`Un-Darkening' the Cosmos: New laws of physics for an expanding universe

NASA Astrophysics Data System (ADS)

George, William

2017-11-01

Dark matter is believed to exist because Newton's Laws are inconsistent with the visible matter in galaxies. Dark energy is necessary to explain the universe expansion. (also available from www.turbulence-online.com) suggested that the equations themselves might be in error because they implicitly assume that time is measured in linear increments. This presentation couples the possible non-linearity of time with an expanding universe. Maxwell's equations for an expanding universe with constant speed of light are shown to be invariant only if time itself is non-linear. Both linear and exponential expansion rates are considered. A linearly expanding universe corresponds to logarithmic time, while exponential expansion corresponds to exponentially varying time. Revised Newton's laws using either leads to different definitions of mass and kinetic energy, both of which appear time-dependent if expressed in linear time. And provide the possibility of explaining the astronomical observations without either dark matter or dark energy. We would have never noticed the differences on earth, since the leading term in both expansions is linear in δ /to where to is the current age.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

The Development of a High Speed Exponential Function Generator for Linearization of Microwave Voltage Controlled Oscillators.

DTIC Science & Technology

1985-10-01

characteristic of a p-n junction to provide exponential linearization in a simple, thermally-stable, wide band circuit. RESME Les oscillateurs A...exponentielle (fr6quence/tension) que V’on 1 retrouve chez plusieurs oscillateurs . Ce circuit, d’une grande largeur de bande, utilise la caractfiristique

Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

PubMed

Zhao, Shouwei

2011-06-01

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

Gauged U(1) clockwork theory

NASA Astrophysics Data System (ADS)

Lee, Hyun Min

2018-03-01

We consider the gauged U (1) clockwork theory with a product of multiple gauge groups and discuss the continuum limit of the theory to a massless gauged U (1) with linear dilaton background in five dimensions. The localization of the lightest state of gauge fields on a site in the theory space naturally leads to exponentially small effective couplings of external matter fields localized away from the site. We discuss the implications of our general discussion with some examples, such as mediators of dark matter interactions, flavor-changing B-meson decays as well as D-term SUSY breaking.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter.

PubMed

Bonny, Jean Marie; Boespflug-Tanguly, Odile; Zanca, Michel; Renou, Jean Pierre

2003-03-01

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Multiple spatially localized dynamical states in friction-excited oscillator chains

NASA Astrophysics Data System (ADS)

Papangelo, A.; Hoffmann, N.; Grolet, A.; Stender, M.; Ciavarella, M.

2018-03-01

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.

Deterioration of abstract reasoning ability in mild cognitive impairment and Alzheimer's disease: correlation with regional grey matter volume loss revealed by diffeomorphic anatomical registration through exponentiated lie algebra analysis.

PubMed

Yoshiura, Takashi; Hiwatashi, Akio; Yamashita, Koji; Ohyagi, Yasumasa; Monji, Akira; Takayama, Yukihisa; Kamano, Norihiro; Kawashima, Toshiro; Kira, Jun-Ichi; Honda, Hiroshi

2011-02-01

To determine which brain regions are relevant to deterioration in abstract reasoning as measured by Raven's Colored Progressive Matrices (CPM) in the context of dementia. MR images of 37 consecutive patients including 19 with Alzheimer's disease (AD) and 18 with amnestic mild cognitive impairment (aMCI) were retrospectively analyzed. All patients were administered the CPM. Regional grey matter (GM) volume was evaluated according to the regimens of voxel-based morphometry, during which a non-linear registration algorithm called Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra was employed. Multiple regression analyses were used to map the regions where GM volumes were correlated with CPM scores. The strongest correlation with CPM scores was seen in the left middle frontal gyrus while a region with the largest volume was identified in the left superior temporal gyrus. Significant correlations were seen in 14 additional regions in the bilateral cerebral hemispheres and right cerebellum. Deterioration of abstract reasoning ability in AD and aMCI measured by CPM is related to GM loss in multiple regions, which is in close agreement with the results of previous activation studies.

Asymmetrical flow field-flow fractionation coupled with multiple detections: A complementary approach in the characterization of egg yolk plasma.

PubMed

Dou, Haiyang; Li, Yueqiu; Choi, Jaeyeong; Huo, Shuying; Ding, Liang; Shen, Shigang; Lee, Seungho

2016-09-23

The capability of asymmetrical flow field-flow fractionation (AF4) coupled with UV/VIS, multiangle light scattering (MALS) and quasi-elastic light scattering (QELS) (AF4-UV-MALS-QELS) for separation and characterization of egg yolk plasma was evaluated. The accuracy of hydrodynamic radius (Rh) obtained from QELS and AF4 theory (using both simplified and full expression of AF4 retention equations) was discussed. The conformation of low density lipoprotein (LDL) and its aggregates in egg yolk plasma was discussed based on the ratio of radius of gyration (Rg) to Rh together with the results from bio-transmission electron microscopy (Bio-TEM). The results indicate that the full retention equation is more relevant than simplified version for the Rh determination at high cross flow rate. The Rh from online QELS is reliable only at a specific range of sample concentration. The effect of programmed cross flow rate (linear and exponential decay) on the analysis of egg yolk plasma was also investigated. It was found that the use of an exponentially decaying cross flow rate