate manner. This result is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The result also shows a key connection between the approaches of discontinuous and continuous representations.

Piecewise adiabatic following in non-Hermitian cycling

NASA Astrophysics Data System (ADS)

Gong, Jiangbin; Wang, Qing-hai

2018-05-01

The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. First, that the network is piecewise convex as a function of the input data. Second, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Third, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize the objective on certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space. Copyright © 2017 Elsevier Ltd. All rights reserved.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Photogrammetric Processing of Planetary Linear Pushbroom Images Based on Approximate Orthophotos

NASA Astrophysics Data System (ADS)

Geng, X.; Xu, Q.; Xing, S.; Hou, Y. F.; Lan, C. Z.; Zhang, J. J.

2018-04-01

It is still a great challenging task to efficiently produce planetary mapping products from orbital remote sensing images. There are many disadvantages in photogrammetric processing of planetary stereo images, such as lacking ground control information and informative features. Among which, image matching is the most difficult job in planetary photogrammetry. This paper designs a photogrammetric processing framework for planetary remote sensing images based on approximate orthophotos. Both tie points extraction for bundle adjustment and dense image matching for generating digital terrain model (DTM) are performed on approximate orthophotos. Since most of planetary remote sensing images are acquired by linear scanner cameras, we mainly deal with linear pushbroom images. In order to improve the computational efficiency of orthophotos generation and coordinates transformation, a fast back-projection algorithm of linear pushbroom images is introduced. Moreover, an iteratively refined DTM and orthophotos scheme was adopted in the DTM generation process, which is helpful to reduce search space of image matching and improve matching accuracy of conjugate points. With the advantages of approximate orthophotos, the matching results of planetary remote sensing images can be greatly improved. We tested the proposed approach with Mars Express (MEX) High Resolution Stereo Camera (HRSC) and Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) images. The preliminary experimental results demonstrate the feasibility of the proposed approach.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

GMX approximation for the linear E ⊗ ɛ Jahn-Teller effect

NASA Astrophysics Data System (ADS)

Mancini, Jay D.; Fessatidis, Vassilios; Bowen, Samuel P.

2006-02-01

A newly developed generalized moments expansion (GMX) based on the t-expansion of Horn and Weinstein is applied to a linear E ⊗ ɛ Jahn-Teller system. Comparisons are made with other moments schemes as well a coupled cluster approximation.

Filtrage Lineaire par Morceaux Avec Petit Bruit d’Observation (Piecewise Linear Filtering with Small Observation Noise)

DTIC Science & Technology

1990-11-19

stir divers exemple-s le comportement des filtres l)r0pose5 par ra.)pDort ceux du processus estliner et dti filtre optimal obtenu de fa~on approch6e...Piecewise monotone filtering with small observation noise, Siam J., Control Optim. 20, 261-285, 1989 . Vii [10 W.ll. Fleming and R.W. Rishel...Milbeiro, de Oliveira : Filtres approch~s pour un probl~me de filtrage non lin~aire discret avec petit bruit d’observation,rapport INVRIA, 1142. 1989

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Active distribution network planning considering linearized system loss

NASA Astrophysics Data System (ADS)

Li, Xiao; Wang, Mingqiang; Xu, Hao

2018-02-01

In this paper, various distribution network planning techniques with DGs are reviewed, and a new distribution network planning method is proposed. It assumes that the location of DGs and the topology of the network are fixed. The proposed model optimizes the capacities of DG and the optimal distribution line capacity simultaneously by a cost/benefit analysis and the benefit is quantified by the reduction of the expected interruption cost. Besides, the network loss is explicitly analyzed in the paper. For simplicity, the network loss is appropriately simplified as a quadratic function of difference of voltage phase angle. Then it is further piecewise linearized. In this paper, a piecewise linearization technique with different segment lengths is proposed. To validate its effectiveness and superiority, the proposed distribution network planning model with elaborate linearization technique is tested on the IEEE 33-bus distribution network system.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

NASA Astrophysics Data System (ADS)

Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

2014-03-01

Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

Exponential Approximations Using Fourier Series Partial Sums

NASA Technical Reports Server (NTRS)

Banerjee, Nana S.; Geer, James F.

1997-01-01

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Sparsest representations and approximations of an underdetermined linear system

NASA Astrophysics Data System (ADS)

Tardivel, Patrick J. C.; Servien, Rémi; Concordet, Didier

2018-05-01

In an underdetermined linear system of equations, constrained l 1 minimization methods such as the basis pursuit or the lasso are often used to recover one of the sparsest representations or approximations of the system. The null space property is a sufficient and ‘almost’ necessary condition to recover a sparsest representation with the basis pursuit. Unfortunately, this property cannot be easily checked. On the other hand, the mutual coherence is an easily checkable sufficient condition insuring the basis pursuit to recover one of the sparsest representations. Because the mutual coherence condition is too strong, it is hardly met in practice. Even if one of these conditions holds, to our knowledge, there is no theoretical result insuring that the lasso solution is one of the sparsest approximations. In this article, we study a novel constrained problem that gives, without any condition, one of the sparsest representations or approximations. To solve this problem, we provide a numerical method and we prove its convergence. Numerical experiments show that this approach gives better results than both the basis pursuit problem and the reweighted l 1 minimization problem.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Piecewise-homotopy analysis method (P-HAM) for first order nonlinear ODE

NASA Astrophysics Data System (ADS)

Chin, F. Y.; Lem, K. H.; Chong, F. S.

2013-09-01

In homotopy analysis method (HAM), the determination for the value of the auxiliary parameter h is based on the valid region of the h-curve in which the horizontal segment of the h-curve will decide the valid h-region. All h-value taken from the valid region, provided that the order of deformation is large enough, will in principle yield an approximation series that converges to the exact solution. However it is found out that the h-value chosen within this valid region does not always promise a good approximation under finite order. This paper suggests an improved method called Piecewise-HAM (P-HAM). In stead of a single h-value, this method suggests using many h-values. Each of the h-values comes from an individual h-curve while each h-curve is plotted by fixing the time t at a different value. Each h-value is claimed to produce a good approximation only about a neighborhood centered at the corresponding t which the h-curve is based on. Each segment of these good approximations is then joined to form the approximation curve. By this, the convergence region is enhanced further. The P-HAM is illustrated and supported by examples.

Exact analytical formulae for linearly distributed vortex and source sheets in uence computation in 2D vortex methods

NASA Astrophysics Data System (ADS)

Kuzmina, K. S.; Marchevsky, I. K.; Ryatina, E. P.

2017-11-01

We consider the methodology of numerical schemes development for two-dimensional vortex method. We describe two different approaches to deriving integral equation for unknown vortex sheet intensity. We simulate the velocity of the surface line of an airfoil as the influence of attached vortex and source sheets. We consider a polygonal approximation of the airfoil and assume intensity distributions of free and attached vortex sheets and attached source sheet to be approximated with piecewise constant or piecewise linear (continuous or discontinuous) functions. We describe several specific numerical schemes that provide different accuracy and have a different computational cost. The study shows that a Galerkin-type approach to solving boundary integral equation requires computing several integrals and double integrals over the panels. We obtain exact analytical formulae for all the necessary integrals, which makes it possible to raise significantly the accuracy of vortex sheet intensity computation and improve the quality of velocity and vorticity field representation, especially in proximity to the surface line of the airfoil. All the formulae are written down in the invariant form and depend only on the geometric relationship between the positions of the beginnings and ends of the panels.

Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Huang, Zhenkun; Han, Maoan

2007-09-01

Certain almost periodic forced perturbed systems with piecewise argument are considered in this paper. By using the contraction mapping principle and some new analysis technique, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of these systems. Furthermore, we study the harmonic and subharmonic solutions of these systems. The obtained results generalize the previous known results such as [A.M. Fink, Almost Periodic Differential Equation, Lecture Notes in Math., volE 377, Springer-Verlag, Berlin, 1974; C.Y. He, Almost Periodic Differential Equations, Higher Education Press, Beijing, 1992 (in Chinese); Z.S. Lin, The existence of almost periodic solution of linear system, Acta Math. Sinica 22 (5) (1979) 515-528 (in Chinese); C.Y. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (2) (1992) 173-181; Y.H. Xia, M. Lin, J. Cao, The existence of almost periodic solutions of certain perturbation system, J. Math. Anal. Appl. 310 (1) (2005) 81-96]. Finally, a tangible example and its numeric simulations show the feasibility of our results, the comparison between non-perturbed system and perturbed system, the relation between systems with and without piecewise argument.

Piecewise exponential survival times and analysis of case-cohort data.

PubMed

Li, Yan; Gail, Mitchell H; Preston, Dale L; Graubard, Barry I; Lubin, Jay H

2012-06-15

Case-cohort designs select a random sample of a cohort to be used as control with cases arising from the follow-up of the cohort. Analyses of case-cohort studies with time-varying exposures that use Cox partial likelihood methods can be computer intensive. We propose a piecewise-exponential approach where Poisson regression model parameters are estimated from a pseudolikelihood and the corresponding variances are derived by applying Taylor linearization methods that are used in survey research. The proposed approach is evaluated using Monte Carlo simulations. An illustration is provided using data from the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study of male smokers in Finland, where a case-cohort study of serum glucose level and pancreatic cancer was analyzed. Copyright © 2012 John Wiley & Sons, Ltd.

Linear stability analysis of collective neutrino oscillations without spurious modes

NASA Astrophysics Data System (ADS)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

Estimating piecewise exponential frailty model with changing prior for baseline hazard function

NASA Astrophysics Data System (ADS)

Thamrin, Sri Astuti; Lawi, Armin

2016-02-01

Piecewise exponential models provide a very flexible framework for modelling univariate survival data. It can be used to estimate the effects of different covariates which are influenced by the survival data. Although in a strict sense it is a parametric model, a piecewise exponential hazard can approximate any shape of a parametric baseline hazard. In the parametric baseline hazard, the hazard function for each individual may depend on a set of risk factors or explanatory variables. However, it usually does not explain all such variables which are known or measurable, and these variables become interesting to be considered. This unknown and unobservable risk factor of the hazard function is often termed as the individual's heterogeneity or frailty. This paper analyses the effects of unobserved population heterogeneity in patients' survival times. The issue of model choice through variable selection is also considered. A sensitivity analysis is conducted to assess the influence of the prior for each parameter. We used the Markov Chain Monte Carlo method in computing the Bayesian estimator on kidney infection data. The results obtained show that the sex and frailty are substantially associated with survival in this study and the models are relatively quite sensitive to the choice of two different priors.

High resolution A/D conversion based on piecewise conversion at lower resolution

DOEpatents

Terwilliger, Steve [Albuquerque, NM

2012-06-05

Piecewise conversion of an analog input signal is performed utilizing a plurality of relatively lower bit resolution A/D conversions. The results of this piecewise conversion are interpreted to achieve a relatively higher bit resolution A/D conversion without sampling frequency penalty.

Fault detection for piecewise affine systems with application to ship propulsion systems.

PubMed

Yang, Ying; Linlin, Li; Ding, Steven X; Qiu, Jianbin; Peng, Kaixiang

2017-09-09

In this paper, the design approach of non-synchronized diagnostic observer-based fault detection (FD) systems is investigated for piecewise affine processes via continuous piecewise Lyapunov functions. Considering that the dynamics of piecewise affine systems in different regions can be considerably different, the weighting matrices are used to weight the residual of each region, so as to optimize the fault detectability. A numerical example and a case study on a ship propulsion system are presented in the end to demonstrate the effectiveness of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

NASA Astrophysics Data System (ADS)

Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu

2015-12-01

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.

Geometric constrained variational calculus I: Piecewise smooth extremals

NASA Astrophysics Data System (ADS)

Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico

2015-05-01

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Cohen, D.

1985-01-01

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

An algorithm for the numerical solution of linear differential games

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

Polovinkin, E S; Ivanov, G E; Balashov, M V

2001-10-31

A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented andmore » estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.« less

Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point

NASA Astrophysics Data System (ADS)

Liang, Feng; Wang, Dechang

In this paper, we suppose that a planar piecewise Hamiltonian system, with a straight line of separation, has a piecewise generalized homoclinic loop passing through a Saddle-Fold point, and assume that there exists a family of piecewise smooth periodic orbits near the loop. By studying the asymptotic expansion of the first order Melnikov function corresponding to the period annulus, we obtain the formulas of the first six coefficients in the expansion, based on which, we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concrete systems are considered. Especially, the first one reveals that a quadratic piecewise Hamiltonian system can have five limit cycles near a generalized homoclinic loop under a quadratic piecewise smooth perturbation. Compared with the smooth case [Horozov & Iliev, 1994; Han et al., 1999], three more limit cycles are found.

A tutorial on the piecewise regression approach applied to bedload transport data

Treesearch

Sandra E. Ryan; Laurie S. Porth

2007-01-01

This tutorial demonstrates the application of piecewise regression to bedload data to define a shift in phase of transport so that the reader may perform similar analyses on available data. The use of piecewise regression analysis implicitly recognizes different functions fit to bedload data over varying ranges of flow. The transition from primarily low rates of sand...

Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

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

Lehtikangas, O., E-mail: Ossi.Lehtikangas@uef.fi; Tarvainen, T.; Department of Computer Science, University College London, Gower Street, London WC1E 6BT

2015-02-01

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena onmore » the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.« less

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Integrate and fire neural networks, piecewise contractive maps and limit cycles.

PubMed

Catsigeras, Eleonora; Guiraud, Pierre

2013-09-01

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincaré map associated to the system. We show that for efficient interactions the Poincaré map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincaré map under study, but also to a wide class of general n-dimensional piecewise contractive maps.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

Cytogenetic effect of low dose gamma-radiation in Hordeum vulgare seedlings: non-linear dose-effect relationship.

PubMed

Geras'kin, Stanislav A; Oudalova, Alla A; Kim, Jin Kyu; Dikarev, Vladimir G; Dikareva, Nina S

2007-03-01

The induction of chromosome aberrations in Hordeum vulgare germinated seeds was studied after ionizing irradiation with doses in the range of 10-1,000 mGy. The relationship between the frequency of aberrant cells and the absorbed dose was found to be nonlinear. A dose-independent plateau in the dose range from about 50 to 500 mGy was observed, where the level of cytogenetic damage was significantly different from the spontaneous level. The comparison of the goodness of the experimental data fitting with mathematical models of different complexity, using the most common quantitative criteria, demonstrated the advantage of a piecewise linear model over linear and polynomial models in approximating the frequency of cytogenetical disturbances. The results of the study support the hypothesis of indirect mechanisms of mutagenesis induced by low doses. Fundamental and applied implications of these findings are discussed.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fishes at river infrastructure.

PubMed

Boys, C A; Robinson, W; Miller, B; Pflugrath, B; Baumgartner, L J; Navarro, A; Brown, R; Deng, Z

2016-05-01

A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species, Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus, following simulated infrastructure passage in a barometric chamber. The probability of injuries such as swimbladder rupture, exophthalmia and haemorrhage, and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change, R(NE:A) ) reduced. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in R(NE:A) that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multispecies precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (R(NE:A) of 0·7) should protect downstream migrating juveniles of these two physoclistous species sufficiently. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones. © 2016 The Fisheries Society of the British Isles.

Planetary Ices and the Linear Mixing Approximation

DOE PAGES

Bethkenhagen, M.; Meyer, Edmund Richard; Hamel, S.; ...

2017-10-10

Here, the validity of the widely used linear mixing approximation (LMA) for the equations of state (EOSs) of planetary ices is investigated at pressure–temperature conditions typical for the interiors of Uranus and Neptune. The basis of this study is ab initio data ranging up to 1000 GPa and 20,000 K, calculated via density functional theory molecular dynamics simulations. In particular, we determine a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the LMA from the results of the real mixture are generally small; for the thermal EOSs they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior (more » $${T}_{\\mathrm{core}}\\sim 4000$$ K).« less

Computation of the anharmonic orbits in two piecewise monotonic maps with a single discontinuity

NASA Astrophysics Data System (ADS)

Li, Yurong; Du, Zhengdong

2017-02-01

In this paper, the bifurcation values for two typical piecewise monotonic maps with a single discontinuity are computed. The variation of the parameter of those maps leads to a sequence of border-collision and period-doubling bifurcations, generating a sequence of anharmonic orbits on the boundary of chaos. The border-collision and period-doubling bifurcation values are computed by the word-lifting technique and the Maple fsolve function or the Newton-Raphson method, respectively. The scaling factors which measure the convergent rates of the bifurcation values and the width of the stable periodic windows, respectively, are investigated. We found that these scaling factors depend on the parameters of the maps, implying that they are not universal. Moreover, if one side of the maps is linear, our numerical results suggest that those quantities converge increasingly. In particular, for the linear-quadratic case, they converge to one of the Feigenbaum constants δ _F= 4.66920160\\cdots.

Fall with Linear Drag and Wien's Displacement Law: Approximate Solution and Lambert Function

ERIC Educational Resources Information Center

Vial, Alexandre

2012-01-01

We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for…

The Linear Bias in the Zeldovich Approximation and a Relation between the Number Density and the Linear Bias of Dark Halos

NASA Astrophysics Data System (ADS)

Fan, Zuhui

2000-01-01

The linear bias of the dark halos from a model under the Zeldovich approximation is derived and compared with the fitting formula of simulation results. While qualitatively similar to the Press-Schechter formula, this model gives a better description for the linear bias around the turnaround point. This advantage, however, may be compromised by the large uncertainty of the actual behavior of the linear bias near the turnaround point. For a broad class of structure formation models in the cold dark matter framework, a general relation exists between the number density and the linear bias of dark halos. This relation can be readily tested by numerical simulations. Thus, instead of laboriously checking these models one by one, numerical simulation studies can falsify a whole category of models. The general validity of this relation is important in identifying key physical processes responsible for the large-scale structure formation in the universe.

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Linear Power Spectra in Cold+Hot Dark Matter Models: Analytical Approximations and Applications

NASA Astrophysics Data System (ADS)

Ma, Chung-Pei

1996-11-01

This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM + HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumbers, neutrino fractions, redshifts, and Hubble constants: k ≤ 1O h Mpc-1, 0.05 ≤ Ωv le; 0.3 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γv = a½Ωvh2, is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γv lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ωv. Linear calculations with these power spectra as input are performed to compare the predictions of Ωv ≤ 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 ≤ n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in 0.t-0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Accurate frequency domain measurement of the best linear time-invariant approximation of linear time-periodic systems including the quantification of the time-periodic distortions

NASA Astrophysics Data System (ADS)

Louarroudi, E.; Pintelon, R.; Lataire, J.

2014-10-01

Time-periodic (TP) phenomena occurring, for instance, in wind turbines, helicopters, anisotropic shaft-bearing systems, and cardiovascular/respiratory systems, are often not addressed when classical frequency response function (FRF) measurements are performed. As the traditional FRF concept is based on the linear time-invariant (LTI) system theory, it is only approximately valid for systems with varying dynamics. Accordingly, the quantification of any deviation from this ideal LTI framework is more than welcome. The “measure of deviation” allows us to define the notion of the best LTI (BLTI) approximation, which yields the best - in mean square sense - LTI description of a linear time-periodic LTP system. By taking into consideration the TP effects, it is shown in this paper that the variability of the BLTI measurement can be reduced significantly compared with that of classical FRF estimators. From a single experiment, the proposed identification methods can handle (non-)linear time-periodic [(N)LTP] systems in open-loop with a quantification of (i) the noise and/or the NL distortions, (ii) the TP distortions and (iii) the transient (leakage) errors. Besides, a geometrical interpretation of the BLTI approximation is provided, leading to a framework called vector FRF analysis. The theory presented is supported by numerical simulations as well as real measurements mimicking the well-known mechanical Mathieu oscillator.

Brittle failure of rock: A review and general linear criterion

NASA Astrophysics Data System (ADS)

Labuz, Joseph F.; Zeng, Feitao; Makhnenko, Roman; Li, Yuan

2018-07-01

A failure criterion typically is phenomenological since few models exist to theoretically derive the mathematical function. Indeed, a successful failure criterion is a generalization of experimental data obtained from strength tests on specimens subjected to known stress states. For isotropic rock that exhibits a pressure dependence on strength, a popular failure criterion is a linear equation in major and minor principal stresses, independent of the intermediate principal stress. A general linear failure criterion called Paul-Mohr-Coulomb (PMC) contains all three principal stresses with three material constants: friction angles for axisymmetric compression ϕc and extension ϕe and isotropic tensile strength V0. PMC provides a framework to describe a nonlinear failure surface by a set of planes "hugging" the curved surface. Brittle failure of rock is reviewed and multiaxial test methods are summarized. Equations are presented to implement PMC for fitting strength data and determining the three material parameters. A piecewise linear approximation to a nonlinear failure surface is illustrated by fitting two planes with six material parameters to form either a 6- to 12-sided pyramid or a 6- to 12- to 6-sided pyramid. The particular nature of the failure surface is dictated by the experimental data.

A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fish at river infrastructure

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

Boys, Craig A.; Robinson, Wayne; Miller, Brett

2016-05-13

Barotrauma injury can occur when fish are exposed to rapid decompression during downstream passage through river infrastructure. A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species (Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus) following simulated infrastructure passage in barometric chambers. The probability of injuries such as swim bladder rupture; exophthalmia; and haemorrhage and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change RPCE/A) fell. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in RPCE/Amore » that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multi-species precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (RPCE/A of 0.7) should sufficiently protect downstream migrating juveniles of these two physoclistous species. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones.« less

Low-complexity piecewise-affine virtual sensors: theory and design

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Poggi, Tomaso; Oliveri, Alberto; Pascucci, Carlo Alberto; Bemporad, Alberto; Storace, Marco

2014-03-01

This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estimation of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical model. The proposed approach allows one to design estimators which mitigate the effect of the so-called 'curse of dimensionality' of simplicial piecewise-affine functions, and can be therefore applied to relatively high-order systems, enjoying convergence and optimality properties. An automatic toolchain is also presented to generate the VHDL code describing the digital circuit implementing the virtual sensor, starting from the set of measured input and output data. The proposed methodology is applied to generate an FPGA implementation of the virtual sensor for the estimation of vehicle lateral velocity, using a hardware-in-the-loop setting.

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

PubMed

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Krill herd and piecewise-linear initialization algorithms for designing Takagi-Sugeno systems

NASA Astrophysics Data System (ADS)

Hodashinsky, I. A.; Filimonenko, I. V.; Sarin, K. S.

2017-07-01

A method for designing Takagi-Sugeno fuzzy systems is proposed which uses a piecewiselinear initialization algorithm for structure generation and a metaheuristic krill herd algorithm for parameter optimization. The obtained systems are tested against real data sets. The influence of some parameters of this algorithm on the approximation accuracy is analyzed. Estimates of the approximation accuracy and the number of fuzzy rules are compared with four known methods of design.

Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor

NASA Astrophysics Data System (ADS)

Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.

2018-01-01

Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Harmonics analysis of the ITER poloidal field converter based on a piecewise method

NASA Astrophysics Data System (ADS)

Xudong, WANG; Liuwei, XU; Peng, FU; Ji, LI; Yanan, WU

2017-12-01

Poloidal field (PF) converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained. In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform. Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

PubMed

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

2015-01-01

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

A sequential method for spline approximation with variable knots. [recursive piecewise polynomial signal processing

NASA Technical Reports Server (NTRS)

Mier Muth, A. M.; Willsky, A. S.

1978-01-01

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

Limit cycles via higher order perturbations for some piecewise differential systems

NASA Astrophysics Data System (ADS)

Buzzi, Claudio A.; Lima, Maurício Firmino Silva; Torregrosa, Joan

2018-05-01

A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x‧ ,y‧) =(- y + εf(x , y , ε) , x + εg(x , y , ε)) . In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n , no more than Nn - 1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Liénard differential systems providing better upper bounds for higher order perturbation in ε, showing also when they are reached. The Poincaré-Pontryagin-Melnikov theory is the main technique used to prove all the results.

Application of the piecewise rational quadratic interpolant to the AUC calculation in the bioavailability study.

PubMed

Akhter, Khalid P; Ahmad, Mahmood; Khan, Shujaat Ali; Ramzan, Munazza; Shafi, Ishrat; Muryam, Burhana; Javed, Zafar; Murtaza, Ghulam

2012-01-01

This study presents an application of the piecewise rational quadratic interpolant to the AUC calculation in the bioavailability study. The objective of this work is to find an area under the plasma concentration-time curve (AUC) for multiple doses of salbutamol sulfate sustained release tablets (Ventolin oral tablets SR 8 mg, GSK, Pakistan) in the group of 24 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. The approximated AUC was computed by using computational mathematics techniques such as extended rectangular, extended trapezium and extended Simpson's rule and compared with exact value of AUC calculated by using software - Kinetica to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin oral tablets were 150.58, 157.81, 164.41 and 162.78 ngxh/mL while the closest approximated AUC values were 149.24, 157.33, 164.25 and 162.28 ngxh/mL, respectively, as found by extended rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the extended rectangular rule gives slightly better approximated values of AUC as compared to extended trapezium and extended Simpson's rules.

The effect of the cosmological constant on a quadrupole signal in the linearized approximation

NASA Astrophysics Data System (ADS)

Somlai, László Ábel; Vasúth, Mátyás

In this study the effects of a nonzero cosmological constant Λ on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of hGW GWs and hΛ background term, originated from Λ. The ΛhGW term was also included in this study. To derive physically relevant consequences of Λ≠0 comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming

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

Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less

Dissociation of Self-Motion and Object Motion by Linear Population Decoding That Approximates Marginalization.

PubMed

Sasaki, Ryo; Angelaki, Dora E; DeAngelis, Gregory C

2017-11-15

We use visual image motion to judge the movement of objects, as well as our own movements through the environment. Generally, image motion components caused by object motion and self-motion are confounded in the retinal image. Thus, to estimate heading, the brain would ideally marginalize out the effects of object motion (or vice versa), but little is known about how this is accomplished neurally. Behavioral studies suggest that vestibular signals play a role in dissociating object motion and self-motion, and recent computational work suggests that a linear decoder can approximate marginalization by taking advantage of diverse multisensory representations. By measuring responses of MSTd neurons in two male rhesus monkeys and by applying a recently-developed method to approximate marginalization by linear population decoding, we tested the hypothesis that vestibular signals help to dissociate self-motion and object motion. We show that vestibular signals stabilize tuning for heading in neurons with congruent visual and vestibular heading preferences, whereas they stabilize tuning for object motion in neurons with discrepant preferences. Thus, vestibular signals enhance the separability of joint tuning for object motion and self-motion. We further show that a linear decoder, designed to approximate marginalization, allows the population to represent either self-motion or object motion with good accuracy. Decoder weights are broadly consistent with a readout strategy, suggested by recent computational work, in which responses are decoded according to the vestibular preferences of multisensory neurons. These results demonstrate, at both single neuron and population levels, that vestibular signals help to dissociate self-motion and object motion. SIGNIFICANCE STATEMENT The brain often needs to estimate one property of a changing environment while ignoring others. This can be difficult because multiple properties of the environment may be confounded in sensory signals

Dissociation of Self-Motion and Object Motion by Linear Population Decoding That Approximates Marginalization

PubMed Central

Sasaki, Ryo; Angelaki, Dora E.

2017-01-01

We use visual image motion to judge the movement of objects, as well as our own movements through the environment. Generally, image motion components caused by object motion and self-motion are confounded in the retinal image. Thus, to estimate heading, the brain would ideally marginalize out the effects of object motion (or vice versa), but little is known about how this is accomplished neurally. Behavioral studies suggest that vestibular signals play a role in dissociating object motion and self-motion, and recent computational work suggests that a linear decoder can approximate marginalization by taking advantage of diverse multisensory representations. By measuring responses of MSTd neurons in two male rhesus monkeys and by applying a recently-developed method to approximate marginalization by linear population decoding, we tested the hypothesis that vestibular signals help to dissociate self-motion and object motion. We show that vestibular signals stabilize tuning for heading in neurons with congruent visual and vestibular heading preferences, whereas they stabilize tuning for object motion in neurons with discrepant preferences. Thus, vestibular signals enhance the separability of joint tuning for object motion and self-motion. We further show that a linear decoder, designed to approximate marginalization, allows the population to represent either self-motion or object motion with good accuracy. Decoder weights are broadly consistent with a readout strategy, suggested by recent computational work, in which responses are decoded according to the vestibular preferences of multisensory neurons. These results demonstrate, at both single neuron and population levels, that vestibular signals help to dissociate self-motion and object motion. SIGNIFICANCE STATEMENT The brain often needs to estimate one property of a changing environment while ignoring others. This can be difficult because multiple properties of the environment may be confounded in sensory signals

Approximate labeling via graph cuts based on linear programming.

PubMed

Komodakis, Nikos; Tziritas, Georgios

2007-08-01

A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

NASA Astrophysics Data System (ADS)

Zheng, Youqi; Choi, Sooyoung; Lee, Deokjung

2017-12-01

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Class Identification Efficacy in Piecewise GMM with Unknown Turning Points

ERIC Educational Resources Information Center

Ning, Ling; Luo, Wen

2018-01-01

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1993-01-01

The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

PubMed

Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

2018-05-08

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

Trajectory Generation by Piecewise Spline Interpolation

DTIC Science & Technology

1976-04-01

Lx) -a 0 + atx + aAx + x (21)0 1 2 3 and the coefficients are obtained from Equation (20) as ao m fl (22)i al " fi, (23) S3(fi + I f ) 2fj + fj+ 1 (24...reference frame to the vehicle fixed frame is pTO’ 0TO’ OTO’ *TO where a if (gZv0 - A >- 0 aCI (64) - azif (gzv0- AzvO < 0 These rotations may be...velocity frame axes directions (velocity frame from the output frame) aO, al , a 2 , a 3 Coefficients of the piecewise cubic polynomials [B ] Tridiagonal

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

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

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

On piecewise interpolation techniques for estimating solar radiation missing values in Kedah

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

Saaban, Azizan; Zainudin, Lutfi; Bakar, Mohd Nazari Abu

2014-12-04

This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Errormore » (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.« less

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

2017-12-01

Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

NASA Technical Reports Server (NTRS)

Olson, Erik D.

2015-01-01

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop

NASA Astrophysics Data System (ADS)

Xiong, Yanqin

2016-06-01

This paper is concerned with the bifurcation problem of limit cycles by perturbing a piecewise Hamiltonian system with a double homoclinic loop. First, the derivative of the first Melnikov function is provided. Then, we use it, together with the analytic method, to derive the asymptotic expansion of the first Melnikov function near the loop. Meanwhile, we present the first coefficients in the expansion, which can be applied to study the limit cycle bifurcation near the loop. We give sufficient conditions for this system to have 14 limit cycles in the neighborhood of the loop. As an application, a piecewise polynomial Liénard system is investigated, finding six limit cycles with the help of the obtained method.

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

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

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1985-01-01

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Holographic representation of space-variant systems: system theory.

PubMed

Marks Ii, R J; Krile, T F

1976-09-01

System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.

Combining global and local approximations

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.

1991-01-01

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

An application of analyzing the trajectories of two disorders: A parallel piecewise growth model of substance use and attention-deficit/hyperactivity disorder.

PubMed

Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G Leonard; Parks, Craig; Roll, John

2015-12-01

Researchers often want to examine 2 comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of 2 disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than 2 growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention-deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive-behavioral therapy treatment for a substance use disorder and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these 2 disorders concurrently allowed us to determine whether elevated levels of 1 disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and substance use separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or substance use disorder) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

An approach for maximizing the smallest eigenfrequency of structure vibration based on piecewise constant level set method

NASA Astrophysics Data System (ADS)

Zhang, Zhengfang; Chen, Weifeng

2018-05-01

Maximization of the smallest eigenfrequency of the linearized elasticity system with area constraint is investigated. The elasticity system is extended into a large background domain, but the void is vacuum and not filled with ersatz material. The piecewise constant level set (PCLS) method is applied to present two regions, the original material region and the void region. A quadratic PCLS function is proposed to represent the characteristic function. Consequently, the functional derivative of the smallest eigenfrequency with respect to PCLS function takes nonzero value in the original material region and zero in the void region. A penalty gradient algorithm is proposed, which initializes the whole background domain with the original material and decreases the area of original material region till the area constraint is satisfied. 2D and 3D numerical examples are presented, illustrating the validity of the proposed algorithm.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Piecewise silence in discrete cosmological models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell

2014-05-01

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon ‘piecewise silence’.

An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects

DOE PAGES

Puso, M. A.; Kokko, E.; Settgast, R.; ...

2014-10-22

An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as non-proportional damping such that the time integration of the scheme is provably stable with a critical timemore » step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.« less

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

A study of different modeling choices for simulating platelets within the immersed boundary method

PubMed Central

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.

2012-01-01

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. PMID:23585704

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1987-01-01

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Integrated Sensing and Processing (ISP) Phase 2: Demonstration and Evaluation for Distributed Sensor Networks and Missile Seeker Systems

DTIC Science & Technology

2007-05-29

International Conference Acoustics Speech and Signal Processing (ICASSP 2007) conference 15 − 20 April 2007 in Honolulu, Hawaii. 1. E. Near Term...from the sensor measured in feet. The detection performance of the footstep in the presence of interfering speech was characterized in previously...investigation, we developed a simple piecewise linear approximation to the probability of detection curve with no interfering speech . This approximation was

An analysis of value function learning with piecewise linear control

NASA Astrophysics Data System (ADS)

Tutsoy, Onder; Brown, Martin

2016-05-01

Reinforcement learning (RL) algorithms attempt to learn optimal control actions by iteratively estimating a long-term measure of system performance, the so-called value function. For example, RL algorithms have been applied to walking robots to examine the connection between robot motion and the brain, which is known as embodied cognition. In this paper, RL algorithms are analysed using an exemplar test problem. A closed form solution for the value function is calculated and this is represented in terms of a set of basis functions and parameters, which is used to investigate parameter convergence. The value function expression is shown to have a polynomial form where the polynomial terms depend on the plant's parameters and the value function's discount factor. It is shown that the temporal difference error introduces a null space for the differenced higher order basis associated with the effects of controller switching (saturated to linear control or terminating an experiment) apart from the time of the switch. This leads to slow convergence in the relevant subspace. It is also shown that badly conditioned learning problems can occur, and this is a function of the value function discount factor and the controller switching points. Finally, a comparison is performed between the residual gradient and TD(0) learning algorithms, and it is shown that the former has a faster rate of convergence for this test problem.

Bayesian hierarchical piecewise regression models: a tool to detect trajectory divergence between groups in long-term observational studies.

PubMed

Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J

2017-06-06

Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non-linear

Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

PubMed

Shukla, Rahul; Dragotti, Pier Luigi; Do, Minh N; Vetterli, Martin

2005-03-01

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.

Millimeter wave attenuation prediction using a piecewise uniform rain rate model

NASA Technical Reports Server (NTRS)

Persinger, R. R.; Stutzman, W. L.; Bostian, C. W.; Castle, R. E., Jr.

1980-01-01

A piecewise uniform rain rate distribution model is introduced as a quasi-physical model of real rain along earth-space millimeter wave propagation paths. It permits calculation of the total attenuation from specific attenuation in a simple fashion. The model predications are verified by comparison with direct attenuation measurements for several frequencies, elevation angles, and locations. Also, coupled with the Rice-Holmberg rain rate model, attenuation statistics are predicated from rainfall accumulation data.

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

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

Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

2016-10-15

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Optimized multiple linear mappings for single image super-resolution

NASA Astrophysics Data System (ADS)

Zhang, Kaibing; Li, Jie; Xiong, Zenggang; Liu, Xiuping; Gao, Xinbo

2017-12-01

Learning piecewise linear regression has been recognized as an effective way for example learning-based single image super-resolution (SR) in literature. In this paper, we employ an expectation-maximization (EM) algorithm to further improve the SR performance of our previous multiple linear mappings (MLM) based SR method. In the training stage, the proposed method starts with a set of linear regressors obtained by the MLM-based method, and then jointly optimizes the clustering results and the low- and high-resolution subdictionary pairs for regression functions by using the metric of the reconstruction errors. In the test stage, we select the optimal regressor for SR reconstruction by accumulating the reconstruction errors of m-nearest neighbors in the training set. Thorough experimental results carried on six publicly available datasets demonstrate that the proposed SR method can yield high-quality images with finer details and sharper edges in terms of both quantitative and perceptual image quality assessments.

Equilibria of an epidemic game with piecewise linear social distancing cost.

PubMed

Reluga, Timothy C

2013-10-01

Around the world, infectious disease epidemics continue to threaten people's health. When epidemics strike, we often respond by changing our behaviors to reduce our risk of infection. This response is sometimes called "social distancing." Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on our behaviors. Differential population game theory provides a method for resolving this circular dependence. Here, I present the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, but bounded below by zero. Equilibrium solutions are constructed in closed-form for an open-ended epidemic. Constructions are also provided for epidemics that are stopped by the deployment of a vaccination that becomes available a fixed-time after the start of the epidemic. This can be used to anticipate a window of opportunity during which mass vaccination can significantly reduce the cost of an epidemic.

Implementation of an approximate self-energy correction scheme in the orthogonalized linear combination of atomic orbitals method of band-structure calculations

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

Gu, Z.; Ching, W.Y.

Based on the Sterne-Inkson model for the self-energy correction to the single-particle energy in the local-density approximation (LDA), we have implemented an approximate energy-dependent and [bold k]-dependent [ital GW] correction scheme to the orthogonalized linear combination of atomic orbital-based local-density calculation for insulators. In contrast to the approach of Jenkins, Srivastava, and Inkson, we evaluate the on-site exchange integrals using the LDA Bloch functions throughout the Brillouin zone. By using a [bold k]-weighted band gap [ital E][sub [ital g

A piecewise-focused high DQE detector for MV imaging.

PubMed

Star-Lack, Josh; Shedlock, Daniel; Swahn, Dennis; Humber, Dave; Wang, Adam; Hirsh, Hayley; Zentai, George; Sawkey, Daren; Kruger, Isaac; Sun, Mingshan; Abel, Eric; Virshup, Gary; Shin, Mihye; Fahrig, Rebecca

2015-09-01

Electronic portal imagers (EPIDs) with high detective quantum efficiencies (DQEs) are sought to facilitate the use of the megavoltage (MV) radiotherapy treatment beam for image guidance. Potential advantages include high quality (treatment) beam's eye view imaging, and improved cone-beam computed tomography (CBCT) generating images with more accurate electron density maps with immunity to metal artifacts. One approach to increasing detector sensitivity is to couple a thick pixelated scintillator array to an active matrix flat panel imager (AMFPI) incorporating amorphous silicon thin film electronics. Cadmium tungstate (CWO) has many desirable scintillation properties including good light output, a high index of refraction, high optical transparency, and reasonable cost. However, due to the 0 1 0 cleave plane inherent in its crystalline structure, the difficulty of cutting and polishing CWO has, in part, limited its study relative to other scintillators such as cesium iodide and bismuth germanate (BGO). The goal of this work was to build and test a focused large-area pixelated "strip" CWO detector. A 361 × 52 mm scintillator assembly that contained a total of 28 072 pixels was constructed. The assembly comprised seven subarrays, each 15 mm thick. Six of the subarrays were fabricated from CWO with a pixel pitch of 0.784 mm, while one array was constructed from BGO for comparison. Focusing was achieved by coupling the arrays to the Varian AS1000 AMFPI through a piecewise linear arc-shaped fiber optic plate. Simulation and experimental studies of modulation transfer function (MTF) and DQE were undertaken using a 6 MV beam, and comparisons were made between the performance of the pixelated strip assembly and the most common EPID configuration comprising a 1 mm-thick copper build-up plate attached to a 133 mg/cm(2) gadolinium oxysulfide scintillator screen (Cu-GOS). Projection radiographs and CBCT images of phantoms were acquired. The work also introduces the use of a

A piecewise-focused high DQE detector for MV imaging

PubMed Central

Star-Lack, Josh; Shedlock, Daniel; Swahn, Dennis; Humber, Dave; Wang, Adam; Hirsh, Hayley; Zentai, George; Sawkey, Daren; Kruger, Isaac; Sun, Mingshan; Abel, Eric; Virshup, Gary; Shin, Mihye; Fahrig, Rebecca

2015-01-01

Purpose: Electronic portal imagers (EPIDs) with high detective quantum efficiencies (DQEs) are sought to facilitate the use of the megavoltage (MV) radiotherapy treatment beam for image guidance. Potential advantages include high quality (treatment) beam’s eye view imaging, and improved cone-beam computed tomography (CBCT) generating images with more accurate electron density maps with immunity to metal artifacts. One approach to increasing detector sensitivity is to couple a thick pixelated scintillator array to an active matrix flat panel imager (AMFPI) incorporating amorphous silicon thin film electronics. Cadmium tungstate (CWO) has many desirable scintillation properties including good light output, a high index of refraction, high optical transparency, and reasonable cost. However, due to the 0 1 0 cleave plane inherent in its crystalline structure, the difficulty of cutting and polishing CWO has, in part, limited its study relative to other scintillators such as cesium iodide and bismuth germanate (BGO). The goal of this work was to build and test a focused large-area pixelated “strip” CWO detector. Methods: A 361  ×  52 mm scintillator assembly that contained a total of 28 072 pixels was constructed. The assembly comprised seven subarrays, each 15 mm thick. Six of the subarrays were fabricated from CWO with a pixel pitch of 0.784 mm, while one array was constructed from BGO for comparison. Focusing was achieved by coupling the arrays to the Varian AS1000 AMFPI through a piecewise linear arc-shaped fiber optic plate. Simulation and experimental studies of modulation transfer function (MTF) and DQE were undertaken using a 6 MV beam, and comparisons were made between the performance of the pixelated strip assembly and the most common EPID configuration comprising a 1 mm-thick copper build-up plate attached to a 133 mg/cm2 gadolinium oxysulfide scintillator screen (Cu-GOS). Projection radiographs and CBCT images of phantoms were acquired. The work

Assessing variance components in multilevel linear models using approximate Bayes factors: A case study of ethnic disparities in birthweight

PubMed Central

Saville, Benjamin R.; Herring, Amy H.; Kaufman, Jay S.

2013-01-01

Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace’s method. PMID:24082430

Focusing of concentric piecewise vector Bessel-Gaussian beam

NASA Astrophysics Data System (ADS)

Li, Jinsong; Fang, Ying; Zhou, Shenghua; Ye, Youxiang

2010-12-01

The focusing properties of a concentric piecewise vector Bessel-Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel-Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

Piecewise-Planar StereoScan: Sequential Structure and Motion using Plane Primitives.

PubMed

Raposo, Carolina; Antunes, Michel; P Barreto, Joao

2017-08-09

The article describes a pipeline that receives as input a sequence of stereo images, and outputs the camera motion and a Piecewise-Planar Reconstruction (PPR) of the scene. The pipeline, named Piecewise-Planar StereoScan (PPSS), works as follows: the planes in the scene are detected for each stereo view using semi-dense depth estimation; the relative pose is computed by a new closed-form minimal algorithm that only uses point correspondences whenever plane detections do not fully constrain the motion; the camera motion and the PPR are jointly refined by alternating between discrete optimization and continuous bundle adjustment; and, finally, the detected 3D planes are segmented in images using a new framework that handles low texture and visibility issues. PPSS is extensively validated in indoor and outdoor datasets, and benchmarked against two popular point-based SfM pipelines. The experiments confirm that plane-based visual odometry is resilient to situations of small image overlap, poor texture, specularity, and perceptual aliasing where the fast LIBVISO2 pipeline fails. The comparison against VisualSfM+CMVS/PMVS shows that, for a similar computational complexity, PPSS is more accurate and provides much more compelling and visually pleasant 3D models. These results strongly suggest that plane primitives are an advantageous alternative to point correspondences for applications of SfM and 3D reconstruction in man-made environments.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

What Can Tobit-Piecewise Regression Tell Us about the Determinants of Household Educational Debt?

ERIC Educational Resources Information Center

Thipbharos, Titirut

2014-01-01

Educational debt as part of household debt remains a problem for Thailand. The significant factors of household characteristics with regard to educational debt are shown by constructing a Tobit-piecewise regression for three different clusters, namely poor, middle and affluent households in Thailand. It was found that household debt is likely to…

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Sparse generalized linear model with L0 approximation for feature selection and prediction with big omics data.

PubMed

Liu, Zhenqiu; Sun, Fengzhu; McGovern, Dermot P

2017-01-01

Feature selection and prediction are the most important tasks for big data mining. The common strategies for feature selection in big data mining are L 1 , SCAD and MC+. However, none of the existing algorithms optimizes L 0 , which penalizes the number of nonzero features directly. In this paper, we develop a novel sparse generalized linear model (GLM) with L 0 approximation for feature selection and prediction with big omics data. The proposed approach approximate the L 0 optimization directly. Even though the original L 0 problem is non-convex, the problem is approximated by sequential convex optimizations with the proposed algorithm. The proposed method is easy to implement with only several lines of code. Novel adaptive ridge algorithms ( L 0 ADRIDGE) for L 0 penalized GLM with ultra high dimensional big data are developed. The proposed approach outperforms the other cutting edge regularization methods including SCAD and MC+ in simulations. When it is applied to integrated analysis of mRNA, microRNA, and methylation data from TCGA ovarian cancer, multilevel gene signatures associated with suboptimal debulking are identified simultaneously. The biological significance and potential clinical importance of those genes are further explored. The developed Software L 0 ADRIDGE in MATLAB is available at https://github.com/liuzqx/L0adridge.

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

NASA Technical Reports Server (NTRS)

Armstrong, Jeffrey B.; Simon, Donald L.

2012-01-01

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear

Examining the Earnings Trajectories of Community College Students Using a Piecewise Growth Curve Modeling Approach

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2016-01-01

Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this article we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from two popular econometric approaches:…

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

DTIC Science & Technology

2012-12-01

acoustics One begins with Eikonal equation for the acoustic phase function S(t,x) as derived from the geometric acoustics (high frequency) approximation to...zb(x) is smooth and reasonably approximated as piecewise linear. The time domain ray (characteristic) equations for the Eikonal equation are ẋ(t)= c...travel time is affected, which is more physically relevant than global error in φ since it provides the phase information for the Eikonal equation (2.1

Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric.

PubMed

Luenser, Arne; Schurkus, Henry F; Ochsenfeld, Christian

2017-04-11

A reformulation of the random phase approximation within the resolution-of-the-identity (RI) scheme is presented, that is competitive to canonical molecular orbital RI-RPA already for small- to medium-sized molecules. For electronically sparse systems drastic speedups due to the reduced scaling behavior compared to the molecular orbital formulation are demonstrated. Our reformulation is based on two ideas, which are independently useful: First, a Cholesky decomposition of density matrices that reduces the scaling with basis set size for a fixed-size molecule by one order, leading to massive performance improvements. Second, replacement of the overlap RI metric used in the original AO-RPA by an attenuated Coulomb metric. Accuracy is significantly improved compared to the overlap metric, while locality and sparsity of the integrals are retained, as is the effective linear scaling behavior.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

A piecewise smooth model of evolutionary game for residential mobility and segregation

NASA Astrophysics Data System (ADS)

Radi, D.; Gardini, L.

2018-05-01

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems

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

Neretin, Yu A

2006-12-31

A family of non-complete orthogonal systems of functions on the ray [0,{infinity}] depending on three real parameters {alpha}, {beta}, {theta} is constructed. The elements of this system are piecewise hypergeometric functions with singularity at x=1. For {theta}=0 these functions vanish on [1,{infinity}) and the system is reduced to the Jacobi polynomials P{sub n}{sup {alpha}}{sup ,{beta}} on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P{sub n+{theta}}{sup {alpha}}{sup ,{beta}}. They are eigenfunctions of an exotic Sturm-Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem ismore » found.« less

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Laplacian versus topography in the solution of the linear gravimetric boundary value problem by means of successive approximations

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations. We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Nonlinear Deformation of a Piecewise Homogeneous Cylinder Under the Action of Rotation

NASA Astrophysics Data System (ADS)

Akhundov, V. M.; Kostrova, M. M.

2018-05-01

Deformation of a piecewise cylinder under the action of rotation is investigated. The cylinder consists of an elastic matrix with circular fibers of square cross section made of a more rigid elastic material and arranged doubly periodically in the cylinder. Behavior of the cylinder under large displacements and deformations is examined using the equations of a nonlinear elasticity theory for cylinder constituents. The problem posed is solved by the finite-difference method using the method of continuation with respect to the rotational speed of the cylinder.

Transformations Based on Continuous Piecewise-Affine Velocity Fields

PubMed Central

Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan; Fisher, Jonn W.

2018-01-01

We propose novel finite-dimensional spaces of well-behaved ℝn → ℝn transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization over monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available. PMID:28092517

Transformations based on continuous piecewise-affine velocity fields

DOE PAGES

Freifeld, Oren; Hauberg, Soren; Batmanghelich, Kayhan; ...

2017-01-11

Here, we propose novel finite-dimensional spaces of well-behaved Rn → Rn transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization overmore » monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available.« less

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

A piecewise mass-spring-damper model of the human breast.

PubMed

Cai, Yiqing; Chen, Lihua; Yu, Winnie; Zhou, Jie; Wan, Frances; Suh, Minyoung; Chow, Daniel Hung-Kay

2018-01-23

Previous models to predict breast movement whilst performing physical activities have, erroneously, assumed uniform elasticity within the breast. Consequently, the predicted displacements have not yet been satisfactorily validated. In this study, real time motion capture of the natural vibrations of a breast that followed, after raising and allowing it to fall freely, revealed an obvious difference in the vibration characteristics above and below the static equilibrium position. This implied that the elastic and viscous damping properties of a breast could vary under extension or compression. Therefore, a new piecewise mass-spring-damper model of a breast was developed with theoretical equations to derive values for its spring constants and damping coefficients from free-falling breast experiments. The effective breast mass was estimated from the breast volume extracted from a 3D body scanned image. The derived spring constant (k a  = 73.5 N m -1 ) above the static equilibrium position was significantly smaller than that below it (k b  = 658 N m -1 ), whereas the respective damping coefficients were similar (c a  = 1.83 N s m -1 , c b  = 2.07 N s m -1 ). These values were used to predict the nipple displacement during bare-breasted running for validation. The predicted and experimental results had a 2.6% or less root-mean-square-error of the theoretical and experimental amplitudes, so the piecewise mass-spring-damper model and equations were considered to have been successfully validated. This provides a theoretical basis for further research into the dynamic, nonlinear viscoelastic properties of different breasts and the prediction of external forces for the necessary breast support during different sports activities. Copyright © 2017 Elsevier Ltd. All rights reserved.

Linearized motion estimation for articulated planes.

PubMed

Datta, Ankur; Sheikh, Yaser; Kanade, Takeo

2011-04-01

In this paper, we describe the explicit application of articulation constraints for estimating the motion of a system of articulated planes. We relate articulations to the relative homography between planes and show that these articulations translate into linearized equality constraints on a linear least-squares system, which can be solved efficiently using a Karush-Kuhn-Tucker system. The articulation constraints can be applied for both gradient-based and feature-based motion estimation algorithms and to illustrate this, we describe a gradient-based motion estimation algorithm for an affine camera and a feature-based motion estimation algorithm for a projective camera that explicitly enforces articulation constraints. We show that explicit application of articulation constraints leads to numerically stable estimates of motion. The simultaneous computation of motion estimates for all of the articulated planes in a scene allows us to handle scene areas where there is limited texture information and areas that leave the field of view. Our results demonstrate the wide applicability of the algorithm in a variety of challenging real-world cases such as human body tracking, motion estimation of rigid, piecewise planar scenes, and motion estimation of triangulated meshes.

Time-temperature effect in adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

The viscoelastic analysis of an adhesively bonded lap joint was reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is linearly viscoelastic. The hereditary integrals are used to model the adhesive. A linear integral differential equations system for the shear and the tensile stress in the adhesive is applied. The equations have constant coefficients and are solved by using Laplace transforms. It is shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms can be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Conventional and Piecewise Growth Modeling Techniques: Applications and Implications for Investigating Head Start Children's Early Literacy Learning

ERIC Educational Resources Information Center

Hindman, Annemarie H.; Cromley, Jennifer G.; Skibbe, Lori E.; Miller, Alison L.

2011-01-01

This article reviews the mechanics of conventional and piecewise growth models to demonstrate the unique affordances of each technique for examining the nature and predictors of children's early literacy learning during the transition from preschool through first grade. Using the nationally representative Family and Child Experiences Survey…

Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

PubMed

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Quadratic spline subroutine package

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

A spatial domain decomposition approach to distributed H ∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

NASA Astrophysics Data System (ADS)

Wang, Jun-Wei; Liu, Ya-Qiang; Hu, Yan-Yan; Sun, Chang-Yin

2017-12-01

This paper discusses the design problem of distributed H∞ Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H∞ performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H∞ observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

NASA Astrophysics Data System (ADS)

Alessandrini, Giovanni; de Hoop, Maarten V.; Gaburro, Romina

2017-12-01

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω\\subset{R}n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Σ of the boundary \\partialΩ . We prove that anisotropic conductivities that are a priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.

Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments.

PubMed

Wu, Ailong; Liu, Ling; Huang, Tingwen; Zeng, Zhigang

2017-01-01

Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Piecewise synonyms for enhanced UMLS source terminology integration.

PubMed

Huang, Kuo-Chuan; Geller, James; Halper, Michael; Cimino, James J

2007-10-11

The UMLS contains more than 100 source vocabularies and is growing via the integration of others. When integrating a new source, the source terms already in the UMLS must first be found. The easiest approach to this is simple string matching. However, string matching usually does not find all concepts that should be found. A new methodology, based on the notion of piecewise synonyms, for enhancing the process of concept discovery in the UMLS is presented. This methodology is supported by first creating a general synonym dictionary based on the UMLS. Each multi-word source term is decomposed into its component words, allowing for the generation of separate synonyms for each word from the general synonym dictionary. The recombination of these synonyms into new terms creates an expanded pool of matching candidates for terms from the source. The methodology is demonstrated with respect to an existing UMLS source. It shows a 34% improvement over simple string matching.

Meta-Regression Approximations to Reduce Publication Selection Bias

ERIC Educational Resources Information Center

Stanley, T. D.; Doucouliagos, Hristos

2014-01-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

Robust Neighboring Optimal Guidance for the Advanced Launch System

NASA Technical Reports Server (NTRS)

Hull, David G.

1993-01-01

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

Stress state of a piecewise uniform layered space with doubly periodic internal cracks

NASA Astrophysics Data System (ADS)

Hakobyan, V. N.; Dashtoyan, L. L.

2018-04-01

The present paper deals with the stress state of a piecewise homogeneous plane formed by alternation junction of two distinct strips of equal height manufactured of different materials. There is a doubly periodic system of cracks on the plane. The governing system of singular integral equations of the first kind for the density of the crack dislocation is derived. The solution of the problem in the case where only one of the repeated strips contains one doubly-periodic crack is obtained by the method of mechanical quadratures.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

NASA Astrophysics Data System (ADS)

Beretta, Elena; Micheletti, Stefano; Perotto, Simona; Santacesaria, Matteo

2018-01-01

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.

Icosahedral quasicrystal Al71Pd21Mn08 and its ξ' approximant: Linear expansivity, specific heat, magnetic susceptibility, electrical resistivity, and elastic constants

NASA Astrophysics Data System (ADS)

Swenson, C. A.; Fisher, I. R.; Anderson, N. E.; Canfield, P. C.; Migliori, A.

2002-05-01

Linear thermal expansivity (α, 1-300 K), heat capacity (Cp, 1-108 K), magnetic susceptibility (χ, 1-300 K), and electrical resistivity (ρ, 1-300 K) measurements are reported for a single-grain i-Al71Pd21Mn08 quasicrystal and its Al72Pd25Mn03 approximant, and 300 K elastic constants for the quasicrystal. The approximant α (αAp) and Cp (CpAp) data show ``metallic'' behavior, while the previously reported onset of a transition to a spin-glass state (Tf<1.8 K) dominates αQ and CpQ below 11 K. CpAp and CpQ superimpose above 16 K when plotted vs T/Θ0 using the experimental Θ0Ap=455(3) K and an adjusted Θ0ApQ=480(4) K. The 300 K elastic constants extrapolated to T=0 give Θel0Q=505(1) K, suggesting that the normalization is valid only above 16 K. The lattice contribution to CpAp (and, indirectly, CpQ) shows strong (unique) deviations from Debye-like behavior (+3% at 0.84 K for the CpAp data fit). The various Grüneisen parameters (Γ) that are calculated from these data all are positive and normal in magnitude except for a large limiting approximant lattice value, Γlat0Ap=11.3, which may be related to the large dispersion effects in Cp. For the approximant, the combination of anisotropic and large resistivities, a small diamagnetic susceptibility, and a ``large'' linear (electronic) contribution to CpAp (γAp=0.794 mJ/mol K2) suggests the existence of a pseudogap in the electronic density of states. The unusually large, highly volume dependent, dispersion at low temperatures for the quasicrystal and its approximant are not consistent with inelastic neutron scattering and other data, and raise questions about the role of phonons in quasicrystals. The present 300 K resistivities can be used with a published correlation to estimate γQ~0.25 mJ/mol K2.

A Dynamical Analysis of a Piecewise Smooth Pest Control SI Model

NASA Astrophysics Data System (ADS)

Liu, Bing; Liu, Wanbo; Tao, Fennmei; Kang, Baolin; Cong, Jiguang

In this paper, we propose a piecewise smooth SI pest control system to model the process of spraying pesticides and releasing infectious pests. We assume that the pest population consists of susceptible pests and infectious pests, and that the disease spreads horizontally between pests. We take the susceptible pest as the control index on whether to implement chemical control and biological control strategies. Based on the theory of Filippov system, the sliding-mode domain and conditions for the existence of real equilibria, virtual equilibria, pseudo-equilibrium and boundary equilibria are given. Further, we show the global stability of real equilibria (or boundary equilibria) and pseudo-equilibrium. Our results can provide theoretical guidance for the problem of pest control.

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

High-Speed Numeric Function Generator Using Piecewise Quadratic Approximations

DTIC Science & Technology

2007-09-01

application; User specifies the fuction to approxiamte. % % This programs turns the function provided into an inline function... PRIMARY = < primary file 1> < primary file 2> #SECONDARY = <secondary file 1> <secondary file 2> #CHIP2 = <file to compile to user chip

Interaction function of oscillating coupled neurons

PubMed Central

Dodla, Ramana; Wilson, Charles J.

2013-01-01

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

AntiClustal: Multiple Sequence Alignment by antipole clustering and linear approximate 1-median computation.

PubMed

Di Pietro, C; Di Pietro, V; Emmanuele, G; Ferro, A; Maugeri, T; Modica, E; Pigola, G; Pulvirenti, A; Purrello, M; Ragusa, M; Scalia, M; Shasha, D; Travali, S; Zimmitti, V

2003-01-01

In this paper we present a new Multiple Sequence Alignment (MSA) algorithm called AntiClusAl. The method makes use of the commonly use idea of aligning homologous sequences belonging to classes generated by some clustering algorithm, and then continue the alignment process ina bottom-up way along a suitable tree structure. The final result is then read at the root of the tree. Multiple sequence alignment in each cluster makes use of the progressive alignment with the 1-median (center) of the cluster. The 1-median of set S of sequences is the element of S which minimizes the average distance from any other sequence in S. Its exact computation requires quadratic time. The basic idea of our proposed algorithm is to make use of a simple and natural algorithmic technique based on randomized tournaments which has been successfully applied to large size search problems in general metric spaces. In particular a clustering algorithm called Antipole tree and an approximate linear 1-median computation are used. Our algorithm compared with Clustal W, a widely used tool to MSA, shows a better running time results with fully comparable alignment quality. A successful biological application showing high aminoacid conservation during evolution of Xenopus laevis SOD2 is also cited.

Burgers approximation for two-dimensional flow past an ellipse

NASA Technical Reports Server (NTRS)

Dorrepaal, J. M.

1982-01-01

A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

NASA Astrophysics Data System (ADS)

Dobronets, B. S.; Popova, O. A.

2018-05-01

Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.

The Stiffness Variation of a Micro-Ring Driven by a Traveling Piecewise-Electrode

PubMed Central

Li, Yingjie; Yu, Tao; Hu, Yuh-Chung

2014-01-01

In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing. PMID:25230308

The stiffness variation of a micro-ring driven by a traveling piecewise-electrode.

PubMed

Li, Yingjie; Yu, Tao; Hu, Yuh-Chung

2014-09-16

In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

How reliable is the linear noise approximation of gene regulatory networks?

PubMed Central

2013-01-01

Background The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations. Conclusion The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing

CMB-lensing beyond the Born approximation

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

Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth

2016-09-01

We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussianmore » nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.« less

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

PubMed

Zuehlsdorff, T J; Hine, N D M; Payne, M C; Haynes, P D

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

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

Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C.; Hine, N. D. M.

2015-11-28

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on amore » small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.« less

Examining the Earnings Trajectories of Community College Students Using a Piecewise Growth Curve Modeling Approach. A CAPSEE Working Paper

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2015-01-01

Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this paper we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from Mincerian and fixed-effects approaches. Our…

Semiparametric methods for estimation of a nonlinear exposure-outcome relationship using instrumental variables with application to Mendelian randomization.

PubMed

Staley, James R; Burgess, Stephen

2017-05-01

Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure-outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure-outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. © 2017 The Authors Genetic Epidemiology Published by Wiley Periodicals, Inc.

Semiparametric methods for estimation of a nonlinear exposure‐outcome relationship using instrumental variables with application to Mendelian randomization

PubMed Central

Staley, James R.

2017-01-01

ABSTRACT Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure‐outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure‐outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure‐outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. PMID:28317167

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout.

PubMed

Udagedara, Indika B; Rukhlenko, Ivan D; Premaratne, Malin

2011-10-10

The energy transport properties of plasmonic waveguides can be analyzed by solving the dispersion relation for surface plasmon-polaritons (SPPs). We use this approach to derive an approximate analytical expression for SPP propagation length when the waveguide is composed of linearly arranged metallic nanoparticles, while assuming that metal losses are small or partially compensated by gain. Applied to metal-dielectric (composite) nanospheres, the obtained expression allows us to optimize the performance of the waveguide and arrive at a number of practical design rules. Specifically, we show that SPP attenuation can be minimized at a certain interparticle distance for transverse modes, but gradually grows for both longitudinal and transverse modes with the increase of particle separation. We also show that the two basic methods of supplying gain to the system, i.e., embedding the particles into a gain medium or having a metal-gain composition for the particles, do not perform equally well and the former method is more efficient, but the way the two methods affect depends on the polarization of SPPs. To investigate the role of the nanoparticles' arrangement in determining SPP characteristics, we follow a purely numerical approach and consider a two-segment bent waveguide as an example. Analyzing the waveguide's transmission shows that it behaves in an oscillatory manner with respect to the angle between the two segments and is therefore higher for certain angles than for the others. This suggests that, in the design of waveguides with bends, careful attention needs to be paid in order to avoid bend angles that yield low transmission and to choose angles that give maximum transmission.

Evaluation of fiber Bragg grating sensor interrogation using InGaAs linear detector arrays and Gaussian approximation on embedded hardware.

PubMed

Kumar, Saurabh; Amrutur, Bharadwaj; Asokan, Sundarrajan

2018-02-01

Fiber Bragg Grating (FBG) sensors have become popular for applications related to structural health monitoring, biomedical engineering, and robotics. However, for successful large scale adoption, FBG interrogation systems are as important as sensor characteristics. Apart from accuracy, the required number of FBG sensors per fiber and the distance between the device in which the sensors are used and the interrogation system also influence the selection of the interrogation technique. For several measurement devices developed for applications in biomedical engineering and robotics, only a few sensors per fiber are required and the device is close to the interrogation system. For these applications, interrogation systems based on InGaAs linear detector arrays provide a good choice. However, their resolution is dependent on the algorithms used for curve fitting. In this work, a detailed analysis of the choice of algorithm using the Gaussian approximation for the FBG spectrum and the number of pixels used for curve fitting on the errors is provided. The points where the maximum errors occur have been identified. All comparisons for wavelength shift detection have been made against another interrogation system based on the tunable swept laser. It has been shown that maximum errors occur when the wavelength shift is such that one new pixel is included for curve fitting. It has also been shown that an algorithm with lower computation cost compared to the more popular methods using iterative non-linear least squares estimation can be used without leading to the loss of accuracy. The algorithm has been implemented on embedded hardware, and a speed-up of approximately six times has been observed.

Evaluation of fiber Bragg grating sensor interrogation using InGaAs linear detector arrays and Gaussian approximation on embedded hardware

NASA Astrophysics Data System (ADS)

Kumar, Saurabh; Amrutur, Bharadwaj; Asokan, Sundarrajan

2018-02-01

Fiber Bragg Grating (FBG) sensors have become popular for applications related to structural health monitoring, biomedical engineering, and robotics. However, for successful large scale adoption, FBG interrogation systems are as important as sensor characteristics. Apart from accuracy, the required number of FBG sensors per fiber and the distance between the device in which the sensors are used and the interrogation system also influence the selection of the interrogation technique. For several measurement devices developed for applications in biomedical engineering and robotics, only a few sensors per fiber are required and the device is close to the interrogation system. For these applications, interrogation systems based on InGaAs linear detector arrays provide a good choice. However, their resolution is dependent on the algorithms used for curve fitting. In this work, a detailed analysis of the choice of algorithm using the Gaussian approximation for the FBG spectrum and the number of pixels used for curve fitting on the errors is provided. The points where the maximum errors occur have been identified. All comparisons for wavelength shift detection have been made against another interrogation system based on the tunable swept laser. It has been shown that maximum errors occur when the wavelength shift is such that one new pixel is included for curve fitting. It has also been shown that an algorithm with lower computation cost compared to the more popular methods using iterative non-linear least squares estimation can be used without leading to the loss of accuracy. The algorithm has been implemented on embedded hardware, and a speed-up of approximately six times has been observed.

An Approximate Approach to Automatic Kernel Selection.

PubMed

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Limit cycles in piecewise-affine gene network models with multiple interaction loops

NASA Astrophysics Data System (ADS)

Farcot, Etienne; Gouzé, Jean-Luc

2010-01-01

In this article, we consider piecewise affine differential equations modelling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph of the system may be rather complex (multiple intricate loops of any sign, multiple thresholds, etc.). Our main result is an alternative theorem showing that if a sequence of region is periodically visited by trajectories, then under our hypotheses, there exists either a unique stable periodic solution, or the origin attracts all trajectories in this sequence of regions. This result extends greatly our previous work on a single negative feedback loop. We give several examples and simulations illustrating different cases.

Locomotion of C. elegans: A Piecewise-Harmonic Curvature Representation of Nematode Behavior

PubMed Central

Padmanabhan, Venkat; Khan, Zeina S.; Solomon, Deepak E.; Armstrong, Andrew; Rumbaugh, Kendra P.; Vanapalli, Siva A.; Blawzdziewicz, Jerzy

2012-01-01

Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase. PMID:22792224

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?

ERIC Educational Resources Information Center

Oud, Johan H. L.; Folmer, Henk

2011-01-01

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

Resonances in piecewise potentials and Supersymmetric Quantum Mechanics (SUSY-QM) for the construction of optical potentials

NASA Astrophysics Data System (ADS)

Orozco Cortés, Luis Fernando; Fernández García, Nicolás

2014-05-01

A method to obtain the general solution of any constant piecewise potential is presented, this is achieved by means of the analysis of the transfer matrices in each cutoff. The resonance phenomenon together with the supersymmetric quantum mechanics technique allow us to construct a wide family of complex potentials which can be used as theoretical models for optical systems. The method is applied to the particular case for which the potential function has six cutoff points.

A Safe Cooperative Framework for Atmospheric Science Missions with Multiple Heterogeneous UAS using Piecewise Bezier Curves

NASA Technical Reports Server (NTRS)

Mehdi, S. Bilal; Puig-Navarro, Javier; Choe, Ronald; Cichella, Venanzio; Hovakimyan, Naira; Chandarana, Meghan; Trujillo, Anna; Rothhaar, Paul M.; Tran, Loc; Neilan, James H.;

Global and local curvature in density functional theory.

PubMed

Zhao, Qing; Ioannidis, Efthymios I; Kulik, Heather J

2016-08-07

Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.

The non-linear association between low-level lead exposure and maternal stress among pregnant women.

PubMed

Li, Shufang; Xu, Jian; Liu, Zhiwei; Yan, Chong-Huai

2017-03-01

Neuro-developmental impairments in the developing fetus due to exposure to low-level lead have been well documented. However, few studies have investigated the relation between maternal stress levels and low-level lead exposure among pregnant women. To investigate the relation between maternal blood lead and stress levels during index pregnancy. 1931 pregnant women (gestational week 28-36) were investigated using stratified-cluster-sampling in Shanghai in 2010. Maternal life event stress and emotional stress were assessed using "Life-Event-Stress-Scale-for-Pregnant-Women" (LESPW) and "Symptom-Checklist-90-Revised" (SCL-90-R), respectively. Maternal whole blood lead levels were determined, and other data on covariates were obtained from maternal interviews and medical records. Two piecewise linear regression models were applied to assess the relations between blood lead and stress levels using a data-driven approach according to spline smoothing fitting of the data. Maternal blood lead levels ranged from 0.80 to 14.84μg/dL, and the geometric mean was 3.97μg/dL. The P-values for the two piecewise linear models against the single linear regression models were 0.010, 0.003 and 0.017 for models predicting GSI, depression and anxiety symptom scores, respectively. When blood lead levels were below 2.57μg/dL, each unit increase in log10 transformed blood lead levels (μg/dL) was associated with about 18% increase in maternal GSI, depression and anxiety symptom scores (P GSI =0.013, P depression =0.002, P anxiety =0.019, respectively). However, no significant relation was found when blood lead levels were above 2.57μg/dL (all P-values>0.05). Our findings suggested a nonlinear relationship between blood lead and emotional stress levels among pregnant women. Emotional stress increased along with blood lead levels, and appeared to be plateaued when blood lead levels reached 2.57μg/dL. Copyright © 2016 Elsevier B.V. All rights reserved.

Optimal control of parametric oscillations of compressed flexible bars

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

In this paper the problem of damping of the linear systems oscillations with piece-wise constant control is solved. The motion of bar construction is reduced to the form described by Hill's differential equation using the Bubnov-Galerkin method. To calculate switching moments of the one-side control the method of sequential linear programming is used. The elements of the fundamental matrix of the Hill's equation are approximated by trigonometric series. Examples of the optimal control of the systems for various initial conditions and different number of control stages have been calculated. The corresponding phase trajectories and transient processes are represented.

A novel approach to piecewise analytic agricultural machinery path reconstruction

NASA Astrophysics Data System (ADS)

Wörz, Sascha; Mederle, Michael; Heizinger, Valentin; Bernhardt, Heinz

2017-12-01

Before analysing machinery operation in fields, it has to be coped with the problem that the GPS signals of GPS receivers located on the machines contain measurement noise, are time-discrete, and the underlying physical system describing the positions, axial and absolute velocities, angular rates and angular orientation of the operating machines during the whole working time are unknown. This research work presents a new three-dimensional mathematical approach using kinematic relations based on control variables as Euler angular velocities and angles and a discrete target control problem, such that the state control function is given by the sum of squared residuals involving the state and control variables to get such a physical system, which yields a noise-free and piecewise analytic representation of the positions, velocities, angular rates and angular orientation. It can be used for a further detailed study and analysis of the problem of why agricultural vehicles operate in practice as they do.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

PubMed

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Superconducting linear actuator

NASA Technical Reports Server (NTRS)

Johnson, Bruce; Hockney, Richard

1993-01-01

Special actuators are needed to control the orientation of large structures in space-based precision pointing systems. Electromagnetic actuators that presently exist are too large in size and their bandwidth is too low. Hydraulic fluid actuation also presents problems for many space-based applications. Hydraulic oil can escape in space and contaminate the environment around the spacecraft. A research study was performed that selected an electrically-powered linear actuator that can be used to control the orientation of a large pointed structure. This research surveyed available products, analyzed the capabilities of conventional linear actuators, and designed a first-cut candidate superconducting linear actuator. The study first examined theoretical capabilities of electrical actuators and determined their problems with respect to the application and then determined if any presently available actuators or any modifications to available actuator designs would meet the required performance. The best actuator was then selected based on available design, modified design, or new design for this application. The last task was to proceed with a conceptual design. No commercially-available linear actuator or modification capable of meeting the specifications was found. A conventional moving-coil dc linear actuator would meet the specification, but the back-iron for this actuator would weigh approximately 12,000 lbs. A superconducting field coil, however, eliminates the need for back iron, resulting in an actuator weight of approximately 1000 lbs.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

PubMed

Casellas, J; Bach, R

2012-06-01

Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.

The dynamical analysis of modified two-compartment neuron model and FPGA implementation

NASA Astrophysics Data System (ADS)

Lin, Qianjin; Wang, Jiang; Yang, Shuangming; Yi, Guosheng; Deng, Bin; Wei, Xile; Yu, Haitao

2017-10-01

The complexity of neural models is increasing with the investigation of larger biological neural network, more various ionic channels and more detailed morphologies, and the implementation of biological neural network is a task with huge computational complexity and power consumption. This paper presents an efficient digital design using piecewise linearization on field programmable gate array (FPGA), to succinctly implement the reduced two-compartment model which retains essential features of more complicated models. The design proposes an approximate neuron model which is composed of a set of piecewise linear equations, and it can reproduce different dynamical behaviors to depict the mechanisms of a single neuron model. The consistency of hardware implementation is verified in terms of dynamical behaviors and bifurcation analysis, and the simulation results including varied ion channel characteristics coincide with the biological neuron model with a high accuracy. Hardware synthesis on FPGA demonstrates that the proposed model has reliable performance and lower hardware resource compared with the original two-compartment model. These investigations are conducive to scalability of biological neural network in reconfigurable large-scale neuromorphic system.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Mixing and the fractal geometry of piecewise isometries.

PubMed

Park, Paul P; Lynn, Thomas F; Umbanhowar, Paul B; Ottino, Julio M; Lueptow, Richard M

2017-04-01

Mathematical concepts often have applicability in areas that may have surprised their original developers. This is the case with piecewise isometries (PWIs), which transform an object by cutting it into pieces that are then rearranged to reconstruct the original object, and which also provide a paradigm to study mixing via cutting and shuffling in physical sciences and engineering. Every PWI is characterized by a geometric structure called the exceptional set, E, whose complement comprises nonmixing regions in the domain. Varying the parameters that define the PWI changes both the structure of E as well as the degree of mixing the PWI produces, which begs the question of how to determine which parameters produce the best mixing. Motivated by mixing of yield stress materials, for example granular media, in physical systems, we use numerical simulations of PWIs on a hemispherical shell and examine how the fat fractal properties of E relate to the degree of mixing for any particular PWI. We present numerical evidence that the fractional coverage of E negatively correlates with the intensity of segregation, a standard measure for the degree of mixing, which suggests that fundamental properties of E such as fractional coverage can be used to predict the effectiveness of a particular PWI as a mixing mechanism.

zeldovich-PLT: Zel'dovich approximation initial conditions generator

NASA Astrophysics Data System (ADS)

Eisenstein, Daniel; Garrison, Lehman

2016-05-01

zeldovich-PLT generates Zel'dovich approximation (ZA) initial conditions (i.e. first-order Lagrangian perturbation theory) for cosmological N-body simulations, optionally applying particle linear theory (PLT) corrections.

Efficient Digital Implementation of The Sigmoidal Function For Artificial Neural Network

NASA Astrophysics Data System (ADS)

Pratap, Rana; Subadra, M.

2011-10-01

An efficient piecewise linear approximation of a nonlinear function (PLAN) is proposed. This uses simulink environment design to perform a direct transformation from X to Y, where X is the input and Y is the approximated sigmoidal output. This PLAN is then used within the outputs of an artificial neural network to perform the nonlinear approximation. In This paper, is proposed a method to implement in FPGA (Field Programmable Gate Array) circuits different approximation of the sigmoid function.. The major benefit of the proposed method resides in the possibility to design neural networks by means of predefined block systems created in System Generator environment and the possibility to create a higher level design tools used to implement neural networks in logical circuits.

Interior region-of-interest reconstruction using a small, nearly piecewise constant subregion

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

Taguchi, Katsuyuki; Xu Jingyan; Srivastava, Somesh

2011-03-15

Purpose: To develop a method to reconstruct an interior region-of-interest (ROI) image with sufficient accuracy that uses differentiated backprojection (DBP) projection onto convex sets (POCS) [H. Kudo et al., ''Tiny a priori knowledge solves the interior problem in computed tomography'', Phys. Med. Biol. 53, 2207-2231 (2008)] and a tiny knowledge that there exists a nearly piecewise constant subregion. Methods: The proposed method first employs filtered backprojection to reconstruct an image on which a tiny region P with a small variation in the pixel values is identified inside the ROI. Total variation minimization [H. Yu and G. Wang, ''Compressed sensing basedmore » interior tomography'', Phys. Med. Biol. 54, 2791-2805 (2009); W. Han et al., ''A general total variation minimization theorem for compressed sensing based interior tomography'', Int. J. Biomed. Imaging 2009, Article 125871 (2009)] is then employed to obtain pixel values in the subregion P, which serve as a priori knowledge in the next step. Finally, DBP-POCS is performed to reconstruct f(x,y) inside the ROI. Clinical data and the reconstructed image obtained by an x-ray computed tomography system (SOMATOM Definition; Siemens Healthcare) were used to validate the proposed method. The detector covers an object with a diameter of {approx}500 mm. The projection data were truncated either moderately to limit the detector coverage to diameter 350 mm of the object or severely to cover diameter 199 mm. Images were reconstructed using the proposed method. Results: The proposed method provided ROI images with correct pixel values in all areas except near the edge of the ROI. The coefficient of variation, i.e., the root mean square error divided by the mean pixel values, was less than 2.0% or 4.5% with the moderate or severe truncation cases, respectively, except near the boundary of the ROI. Conclusions: The proposed method allows for reconstructing interior ROI images with sufficient accuracy with a tiny

Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks

NASA Astrophysics Data System (ADS)

Yang, Tao; Chen, Xue; Shi, Sheping; Sun, Erkun; Shi, Chen

2018-03-01

We propose a low-complexity and modulation-format-independent carrier phase estimation (CPE) scheme based on two-stage modified blind phase search (MBPS) with linear approximation to compensate the phase noise of arbitrary m-ary quadrature amplitude modulation (m-QAM) signals in elastic optical networks (EONs). Comprehensive numerical simulations are carried out in the case that the highest possible modulation format in EONs is 256-QAM. The simulation results not only verify its advantages of higher estimation accuracy and modulation-format independence, i.e., universality, but also demonstrate that the implementation complexity is significantly reduced by at least one-fourth in comparison with the traditional BPS scheme. In addition, the proposed scheme shows similar laser linewidth tolerance with the traditional BPS scheme. The slightly better OSNR performance of the scheme is also experimentally validated for PM-QPSK and PM-16QAM systems, respectively. The coexistent advantages of low-complexity and modulation-format-independence could make the proposed scheme an attractive candidate for flexible receiver-side DSP unit in EONs.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

NoRMCorre: An online algorithm for piecewise rigid motion correction of calcium imaging data.

PubMed

Pnevmatikakis, Eftychios A; Giovannucci, Andrea

2017-11-01

Motion correction is a challenging pre-processing problem that arises early in the analysis pipeline of calcium imaging data sequences. The motion artifacts in two-photon microscopy recordings can be non-rigid, arising from the finite time of raster scanning and non-uniform deformations of the brain medium. We introduce an algorithm for fast Non-Rigid Motion Correction (NoRMCorre) based on template matching. NoRMCorre operates by splitting the field of view (FOV) into overlapping spatial patches along all directions. The patches are registered at a sub-pixel resolution for rigid translation against a regularly updated template. The estimated alignments are subsequently up-sampled to create a smooth motion field for each frame that can efficiently approximate non-rigid artifacts in a piecewise-rigid manner. Existing approaches either do not scale well in terms of computational performance or are targeted to non-rigid artifacts arising just from the finite speed of raster scanning, and thus cannot correct for non-rigid motion observable in datasets from a large FOV. NoRMCorre can be run in an online mode resulting in comparable to or even faster than real time motion registration of streaming data. We evaluate its performance with simple yet intuitive metrics and compare against other non-rigid registration methods on simulated data and in vivo two-photon calcium imaging datasets. Open source Matlab and Python code is also made available. The proposed method and accompanying code can be useful for solving large scale image registration problems in calcium imaging, especially in the presence of non-rigid deformations. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

Non linear shock wave propagation in heterogeneous fluids: a numerical approach beyond the parabolic approximation with application to sonic boom.

NASA Astrophysics Data System (ADS)

Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas

2008-06-01

Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the

Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures

NASA Astrophysics Data System (ADS)

Krauze, W.; Makowski, P.; Kujawińska, M.

2015-06-01

Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography - Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.

A hybrid approach to modeling and control of vehicle height for electronically controlled air suspension

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Cai, Yingfeng; Wang, Shaohua; Liu, Yanling; Chen, Long

2016-01-01

The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical (MLD) modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller (HMPC) is tuned based on online mixed-integer quadratic optimization (MIQP). Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology (MPT), thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

Advanced analysis technique for the evaluation of linear alternators and linear motors

NASA Technical Reports Server (NTRS)

Holliday, Jeffrey C.

1995-01-01

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Spline smoothing of histograms by linear programming

NASA Technical Reports Server (NTRS)

Bennett, J. O.

1972-01-01

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Implementing Linear Algebra Related Algorithms on the TI-92+ Calculator.

ERIC Educational Resources Information Center

Alexopoulos, John; Abraham, Paul

2001-01-01

Demonstrates a less utilized feature of the TI-92+: its natural and powerful programming language. Shows how to implement several linear algebra related algorithms including the Gram-Schmidt process, Least Squares Approximations, Wronskians, Cholesky Decompositions, and Generalized Linear Least Square Approximations with QR Decompositions.…

Harmonic-phase path-integral approximation of thermal quantum correlation functions

NASA Astrophysics Data System (ADS)

Robertson, Christopher; Habershon, Scott

2018-03-01

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

The Use of Piecewise Growth Models to Estimate Learning Trajectories and RtI Instructional Effects in a Comparative Interrupted Time-Series Design

ERIC Educational Resources Information Center

Zvoch, Keith

2016-01-01

Piecewise growth models (PGMs) were used to estimate and model changes in the preliteracy skill development of kindergartners in a moderately sized school district in the Pacific Northwest. PGMs were applied to interrupted time-series (ITS) data that arose within the context of a response-to-intervention (RtI) instructional framework. During the…

Rational-spline approximation with automatic tension adjustment

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Kerr, P. A.

1984-01-01

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Changes in Clavicle Length and Maturation in Americans: 1840-1980.

PubMed

Langley, Natalie R; Cridlin, Sandra

2016-01-01

Secular changes refer to short-term biological changes ostensibly due to environmental factors. Two well-documented secular trends in many populations are earlier age of menarche and increasing stature. This study synthesizes data on maximum clavicle length and fusion of the medial epiphysis in 1840-1980 American birth cohorts to provide a comprehensive assessment of developmental and morphological change in the clavicle. Clavicles from the Hamann-Todd Human Osteological Collection (n = 354), McKern and Stewart Korean War males (n = 341), Forensic Anthropology Data Bank (n = 1,239), and the McCormick Clavicle Collection (n = 1,137) were used in the analysis. Transition analysis was used to evaluate fusion of the medial epiphysis (scored as unfused, fusing, or fused). Several statistical treatments were used to assess fluctuations in maximum clavicle length. First, Durbin-Watson tests were used to evaluate autocorrelation, and a local regression (LOESS) was used to identify visual shifts in the regression slope. Next, piecewise regression was used to fit linear regression models before and after the estimated breakpoints. Multiple starting parameters were tested in the range determined to contain the breakpoint, and the model with the smallest mean squared error was chosen as the best fit. The parameters from the best-fit models were then used to derive the piecewise models, which were compared with the initial simple linear regression models to determine which model provided the best fit for the secular change data. The epiphyseal union data indicate a decline in the age at onset of fusion since the early twentieth century. Fusion commences approximately four years earlier in mid- to late twentieth-century birth cohorts than in late nineteenth- and early twentieth-century birth cohorts. However, fusion is completed at roughly the same age across cohorts. The most significant decline in age at onset of epiphyseal union appears to have occurred since the mid

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response.

PubMed

Caricato, Marco

2018-04-07

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

NASA Astrophysics Data System (ADS)

Caricato, Marco

2018-04-01

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Progress in linear optics, non-linear optics and surface alignment of liquid crystals

NASA Astrophysics Data System (ADS)

Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.

We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.

Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime

NASA Astrophysics Data System (ADS)

Lorin, E.; Yang, X.; Antoine, X.

2016-06-01

The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.

Quasi-linear regime of gravitational instability: Implication to density-velocity relation

NASA Technical Reports Server (NTRS)

Shandarin, Sergei F.

1993-01-01

The well known linear relation between density and peculiar velocity distributions is a powerful tool for studying the large-scale structure in the Universe. Potentially it can test the gravitational instability theory and measure Omega. At present it is used in both ways: the velocity is reconstructed, provided the density is given, and vice versa. Reconstructing the density from the velocity field usually makes use of the Zel'dovich approximation. However, the standard linear approximation in Eulerian space is used when the velocity is reconstructed from the density distribution. I show that the linearized Zel'dovich approximation, in other words the linear approximation in the Lagrangian space, is more accurate for reconstructing velocity. In principle, a simple iteration technique can recover both the density and velocity distributions in Lagrangian space, but its practical application may need an additional study.

A pitfall of piecewise-polytropic equation of state inference

NASA Astrophysics Data System (ADS)

Raaijmakers, Geert; Riley, Thomas E.; Watts, Anna L.

2018-05-01

The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between spaces of local (interior source matter) and global (exterior spacetime) parameters. In a companion paper, these issues were raised on a theoretical basis. In this study we reproduce a probability transformation procedure from the literature in order to map a joint posterior distribution of Schwarzschild gravitational masses and radii into a joint posterior distribution of EOS parameters. We demonstrate computationally that EOS parameter inferences are sensitive to the choice to define a prior on a joint space of these masses and radii, instead of on a joint space interior source matter parameters. We focus on the piecewise-polytropic EOS model, which is currently standard in the field of astrophysical dense matter study. We discuss the implications of this issue for the field.

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

NASA Astrophysics Data System (ADS)

Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

2012-08-01

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

An approximation method for configuration optimization of trusses

NASA Technical Reports Server (NTRS)

Hansen, Scott R.; Vanderplaats, Garret N.

1988-01-01

Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

Variational models for discontinuity detection

NASA Astrophysics Data System (ADS)

Vitti, Alfonso; Battista Benciolini, G.

2010-05-01

The Mumford-Shah variational model produces a smooth approximation of the data and detects data discontinuities by solving a minimum problem involving an energy functional. The Blake-Zisserman model permits also the detection of discontinuities in the first derivative of the approximation. This model can result in a quasi piece-wise linear approximation, whereas the Mumford-Shah can result in a quasi piece-wise constant approximation. The two models are well known in the mathematical literature and are widely adopted in computer vision for image segmentation. In Geodesy the Blake-Zisserman model has been applied successfully to the detection of cycle-slips in linear combinations of GPS measurements. Few attempts to apply the model to time series of coordinates have been done so far. The problem of detecting discontinuities in time series of GNSS coordinates is well know and its relevance increases as the quality of geodetic measurements, analysis techniques, models and products improves. The application of the Blake-Zisserman model appears reasonable and promising due to the model characteristic to detect both position and velocity discontinuities in the same time series. The detection of position and velocity changes is of great interest in geophysics where the discontinuity itself can be the very relevant object. In the work for the realization of reference frames, detecting position and velocity discontinuities may help to define models that can handle non-linear motions. In this work the Mumford-Shah and the Blake-Zisserman models are briefly presented, the treatment is carried out from a practical viewpoint rather than from a theoretical one. A set of time series of GNSS coordinates has been processed and the results are presented in order to highlight the capabilities and the weakness of the variational approach. A first attempt to derive some indication for the automatic set up of the model parameters has been done. The underlying relation that could links

Piecewise-Constant-Model-Based Interior Tomography Applied to Dentin Tubules

DOE PAGES

He, Peng; Wei, Biao; Wang, Steve; ...

2013-01-01

Dentin is a hierarchically structured biomineralized composite material, and dentin’s tubules are difficult to study in situ. Nano-CT provides the requisite resolution, but the field of view typically contains only a few tubules. Using a plate-like specimen allows reconstruction of a volume containing specific tubules from a number of truncated projections typically collected over an angular range of about 140°, which is practically accessible. Classical computed tomography (CT) theory cannot exactly reconstruct an object only from truncated projections, needless to say a limited angular range. Recently, interior tomography was developed to reconstruct a region-of-interest (ROI) from truncated data in amore » theoretically exact fashion via the total variation (TV) minimization under the condition that the ROI is piecewise constant. In this paper, we employ a TV minimization interior tomography algorithm to reconstruct interior microstructures in dentin from truncated projections over a limited angular range. Compared to the filtered backprojection (FBP) reconstruction, our reconstruction method reduces noise and suppresses artifacts. Volume rendering confirms the merits of our method in terms of preserving the interior microstructure of the dentin specimen.« less

The piecewise parabolic method for Riemann problems in nonlinear elasticity.

PubMed

Zhang, Wei; Wang, Tao; Bai, Jing-Song; Li, Ping; Wan, Zhen-Hua; Sun, De-Jun

2017-10-18

We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD ("D" denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC ("C" denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid "stick" problem with the same material at the two sides of contact interface and the solid/solid "slip" problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Multilayer neural networks for reduced-rank approximation.

PubMed

Diamantaras, K I; Kung, S Y

1994-01-01

This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the

Semilinear programming: applications and implementation

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

Mohan, S.

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program. [subroutines and flow charts

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Non-linear HRV indices under autonomic nervous system blockade.

PubMed

Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel

2014-01-01

Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.

Optimal Design of Spring Characteristics of Damper for Subharmonic Vibration in Automatic Transmission Powertrain

NASA Astrophysics Data System (ADS)

Nakae, T.; Ryu, T.; Matsuzaki, K.; Rosbi, S.; Sueoka, A.; Takikawa, Y.; Ooi, Y.

2016-09-01

In the torque converter, the damper of the lock-up clutch is used to effectively absorb the torsional vibration. The damper is designed using a piecewise-linear spring with three stiffness stages. However, a nonlinear vibration, referred to as a subharmonic vibration of order 1/2, occurred around the switching point in the piecewise-linear restoring torque characteristics because of the nonlinearity. In the present study, we analyze vibration reduction for subharmonic vibration. The model used herein includes the torque converter, the gear train, and the differential gear. The damper is modeled by a nonlinear rotational spring of the piecewise-linear spring. We focus on the optimum design of the spring characteristics of the damper in order to suppress the subharmonic vibration. A piecewise-linear spring with five stiffness stages is proposed, and the effect of the distance between switching points on the subharmonic vibration is investigated. The results of our analysis indicate that the subharmonic vibration can be suppressed by designing a damper with five stiffness stages to have a small spring constant ratio between the neighboring springs. The distances between switching points must be designed to be large enough that the amplitude of the main frequency component of the systems does not reach the neighboring switching point.

Piecewise parabolic method for simulating one-dimensional shear shock wave propagation in tissue-mimicking phantoms

NASA Astrophysics Data System (ADS)

Tripathi, B. B.; Espíndola, D.; Pinton, G. F.

2017-11-01

The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.

A variable-step-size robust delta modulator.

NASA Technical Reports Server (NTRS)

Song, C. L.; Garodnick, J.; Schilling, D. L.

1971-01-01

Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Piecewise mass flows within a solar prominence observed by the New Vacuum Solar Telescope

NASA Astrophysics Data System (ADS)

Li, Hongbo; Liu, Yu; Tam, Kuan Vai; Zhao, Mingyu; Zhang, Xuefei

2018-06-01

The material of solar prominences is often observed in a state of flowing. These mass flows (MF) are important and useful for us to understand the internal structure and dynamics of prominences. In this paper, we present a high resolution Hα observation of MFs within a quiescent solar prominence. From the observation, we find that the plasma primarily has a circular motion and a downward motion separately in the middle section and legs of the prominence, which creates a piecewise mass flow along the observed prominence. Moreover, the observation also shows a clear displacement of MF's velocity peaks in the middle section of the prominence. All of these provide us with a detailed record of MFs within a solar prominence and show a new approach to detecting the physical properties of prominence.

LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL

NASA Technical Reports Server (NTRS)

Duke, E. L.

1994-01-01

interest, or a full non-linear aerodynamic model as used in simulations. LINEAR is written in FORTRAN and has been implemented on a DEC VAX computer operating under VMS with a virtual memory requirement of approximately 296K of 8 bit bytes. Both an interactive and batch version are included. LINEAR was developed in 1988.

Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy

NASA Astrophysics Data System (ADS)

Loring, Roger F.

2017-04-01

Mean-trajectory approximations permit the calculation of nonlinear vibrational spectra from semiclassically quantized trajectories on a single electronically adiabatic potential surface. By describing electronic degrees of freedom with classical phase-space variables and subjecting these to semiclassical quantization, mean-trajectory approximations may be extended to compute both nonlinear electronic spectra and vibrational-electronic spectra. A general mean-trajectory approximation for both electronic and nuclear degrees of freedom is presented, and the results for purely electronic and for vibrational-electronic four-wave mixing experiments are quantitatively assessed for harmonic surfaces with linear electronic-nuclear coupling.

The convergence rate of approximate solutions for nonlinear scalar conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1991-01-01

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates.

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

2018-04-01

We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

Conduction cooling systems for linear accelerator cavities

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

Kephart, Robert

A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

On Algorithms for Generating Computationally Simple Piecewise Linear Classifiers

DTIC Science & Technology

1989-05-01

suffers. - Waveform classification, e.g. speech recognition, seismic analysis (i.e. discrimination between earthquakes and nuclear explosions), target...assuming Gaussian distributions (B-G) d) Bayes classifier with probability densities estimated with the k-N-N method (B- kNN ) e) The -arest neighbour...range of classifiers are chosen including a fast, easy computable and often used classifier (B-G), reliable and complex classifiers (B- kNN and NNR

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Linearly Adjustable International Portfolios

NASA Astrophysics Data System (ADS)

Fonseca, R. J.; Kuhn, D.; Rustem, B.

2010-09-01

We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

Analysis of single-degree-of-freedom piezoelectric energy harvester with stopper by incremental harmonic balance method

NASA Astrophysics Data System (ADS)

Zhao, Dan; Wang, Xiaoman; Cheng, Yuan; Liu, Shaogang; Wu, Yanhong; Chai, Liqin; Liu, Yang; Cheng, Qianju

2018-05-01

Piecewise-linear structure can effectively broaden the working frequency band of the piezoelectric energy harvester, and improvement of its research can promote the practical process of energy collection device to meet the requirements for powering microelectronic components. In this paper, the incremental harmonic balance (IHB) method is introduced for the complicated and difficult analysis process of the piezoelectric energy harvester to solve these problems. After obtaining the nonlinear dynamic equation of the single-degree-of-freedom piecewise-linear energy harvester by mathematical modeling and the equation is solved based on the IHB method, the theoretical amplitude-frequency curve of open-circuit voltage is achieved. Under 0.2 g harmonic excitation, a piecewise-linear energy harvester is experimentally tested by unidirectional frequency-increasing scanning. The results demonstrate that the theoretical and experimental amplitudes have the same trend, and the width of the working band with high voltage output are 4.9 Hz and 4.7 Hz, respectively, and the relative error is 4.08%. The open-output peak voltage are 21.53 V and 18.25 V, respectively, and the relative error is 15.23%. Since the theoretical value is consistent with the experimental results, the theoretical model and the incremental harmonic balance method used in this paper are suitable for solving single-degree-of-freedom piecewise-linear piezoelectric energy harvester and can be applied to further parameter optimized design.

Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1990-01-01

In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

Adaptive control using neural networks and approximate models.

PubMed

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

Moment method analysis of linearly tapered slot antennas

NASA Technical Reports Server (NTRS)

Koeksal, Adnan

1993-01-01

A method of moments (MOM) model for the analysis of the Linearly Tapered Slot Antenna (LTSA) is developed and implemented. The model employs an unequal size rectangular sectioning for conducting parts of the antenna. Piecewise sinusoidal basis functions are used for the expansion of conductor current. The effect of the dielectric is incorporated in the model by using equivalent volume polarization current density and solving the equivalent problem in free-space. The feed section of the antenna including the microstripline is handled rigorously in the MOM model by including slotline short circuit and microstripline currents among the unknowns. Comparison with measurements is made to demonstrate the validity of the model for both the air case and the dielectric case. Validity of the model is also verified by extending the model to handle the analysis of the skew-plate antenna and comparing the results to those of a skew-segmentation modeling results of the same structure and to available data in the literature. Variation of the radiation pattern for the air LTSA with length, height, and taper angle is investigated, and the results are tabulated. Numerical results for the effect of the dielectric thickness and permittivity are presented.

Control algorithms for dynamic attenuators

PubMed Central

Hsieh, Scott S.; Pelc, Norbert J.

2014-01-01

Purpose: The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. Methods: The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. Results: The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current

Control algorithms for dynamic attenuators.

PubMed

Hsieh, Scott S; Pelc, Norbert J

2014-06-01

The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

PubMed Central

2012-01-01

Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a

Global dynamics for switching systems and their extensions by linear differential equations

NASA Astrophysics Data System (ADS)

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-01

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Global dynamics for switching systems and their extensions by linear differential equations.

PubMed

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-15

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Sensitivity analysis and approximation methods for general eigenvalue problems

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1986-01-01

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

NASA Technical Reports Server (NTRS)

Fukumori, I.

1995-01-01

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Stochastic Swift-Hohenberg Equation with Degenerate Linear Multiplicative Noise

NASA Astrophysics Data System (ADS)

Hernández, Marco; Ong, Kiah Wah

2018-03-01

We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

Approximate formulas for elasticity of the Tornquist functions and some their advantages

NASA Astrophysics Data System (ADS)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

A linear and nonlinear study of Mira

NASA Astrophysics Data System (ADS)

Cox, A. N.; Ostlie, D. A.

1993-12-01

Both linear and nonlinear calculations of the 331 day, long period variable star Mira have been undertaken to see what radial pulsation mode is naturally selected. Models are similar to those considered in the linear nonadiabatic stellar pulsation study of Ostlie and Cox (1986). Models are considered with masses near one solar mass, luminosities between 4000 and 5000 solar luminosities, and effective temperatures of approximately 3000 K. These models have fundamental mode periods that closely match the pulsation period of Mira. The equation of state for the stellar material is given by the Stellingwerf (1975ab) procedure, and the opacity is obtained from a fit by Cahn that matches the low temperature molecular absorption data for the poplulation I Ross-Aller 1 mixture calculated from the Los Alamos Astrophysical Opacity Library. For the linear study, the Cox, Brownlee, and Eilers (1966) approximation is used for the linear theory variation of the convection luminosity. For the nonlinear work, the method described by Ostlie (1990) and Cox (1990) is followed. Results showing internal details of the radial fundamental and first overtone modes behavior in linear theory are presented. Preliminary radial fundamental mode nonlinear calculations are discussed. The very tentative conclusion is that neither the fundamental or first overtone mode is excluded from being the actual observed one.

Gain in stochastic resonance: Precise numerics versus linear response theory beyond the two-mode approximation

NASA Astrophysics Data System (ADS)

Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter

2003-03-01

In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545 548; Fluct. Noise Lett. 1, L181 (2001)].

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

Filter-based multiscale entropy analysis of complex physiological time series.

PubMed

Xu, Yuesheng; Zhao, Liang

2013-08-01

Multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiological time series. We reinterpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce filter-based multiscale entropy (FME), which filters a time series to generate multiple frequency components, and then we compute the blockwise entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory, which suggests that the human heartbeat interval time series can be described in piecewise linear patterns, we propose piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. The numerical performance of the adaptive piecewise constant filter multiscale entropy without prior information is comparable to that of PLFME, whose design takes prior information into account.

Application of Linear and Non-Linear Harmonic Methods for Unsteady Transonic Flow

NASA Astrophysics Data System (ADS)

Gundevia, Rayomand

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.

COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

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

Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme,more » we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less

PV Degradation Curves: Non-Linearities and Failure Modes

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

Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill

Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually,more » in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.« less

Slow relaxation in weakly open rational polygons.

PubMed

Kokshenev, Valery B; Vicentini, Eduardo

2003-07-01

The interplay between the regular (piecewise-linear) and irregular (vertex-angle) boundary effects in nonintegrable rational polygonal billiards (of m equal sides) is discussed. Decay dynamics in polygons (of perimeter P(m) and small opening Delta) is analyzed through the late-time survival probability S(m) approximately equal t(-delta). Two distinct slow relaxation channels are established. The primary universal channel exhibits relaxation of regular sliding orbits, with delta=1. The secondary channel is given by delta>1 and becomes open when m>P(m)/Delta. It originates from vertex order-disorder dual effects and is due to relaxation of chaoticlike excitations.

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

Multivariate test power approximations for balanced linear mixed models in studies with missing data.

PubMed

Ringham, Brandy M; Kreidler, Sarah M; Muller, Keith E; Glueck, Deborah H

2016-07-30

Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of (i) the expected number of complete cases, (ii) the expected number of non-missing pairs of responses, or (iii) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

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

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-03-10

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

Dynamic Programming for Structured Continuous Markov Decision Problems

NASA Technical Reports Server (NTRS)

Dearden, Richard; Meuleau, Nicholas; Washington, Richard; Feng, Zhengzhu

2004-01-01

We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions can be computed efficiently.

Numerical linear algebra in data mining

NASA Astrophysics Data System (ADS)

Eldén, Lars

Ideas and algorithms from numerical linear algebra are important in several areas of data mining. We give an overview of linear algebra methods in text mining (information retrieval), pattern recognition (classification of handwritten digits), and PageRank computations for web search engines. The emphasis is on rank reduction as a method of extracting information from a data matrix, low-rank approximation of matrices using the singular value decomposition and clustering, and on eigenvalue methods for network analysis.

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

Resistance thermometer has linear resistance-temperature coefficient at low temperatures

NASA Technical Reports Server (NTRS)

Kuzyk, W.

1966-01-01

Resistance thermometer incorporating a germanium resistance element with a platinum resistance element in a wheatstone bridge circuit has a linear temperature-resistance coefficient over a range from approximately minus 140 deg C to approximately minus 253 deg C.

Analytical approximations to the Hotelling trace for digital x-ray detectors

NASA Astrophysics Data System (ADS)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

Strong shock implosion, approximate solution

NASA Astrophysics Data System (ADS)

Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.

1983-01-01

The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.

Piecewise Structural Equation Model (SEM) Disentangles the Environmental Conditions Favoring Diatom Diazotroph Associations (DDAs) in the Western Tropical North Atlantic (WTNA).

PubMed

Stenegren, Marcus; Berg, Carlo; Padilla, Cory C; David, Stefan-Sebastian; Montoya, Joseph P; Yager, Patricia L; Foster, Rachel A

2017-01-01

Diatom diazotroph associations (DDAs) are important components in the world's oceans, especially in the western tropical north Atlantic (WTNA), where blooms have a significant impact on carbon and nitrogen cycling. However, drivers of their abundances and distribution patterns remain unknown. Here, we examined abundance and distribution patterns for two DDA populations in relation to the Amazon River (AR) plume in the WTNA. Quantitative PCR assays, targeting two DDAs (het-1 and het-2) by their symbiont's nifH gene, served as input in a piecewise structural equation model (SEM). Collections were made during high (spring 2010) and low (fall 2011) flow discharges of the AR. The distributions of dissolved nutrients, chlorophyll- a , and DDAs showed coherent patterns indicative of areas influenced by the AR. A symbiotic Hemiaulus hauckii-Richelia (het-2) bloom (>10 6 cells L -1 ) occurred during higher discharge of the AR and was coincident with mesohaline to oceanic (30-35) sea surface salinities (SSS), and regions devoid of dissolved inorganic nitrogen (DIN), low concentrations of both DIP (>0.1 μmol L -1 ) and Si (>1.0 μmol L -1 ). The Richelia (het-1) associated with Rhizosolenia was only present in 2010 and at lower densities (10-1.76 × 10 5 nifH copies L -1 ) than het-2 and limited to regions of oceanic SSS (>36). The het-2 symbiont detected in 2011 was associated with H. membranaceus (>10 3 nifH copies L -1 ) and were restricted to regions with mesohaline SSS (31.8-34.3), immeasurable DIN, moderate DIP (0.1-0.60 μmol L -1 ) and higher Si (4.19-22.1 μmol L -1 ). The piecewise SEM identified a profound direct negative effect of turbidity on the het-2 abundance in spring 2010, while DIP and water turbidity had a more positive influence in fall 2011, corroborating our observations of DDAs at subsurface maximas. We also found a striking difference in the influence of salinity on DDA symbionts suggesting a niche differentiation and preferences in oceanic and

Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

NASA Astrophysics Data System (ADS)

Hellgren, Maria; Gross, E. K. U.

2013-11-01

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.022514 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Algorithms for sorting unsigned linear genomes by the DCJ operations.

PubMed

Jiang, Haitao; Zhu, Binhai; Zhu, Daming

2011-02-01

The double cut and join operation (abbreviated as DCJ) has been extensively used for genomic rearrangement. Although the DCJ distance between signed genomes with both linear and circular (uni- and multi-) chromosomes is well studied, the only known result for the NP-complete unsigned DCJ distance problem is an approximation algorithm for unsigned linear unichromosomal genomes. In this article, we study the problem of computing the DCJ distance on two unsigned linear multichromosomal genomes (abbreviated as UDCJ). We devise a 1.5-approximation algorithm for UDCJ by exploiting the distance formula for signed genomes. In addition, we show that UDCJ admits a weak kernel of size 2k and hence an FPT algorithm running in O(2(2k)n) time.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor.

PubMed

Du, Yuhuan; Guo, Yingqing

2016-07-15

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor

PubMed Central

Du, Yuhuan; Guo, Yingqing

2016-01-01

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter. PMID:27428976

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

NASA Technical Reports Server (NTRS)

Fadel, G. M.

1991-01-01

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Linear time relational prototype based learning.

PubMed

Gisbrecht, Andrej; Mokbel, Bassam; Schleif, Frank-Michael; Zhu, Xibin; Hammer, Barbara

2012-10-01

Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, they are infeasible already for medium sized data sets. The contribution of this article is twofold: On the one hand we propose a novel supervised prototype based classification technique for dissimilarity data based on popular learning vector quantization (LVQ), on the other hand we transfer a linear time approximation technique, the Nyström approximation, to this algorithm and an unsupervised counterpart, the relational generative topographic mapping (GTM). This way, linear time and space methods result. We evaluate the techniques on three examples from the biomedical domain.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Bilinear effect in complex systems

NASA Astrophysics Data System (ADS)

Lam, Lui; Bellavia, David C.; Han, Xiao-Pu; Alston Liu, Chih-Hui; Shu, Chang-Qing; Wei, Zhengjin; Zhou, Tao; Zhu, Jichen

2010-09-01

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.

Big geo data surface approximation using radial basis functions: A comparative study

NASA Astrophysics Data System (ADS)

Majdisova, Zuzana; Skala, Vaclav

2017-12-01

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.

Meta-regression approximations to reduce publication selection bias.

PubMed

Stanley, T D; Doucouliagos, Hristos

2014-03-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with standard error (PEESE), is shown to have the smallest bias and mean squared error in most cases and to outperform conventional meta-analysis estimators, often by a great deal. Monte Carlo simulations also demonstrate how a new hybrid estimator that conditionally combines PEESE and the Egger regression intercept can provide a practical solution to publication selection bias. PEESE is easily expanded to accommodate systematic heterogeneity along with complex and differential publication selection bias that is related to moderator variables. By providing an intuitive reason for these approximations, we can also explain why the Egger regression works so well and when it does not. These meta-regression methods are applied to several policy-relevant areas of research including antidepressant effectiveness, the value of a statistical life, the minimum wage, and nicotine replacement therapy. Copyright © 2013 John Wiley & Sons, Ltd.

Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.

PubMed

Petrinović, Davor; Brezović, Marko

2011-04-01

We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device. © 2011 IEEE

Calculating Resonance Positions and Widths Using the Siegert Approximation Method

ERIC Educational Resources Information Center

Rapedius, Kevin

2011-01-01

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

An unsteady lifting surface method for single rotation propellers

NASA Technical Reports Server (NTRS)

Williams, Marc H.

1990-01-01

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

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

Brabec, Jiri; Lin, Lin; Shao, Meiyue

We present two iterative algorithms for approximating the absorption spectrum of molecules within linear response of time-dependent density functional theory (TDDFT) framework. These methods do not attempt to compute eigenvalues or eigenvectors of the linear response matrix. They are designed to approximate the absorption spectrum as a function directly. They take advantage of the special structure of the linear response matrix. Neither method requires the linear response matrix to be constructed explicitly. They only require a procedure that performs the multiplication of the linear response matrix with a vector. These methods can also be easily modified to efficiently estimate themore » density of states (DOS) of the linear response matrix without computing the eigenvalues of this matrix. We show by computational experiments that the methods proposed in this paper can be much more efficient than methods that are based on the exact diagonalization of the linear response matrix. We show that they can also be more efficient than real-time TDDFT simulations. We compare the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost.« less

Classical Testing in Functional Linear Models.

PubMed

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

Classical Testing in Functional Linear Models

PubMed Central

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. PMID:28955155

Structure of Salt-free Linear Polyelectrolytes in the Debye-Hückel Approximation

NASA Astrophysics Data System (ADS)

Stevens, Mark J.; Kremer, Kurt

1996-11-01

We examine the effects of the common Debye-Hückel approximation used in theories of polyelectrolytes. Molecular dynamics simulations using the Debye-Hückel pair potential of salt-free polyelectrolytes have been performed. The results of these simulations are compared to earlier “Coulomb" simulations which explicitly treated the counterions. We report here the comparisons of the osmotic pressure, the end-to-end distance and the single chain structure factor. In the dilute regime the Debye-Hückel chains are more elongated than the Coulomb chains implying that the counterion screening is stronger than the Debye-Hückel prediction. Like the Coulomb chains the Debye-Hückel chains contract significantly below the overlap density in contradiction to all theories. Entropy thus plays an important and sorely neglected role in theory.

Approximation methods for control of structural acoustics models with piezoceramic actuators

NASA Astrophysics Data System (ADS)

Banks, H. T.; Fang, W.; Silcox, R. J.; Smith, R. C.

1993-01-01

The active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Specifically, this control is implemented via piezoceramic patches on the beam which produces pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation methods in this manner leads to a system with an unbounded input term. Approximation methods in this manner leads to a system with an unbounded input team. Approximation methods in the context of linear quadratic regulator (LQR) state space control formulation are discussed and numerical results demonstrating the effectiveness of this approach in computing feedback controls for noise reduction are presented.

Chua's Equation was Proved to BE Chaotic in Two Years, Lorenz Equation in Thirty Six Years

NASA Astrophysics Data System (ADS)

Muthuswamy, Bharathwaj

2013-01-01

Although there are probably more publications on Chua's circuit than any other chaotic circuit, a tutorial with a historical emphasis is still lacking. Hence the goal of this chapter is to provide such a tutorial. This chapter will prove useful for a novice who is looking to understand the basics behind chaotic circuits without too much technical details. The chapter also includes a cookbook approach to a rigorous proof of chaos in piecewise-linear systems. The proof is a summary of the original piecewise-linear proof of chaos in Chua's circuit. The chapter concludes with a discussion of circuits derived from Chua's circuit.

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

The Zeldovich approximation and wide-angle redshift-space distortions

NASA Astrophysics Data System (ADS)

Castorina, Emanuele; White, Martin

2018-06-01

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum . In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

Piecewise compensation for the nonlinear error of fiber-optic gyroscope scale factor

NASA Astrophysics Data System (ADS)

Zhang, Yonggang; Wu, Xunfeng; Yuan, Shun; Wu, Lei

2013-08-01

Fiber-Optic Gyroscope (FOG) scale factor nonlinear error will result in errors in Strapdown Inertial Navigation System (SINS). In order to reduce nonlinear error of FOG scale factor in SINS, a compensation method is proposed in this paper based on curve piecewise fitting of FOG output. Firstly, reasons which can result in FOG scale factor error are introduced and the definition of nonlinear degree is provided. Then we introduce the method to divide the output range of FOG into several small pieces, and curve fitting is performed in each output range of FOG to obtain scale factor parameter. Different scale factor parameters of FOG are used in different pieces to improve FOG output precision. These parameters are identified by using three-axis turntable, and nonlinear error of FOG scale factor can be reduced. Finally, three-axis swing experiment of SINS verifies that the proposed method can reduce attitude output errors of SINS by compensating the nonlinear error of FOG scale factor and improve the precision of navigation. The results of experiments also demonstrate that the compensation scheme is easy to implement. It can effectively compensate the nonlinear error of FOG scale factor with slightly increased computation complexity. This method can be used in inertial technology based on FOG to improve precision.

Involvement of Linear Plasmids in Aerobic Biodegradation of Vinyl Chloride

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

BRIGMON, ROBINL.

2004-06-14

Pseudomonas putida strain AJ and Ochrobactrum strain TD were isolated from hazardous waste sites based on their ability to use vinyl chloride (VC) as a sole source of carbon and energy under aerobic conditions. Strains AJ and TD also use ethene and ethylene oxide as growth substrates. Strain AJ contained a linear megaplasmid (approximately 260 kb) when grown on VC or ethene, but no circular plasmids. While growing on ethylene oxide, the size of the linear plasmid in strain AJ decreased to approximately 100 kb, although its ability to use VC as a substrate was retained. The linear plasmids inmore » strain AJ were cured and its ability to consume VC, ethene, and ethylene oxide was lost following growth on a rich substrate (Luria-Bertani broth) through at least three transfers. Strain TD contained three linear plasmids, ranging in size from approximately 100 kb to 320 kb, when growing on VC or ethene. As with strain AJ, the linear plasmids in strain TD were cured following growth on Luria -Bertani broth and its ability to consume VC and ethene was lost. Further analysis of these linear plasmids may help reveal the pathway for VC biodegradation in strains AJ and TD and explain why this process occurs at many but not all sites where groundwater is contaminated with chloroethenes. Metabolism of VC and ethene by strains AJ and TD is initiated by an alkene monooxygenase. Their yields during growth on VC (0.15-0.20 mg total suspended solids per mg VC) are similar to the yields reported for other isolates i.e., Mycobacterium sp., Nocardioides sp., and Pseudomonas sp.« less

Development of models of the magnetorheological fluid damper

NASA Astrophysics Data System (ADS)

Kazakov, Yu. B.; Morozov, N. A.; Nesterov, S. A.

2017-06-01

The algorithm for analytical calculation of a power characteristic of magnetorheological (MR) dampers taking into account the rheological properties of MR fluid is considered. The nonlinear magnetorheological characteristics are represented by piecewise linear approximation to MR fluid areas with different viscosities. The extended calculated power characteristics of a MR damper are received and they coincide with actual results. The finite element model of a MR damper is developed; it allows carrying out the analysis of a MR damper taking into account the mutual influence of electromagnetic, hydrodynamic and thermal fields. The results of finite element simulation coincide with analytical solutions that allows using them for design development of a MR damper.

Design of multi-body Lambert type orbits with specified departure and arrival positions

NASA Astrophysics Data System (ADS)

Ishii, Nobuaki; Kawaguchi, Jun'ichiro; Matsuo, Hiroki

1991-10-01

A new procedure for designing a multi-body Lambert type orbit comprising a multiple swingby process is developed, aiming at relieving a numerical difficulty inherent to a highly nonlinear swingby mechanism. The proposed algorithm, Recursive Multi-Step Linearization, first divides a whole orbit into several trajectory segments. Then, with a maximum use of piecewised transition matrices, a segmentized orbit is repeatedly upgraded until an approximated orbit initially based on a patched conics method eventually converges. In application to the four body earth-moon system with sun's gravitation, one of the double lunar swingby orbits including 12 lunar swingbys is successfully designed without any velocity mismatch.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Linear Chebyshev Complex Function Approximation.

DTIC Science & Technology

1981-02-26

CONTINUE C C C LEVEL I C C LEVaI KwC 30 KUKeI C C THE NEXT VARIABLE IS NOT USED, BUT IS IN THE PUBLISHED CODE. KPIuKi1 C NPI MK=NP 1-K MODE2 0 DO 40 J=K,M...WEAPONS CENTER, Silver Spring, Code 432-4 (Egbert H. Jackson)I DWTNSRDC ANNAI DWTNSRDC CARDI NRL, Code 5330 (Dr. Robert J. Adams ), 5209 (Russell M. Brown

Approximation of a Brittle Fracture Energy with a Constraint of Non-interpenetration

NASA Astrophysics Data System (ADS)

Chambolle, Antonin; Conti, Sergio; Francfort, Gilles A.

2018-06-01

Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over an SBD type space. The corresponding functional can in turn be approximated in the sense of {Γ}-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Homogenization of one-dimensional draining through heterogeneous porous media including higher-order approximations

NASA Astrophysics Data System (ADS)

Anderson, Daniel M.; McLaughlin, Richard M.; Miller, Cass T.

2018-02-01

We examine a mathematical model of one-dimensional draining of a fluid through a periodically-layered porous medium. A porous medium, initially saturated with a fluid of a high density is assumed to drain out the bottom of the porous medium with a second lighter fluid replacing the draining fluid. We assume that the draining layer is sufficiently dense that the dynamics of the lighter fluid can be neglected with respect to the dynamics of the heavier draining fluid and that the height of the draining fluid, represented as a free boundary in the model, evolves in time. In this context, we neglect interfacial tension effects at the boundary between the two fluids. We show that this problem admits an exact solution. Our primary objective is to develop a homogenization theory in which we find not only leading-order, or effective, trends but also capture higher-order corrections to these effective draining rates. The approximate solution obtained by this homogenization theory is compared to the exact solution for two cases: (1) the permeability of the porous medium varies smoothly but rapidly and (2) the permeability varies as a piecewise constant function representing discrete layers of alternating high/low permeability. In both cases we are able to show that the corrections in the homogenization theory accurately predict the position of the free boundary moving through the porous medium.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

PubMed

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

NASA Astrophysics Data System (ADS)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Signal-to-noise ratio estimation using adaptive tuning on the piecewise cubic Hermite interpolation model for images.

PubMed

Sim, K S; Yeap, Z X; Tso, C P

2016-11-01

An improvement to the existing technique of quantifying signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images using piecewise cubic Hermite interpolation (PCHIP) technique is proposed. The new technique uses an adaptive tuning onto the PCHIP, and is thus named as ATPCHIP. To test its accuracy, 70 images are corrupted with noise and their autocorrelation functions are then plotted. The ATPCHIP technique is applied to estimate the uncorrupted noise-free zero offset point from a corrupted image. Three existing methods, the nearest neighborhood, first order interpolation and original PCHIP, are used to compare with the performance of the proposed ATPCHIP method, with respect to their calculated SNR values. Results show that ATPCHIP is an accurate and reliable method to estimate SNR values from SEM images. SCANNING 38:502-514, 2016. © 2015 Wiley Periodicals, Inc. © Wiley Periodicals, Inc.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Approximation methods for control of acoustic/structure models with piezoceramic actuators

NASA Technical Reports Server (NTRS)

Banks, H. T.; Fang, W.; Silcox, R. J.; Smith, R. C.

1991-01-01

The active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Specifically, this control is implemented via piezoceramic patches on the beam which produces pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation methods in this manner leads to a system with an unbounded input term. Approximation methods in the context of linear quadratic regulator (LQR) state space control formulation are discussed and numerical results demonstrating the effectiveness of this approach in computing feedback controls for noise reduction are presented.

Free-piston engine linear generator for hybrid vehicles modeling study

NASA Astrophysics Data System (ADS)

Callahan, T. J.; Ingram, S. K.

1995-05-01

Development of a free piston engine linear generator was investigated for use as an auxiliary power unit for a hybrid electric vehicle. The main focus of the program was to develop an efficient linear generator concept to convert the piston motion directly into electrical power. Computer modeling techniques were used to evaluate five different designs for linear generators. These designs included permanent magnet generators, reluctance generators, linear DC generators, and two and three-coil induction generators. The efficiency of the linear generator was highly dependent on the design concept. The two-coil induction generator was determined to be the best design, with an efficiency of approximately 90 percent.

Corrections to the one-photon approximation in the 0+-->2+ transition of 12C

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

Paul Gueye; Madeleine Bernheim; J. F. Danel

2001-04-18

Contribution of higher order effects to the one-photon exchange approximation were studied in the first excited state of 12C by comparing inclusive inelastic scattering cross sections of electrons and positrons obtained at the Saclay Linear Accelerator. The data were compared to a distorted wave Born approximation (DWBA)calculation. The results indicate an effect less than 2% within 2sigma, compatible with what was observed in recent elastic scattering measurements.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

NASA Technical Reports Server (NTRS)

Cliff, E. M.

1975-01-01

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Linear Water Waves

NASA Astrophysics Data System (ADS)

Kuznetsov, N.; Maz'ya, V.; Vainberg, B.

2002-08-01

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

2009-01-01

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Linear and non-linear Modified Gravity forecasts with future surveys

NASA Astrophysics Data System (ADS)

Casas, Santiago; Kunz, Martin; Martinelli, Matteo; Pettorino, Valeria

2017-12-01

Modified Gravity theories generally affect the Poisson equation and the gravitational slip in an observable way, that can be parameterized by two generic functions (η and μ) of time and space. We bin their time dependence in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. In this work we neglect the information from the cross correlation of these observables, and treat them as independent. Our results show that η and μ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further apply a Zero-phase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We extend the analysis to two particular parameterizations of μ and η and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of η and μ at the 2-5% level when using only linear scales (wavevector k < 0 . 15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about 1% when non-linearities are included.

Piecewise Potential Vorticity Inversion for Intense Extratropical Cyclones

NASA Astrophysics Data System (ADS)

Seiler, C.; Zwiers, F. W.

2017-12-01

Global climate models (GCMs) tend to simulate too few intense extratropical cyclones (ETCs) in the Northern Hemisphere (NH) under historic climate conditions. This bias may arise from the interactions of multiple drivers, including surface temperature gradients, latent heating in the lower troposphere, and the upper-level jet stream. Previous attempts to quantify the importance of these drivers include idealized model experiments or statistical approaches. The first method however cannot easily be implemented for a multi-GCM ensemble, and the second approach does not disentangle the interactions among drivers, nor does it prove causality. An alternative method that overcomes these limitations is piecewise potential vorticity inversion (PPVI). PPVI derives the wind and geopotential height fields by inverting potential vorticity (PV) for discrete atmospheric levels. Despite being a powerful diagnostic tool, PPVI has primarily been used to study the dynamics of individual events only. This study presents the first PPVI climatology for the 5% most intense NH ETCs that occurred from 1980 to 2016. Conducting PPVI to 3273 ETC tracks identified in ERA-Interim reanalysis, we quantified the contributions from 3 atmospheric layers to ETC intensity. The respective layers are the surface (1000 hPa), a lower atmospheric level (700-850 hPa) and an upper atmospheric level (100-500 hPa) that are associated with the contributions from surface temperature gradients, latent heating, and the jet stream, respectively. Results show that contributions are dominated by the lower level (40%), followed by the upper level (20%) and the surface (17%), while the remaining 23% are associated with the background flow. Contributions from the surface and the lower level are stronger in the western ocean basins owed to the presence of the warm ocean currents, while contributions from the upper level are stronger in the eastern basins. Vertical cross sections of ETC-centered composites show an

Oscillating-Linear-Drive Vacuum Compressor for CO2

NASA Technical Reports Server (NTRS)

Izenson, Michael G.; Shimko, Martin

2005-01-01

A vacuum compressor has been designed to compress CO2 from approximately equal to 1 psia (approximately equal to 6.9 kPa absolute pressure) to approximately equal to 75 psia (approximately equal to 0.52 MPa), to be insensitive to moisture, to have a long operational life, and to be lightweight, compact, and efficient. The compressor consists mainly of (1) a compression head that includes hydraulic diaphragms, a gas-compression diaphragm, and check valves; and (2) oscillating linear drive that includes a linear motor and a drive spring, through which compression force is applied to the hydraulic diaphragms. The motor is driven at the resonance vibrational frequency of the motor/spring/compression-head system, the compression head acting as a damper that takes energy out of the oscillation. The net effect of the oscillation is to cause cyclic expansion and contraction of the gas-compression diaphragm, and, hence, of the volume bounded by this diaphragm. One-way check valves admit gas into this volume from the low-pressure side during expansion and allow the gas to flow out to the high-pressure side during contraction. Fatigue data and the results of diaphragm stress calculations have been interpreted as signifying that the compressor can be expected to have an operational life of greater than 30 years with a confidence level of 99.9 percent.

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

NASA Technical Reports Server (NTRS)

Kvernadze, George; Hagstrom,Thomas; Shapiro, Henry

1997-01-01

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

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

Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, ourmore » FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.« less

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Laplace transform homotopy perturbation method for the approximation of variational problems.

PubMed

Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R

2016-01-01

This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

Estimating linear effects in ANOVA designs: the easy way.

PubMed

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

Error Estimation for the Linearized Auto-Localization Algorithm

PubMed Central

Guevara, Jorge; Jiménez, Antonio R.; Prieto, Jose Carlos; Seco, Fernando

2012-01-01

The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons’ positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method. PMID:22736965

Improved Displacement Transfer Functions for Structure Deformed Shape Predictions Using Discretely Distributed Surface Strains

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2012-01-01

In the formulations of earlier Displacement Transfer Functions for structure shape predictions, the surface strain distributions, along a strain-sensing line, were represented with piecewise linear functions. To improve the shape-prediction accuracies, Improved Displacement Transfer Functions were formulated using piecewise nonlinear strain representations. Through discretization of an embedded beam (depth-wise cross section of a structure along a strain-sensing line) into multiple small domains, piecewise nonlinear functions were used to describe the surface strain distributions along the discretized embedded beam. Such piecewise approach enabled the piecewise integrations of the embedded beam curvature equations to yield slope and deflection equations in recursive forms. The resulting Improved Displacement Transfer Functions, written in summation forms, were expressed in terms of beam geometrical parameters and surface strains along the strain-sensing line. By feeding the surface strains into the Improved Displacement Transfer Functions, structural deflections could be calculated at multiple points for mapping out the overall structural deformed shapes for visual display. The shape-prediction accuracies of the Improved Displacement Transfer Functions were then examined in view of finite-element-calculated deflections using different tapered cantilever tubular beams. It was found that by using the piecewise nonlinear strain representations, the shape-prediction accuracies could be greatly improved, especially for highly-tapered cantilever tubular beams.

Testing the Linearity of the Cosmic Origins Spectrograph FUV Channel Thermal Correction

NASA Astrophysics Data System (ADS)

Fix, Mees B.; De Rosa, Gisella; Sahnow, David

2018-05-01

The Far Ultraviolet Cross Delay Line (FUV XDL) detector on the Cosmic Origins Spectrograph (COS) is subject to temperature-dependent distortions. The correction performed by the COS calibration pipeline (CalCOS) assumes that these changes are linear across the detector. In this report we evaluate the accuracy of the linear approximations using data obtained on orbit. Our results show that the thermal distortions are consistent with our current linear model.

Quasi-linear theory via the cumulant expansion approach

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1974-01-01

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum

ERIC Educational Resources Information Center

Weltner, Klaus; Esperidiao, Antonio Sergio C.; Miranda, Paulo

2004-01-01

We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are…

Localization and stationary phase approximation on supermanifolds

NASA Astrophysics Data System (ADS)

Zakharevich, Valentin

2017-08-01

Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Linear transformer driver for pulse generation

DOEpatents

Kim, Alexander A; Mazarakis, Michael G; Sinebryukhov, Vadim A; Volkov, Sergey N; Kondratiev, Sergey S; Alexeenko, Vitaly M; Bayol, Frederic; Demol, Gauthier; Stygar, William A

2015-04-07

A linear transformer driver includes at least one ferrite ring positioned to accept a load. The linear transformer driver also includes a first power delivery module that includes a first charge storage devices and a first switch. The first power delivery module sends a first energy in the form of a first pulse to the load. The linear transformer driver also includes a second power delivery module including a second charge storage device and a second switch. The second power delivery module sends a second energy in the form of a second pulse to the load. The second pulse has a frequency that is approximately three times the frequency of the first pulse. The at least one ferrite ring is positioned to force the first pulse and the second pulse to the load by temporarily isolating the first pulse and the second pulse from an electrical ground.

Analytical expression for the relaxation moduli of linear viscoelastic composites with periodic microstructure

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

Luciano, R.; Barbero, E.J.

Many micromechanical models have been used to estimate the overall stiffness of heterogeneous- materials and a large number of results and experimental data have been obtained. However, few theoretical and experimental results are available in the field of viscoelastic behavior of heterogeneous media. In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constantmore » in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take in account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four parameters model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.« less

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

Engine With Regression and Neural Network Approximators Designed

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2001-01-01

At the NASA Glenn Research Center, the NASA engine performance program (NEPP, ref. 1) and the design optimization testbed COMETBOARDS (ref. 2) with regression and neural network analysis-approximators have been coupled to obtain a preliminary engine design methodology. The solution to a high-bypass-ratio subsonic waverotor-topped turbofan engine, which is shown in the preceding figure, was obtained by the simulation depicted in the following figure. This engine is made of 16 components mounted on two shafts with 21 flow stations. The engine is designed for a flight envelope with 47 operating points. The design optimization utilized both neural network and regression approximations, along with the cascade strategy (ref. 3). The cascade used three algorithms in sequence: the method of feasible directions, the sequence of unconstrained minimizations technique, and sequential quadratic programming. The normalized optimum thrusts obtained by the three methods are shown in the following figure: the cascade algorithm with regression approximation is represented by a triangle, a circle is shown for the neural network solution, and a solid line indicates original NEPP results. The solutions obtained from both approximate methods lie within one standard deviation of the benchmark solution for each operating point. The simulation improved the maximum thrust by 5 percent. The performance of the linear regression and neural network methods as alternate engine analyzers was found to be satisfactory for the analysis and operation optimization of air-breathing propulsion engines (ref. 4).

A new method to approximate load-displacement relationships of spinal motion segments for patient-specific multi-body models of scoliotic spine.

PubMed

Jalalian, Athena; Tay, Francis E H; Arastehfar, Soheil; Liu, Gabriel

2017-06-01

Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.

Linear and nonlinear response in sheared soft spheres

NASA Astrophysics Data System (ADS)

Tighe, Brian

2013-11-01

Packings of soft spheres provide an idealized model of foams, emulsions, and grains, while also serving as the canonical example of a system undergoing a jamming transition. Packings' mechanical response has now been studied exhaustively in the context of ``strict linear response,'' i.e. by linearizing about a stable static packing and solving the resulting equations of motion. Both because the system is close to a critical point and because the soft sphere pair potential is non-analytic at the point of contact, it is reasonable to ask under what circumstances strict linear response provides a good approximation to the actual response. We simulate sheared soft sphere packings close to jamming and identify two distinct strain scales: (i) the scale on which strict linear response fails, coinciding with a topological change in the packing's contact network; and (ii) the scale on which linear superposition of the averaged stress-strain curve breaks down. This latter scale provides a ``weak linear response'' criterion and is likely to be more experimentally relevant.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Payment contracts in a preventive health care system: a perspective from operations management.

PubMed

Yaesoubi, Reza; Roberts, Stephen D

2011-12-01

We consider a health care system consisting of two noncooperative parties: a health purchaser (payer) and a health provider, where the interaction between the two parties is governed by a payment contract. We determine the contracts that coordinate the health purchaser-health provider relationship; i.e. the contracts that maximize the population's welfare while allowing each entity to optimize its own objective function. We show that under certain conditions (1) when the number of customers for a preventive medical intervention is verifiable, there exists a gate-keeping contract and a set of concave piecewise linear contracts that coordinate the system, and (2) when the number of customers is not verifiable, there exists a contract of bounded linear form and a set of incentive-feasible concave piecewise linear contracts that coordinate the system. Copyright © 2011 Elsevier B.V. All rights reserved.

Dense grid sibling frames with linear phase filters

NASA Astrophysics Data System (ADS)

Abdelnour, Farras

2013-09-01

We introduce new 5-band dyadic sibling frames with dense time-frequency grid. Given a lowpass filter satisfying certain conditions, the remaining filters are obtained using spectral factorization. The analysis and synthesis filterbanks share the same lowpass and bandpass filters but have different and oversampled highpass filters. This leads to wavelets approximating shift-invariance. The filters are FIR, have linear phase, and the resulting wavelets have vanishing moments. The filters are designed using spectral factorization method. The proposed method leads to smooth limit functions with higher approximation order, and computationally stable filterbanks.

Identification of piecewise affine systems based on fuzzy PCA-guided robust clustering technique

NASA Astrophysics Data System (ADS)

Khanmirza, Esmaeel; Nazarahari, Milad; Mousavi, Alireza

2016-12-01

Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors. Since a general method for the analysis of hybrid systems is not available, some researchers have focused on specific types of hybrid systems. Piecewise affine (PWA) systems are one of the subsets of hybrid systems. The identification of PWA systems includes the estimation of the parameters of affine subsystems and the coefficients of the hyperplanes defining the partition of the state-input domain. In this paper, we have proposed a PWA identification approach based on a modified clustering technique. By using a fuzzy PCA-guided robust k-means clustering algorithm along with neighborhood outlier detection, the two main drawbacks of the well-known clustering algorithms, i.e., the poor initialization and the presence of outliers, are eliminated. Furthermore, this modified clustering technique enables us to determine the number of subsystems without any prior knowledge about system. In addition, applying the structure of the state-input domain, that is, considering the time sequence of input-output pairs, provides a more efficient clustering algorithm, which is the other novelty of this work. Finally, the proposed algorithm has been evaluated by parameter identification of an IGV servo actuator. Simulation together with experiment analysis has proved the effectiveness of the proposed method.

Parameterized Linear Longitudinal Airship Model

NASA Technical Reports Server (NTRS)

Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph

2010-01-01

A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics

The linear regulator problem for parabolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1983-01-01

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

Asymptotic approximations for pure bending of thin cylindrical shells

NASA Astrophysics Data System (ADS)

Coman, Ciprian D.

2017-08-01

A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel-Mushtari-Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.

The application of rational approximation in the calculation of a temperature field with a non-linear surface heat-transfer coefficient during quenching for 42CrMo steel cylinder

NASA Astrophysics Data System (ADS)

Cheng, Heming; Huang, Xieqing; Fan, Jiang; Wang, Honggang

1999-10-01

The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

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

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

Analytical approximations for spiral waves

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

Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald

2013-12-15

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +}more » with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.« less

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Karpel, Mordechay

1989-01-01

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

GWAS with longitudinal phenotypes: performance of approximate procedures

PubMed Central

Sikorska, Karolina; Montazeri, Nahid Mostafavi; Uitterlinden, André; Rivadeneira, Fernando; Eilers, Paul HC; Lesaffre, Emmanuel

2015-01-01

Analysis of genome-wide association studies with longitudinal data using standard procedures, such as linear mixed model (LMM) fitting, leads to discouragingly long computation times. There is a need to speed up the computations significantly. In our previous work (Sikorska et al: Fast linear mixed model computations for genome-wide association studies with longitudinal data. Stat Med 2012; 32.1: 165–180), we proposed the conditional two-step (CTS) approach as a fast method providing an approximation to the P-value for the longitudinal single-nucleotide polymorphism (SNP) effect. In the first step a reduced conditional LMM is fit, omitting all the SNP terms. In the second step, the estimated random slopes are regressed on SNPs. The CTS has been applied to the bone mineral density data from the Rotterdam Study and proved to work very well even in unbalanced situations. In another article (Sikorska et al: GWAS on your notebook: fast semi-parallel linear and logistic regression for genome-wide association studies. BMC Bioinformatics 2013; 14: 166), we suggested semi-parallel computations, greatly speeding up fitting many linear regressions. Combining CTS with fast linear regression reduces the computation time from several weeks to a few minutes on a single computer. Here, we explore further the properties of the CTS both analytically and by simulations. We investigate the performance of our proposal in comparison with a related but different approach, the two-step procedure. It is analytically shown that for the balanced case, under mild assumptions, the P-value provided by the CTS is the same as from the LMM. For unbalanced data and in realistic situations, simulations show that the CTS method does not inflate the type I error rate and implies only a minimal loss of power. PMID:25712081

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Boskovic, Jovan D.

2008-01-01

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions.

PubMed

Brighenti, Chiara; Gnudi, Gianni; Avanzolini, Guido

2003-05-01

This paper presents a mathematical model of the oxygen alveolo-capillary exchange to provide the capillary oxygen partial pressure profile in normal and pathological conditions. In fact, a thickening of the blood-gas barrier, heavy exercise or a low oxygen partial pressure (PO2) in the alveolar space can reduce the O2 alveolo-capillary exchange. Since the reversible binding between haemoglobin and oxygen makes it impossible to determine the closed form for the mathematical description of the PO2 profile along the pulmonary capillaries, an approximate analytical solution of the capillary PO2 profile is proposed. Simulation results are compared with the capillary PO2 profile obtained by numerical integration and by a piecewise linear interpolation of the oxyhaemoglobin dissociation curve. Finally, the proposed model is evaluated in a large range of physiopathological diffusive conditions. The good fit to numerical solutions in all experimental conditions seems to represent a substantial improvement with respect to the approach based on a linear approximation of the oxyhaemoglobin dissociation curve, and makes this model a candidate to be incorporated into the integrated descriptions of the entire respiratory system, where the datum of primary interest is the value of end capillary PO2.

Adaptive optics system performance approximations for atmospheric turbulence correction

NASA Astrophysics Data System (ADS)

Tyson, Robert K.

1990-10-01

Analysis of adaptive optics system behavior often can be reduced to a few approximations and scaling laws. For atmospheric turbulence correction, the deformable mirror (DM) fitting error is most often used to determine a priori the interactuator spacing and the total number of correction zones required. This paper examines the mirror fitting error in terms of its most commonly used exponential form. The explicit constant in the error term is dependent on deformable mirror influence function shape and actuator geometry. The method of least squares fitting of discrete influence functions to the turbulent wavefront is compared to the linear spatial filtering approximation of system performance. It is found that the spatial filtering method overstimates the correctability of the adaptive optics system by a small amount. By evaluating fitting error for a number of DM configurations, actuator geometries, and influence functions, fitting error constants verify some earlier investigations.

Typical performance of approximation algorithms for NP-hard problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-11-01

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

Does transport time help explain the high trauma mortality rates in rural areas? New and traditional predictors assessed by new and traditional statistical methods

PubMed Central

Røislien, Jo; Lossius, Hans Morten; Kristiansen, Thomas

2015-01-01

Background Trauma is a leading global cause of death. Trauma mortality rates are higher in rural areas, constituting a challenge for quality and equality in trauma care. The aim of the study was to explore population density and transport time to hospital care as possible predictors of geographical differences in mortality rates, and to what extent choice of statistical method might affect the analytical results and accompanying clinical conclusions. Methods Using data from the Norwegian Cause of Death registry, deaths from external causes 1998–2007 were analysed. Norway consists of 434 municipalities, and municipality population density and travel time to hospital care were entered as predictors of municipality mortality rates in univariate and multiple regression models of increasing model complexity. We fitted linear regression models with continuous and categorised predictors, as well as piecewise linear and generalised additive models (GAMs). Models were compared using Akaike's information criterion (AIC). Results Population density was an independent predictor of trauma mortality rates, while the contribution of transport time to hospital care was highly dependent on choice of statistical model. A multiple GAM or piecewise linear model was superior, and similar, in terms of AIC. However, while transport time was statistically significant in multiple models with piecewise linear or categorised predictors, it was not in GAM or standard linear regression. Conclusions Population density is an independent predictor of trauma mortality rates. The added explanatory value of transport time to hospital care is marginal and model-dependent, highlighting the importance of exploring several statistical models when studying complex associations in observational data. PMID:25972600

Meshless analysis of shear deformable shells: the linear model

NASA Astrophysics Data System (ADS)

Costa, Jorge C.; Tiago, Carlos M.; Pimenta, Paulo M.

2013-10-01

This work develops a kinematically linear shell model departing from a consistent nonlinear theory. The initial geometry is mapped from a flat reference configuration by a stress-free finite deformation, after which, the actual shell motion takes place. The model maintains the features of a complete stress-resultant theory with Reissner-Mindlin kinematics based on an inextensible director. A hybrid displacement variational formulation is presented, where the domain displacements and kinematic boundary reactions are independently approximated. The resort to a flat reference configuration allows the discretization using 2-D Multiple Fixed Least-Squares (MFLS) on the domain. The consistent definition of stress resultants and consequent plane stress assumption led to a neat formulation for the analysis of shells. The consistent linear approximation, combined with MFLS, made possible efficient computations with a desired continuity degree, leading to smooth results for the displacement, strain and stress fields, as shown by several numerical examples.

Local facet approximation for image stitching

NASA Astrophysics Data System (ADS)

Li, Jing; Lai, Shiming; Liu, Yu; Wang, Zhengming; Zhang, Maojun

2018-01-01

Image stitching aims at eliminating multiview parallax and generating a seamless panorama given a set of input images. This paper proposes a local adaptive stitching method, which could achieve both accurate and robust image alignments across the whole panorama. A transformation estimation model is introduced by approximating the scene as a combination of neighboring facets. Then, the local adaptive stitching field is constructed using a series of linear systems of the facet parameters, which enables the parallax handling in three-dimensional space. We also provide a concise but effective global projectivity preserving technique that smoothly varies the transformations from local adaptive to global planar. The proposed model is capable of stitching both normal images and fisheye images. The efficiency of our method is quantitatively demonstrated in the comparative experiments on several challenging cases.

An Approximation Solution to Refinery Crude Oil Scheduling Problem with Demand Uncertainty Using Joint Constrained Programming

PubMed Central

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation. PMID:24757433

An approximation solution to refinery crude oil scheduling problem with demand uncertainty using joint constrained programming.

PubMed

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation.

Recursive inversion of externally defined linear systems

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1988-01-01

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

Approximate Linear Regulator and Kalman Filter

DTIC Science & Technology

1980-09-01

of Equivalent Dominant Poles and Zeros Using Industrial Specifications," IEEE Trans. on Industrial Electronics and Control Instrumentation, Vol. IECI...true. In recent years, the rapid development of powerful minicomputers and microprocessors makes the industrial applications of optimal control...1976, pp. 677-687. [21] Y. Takahashi, M. Tomizuka and D. I. Auslander, Simple discrete control of industrial processes, Trans. on ASME J. of Dynamic

Characterization of intermittency in renewal processes: Application to earthquakes

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

Akimoto, Takuma; Hasumi, Tomohiro; Aizawa, Yoji

2010-03-15

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variablesmore » but that the conditional probability distribution functions in the tail obey the Weibull distribution.« less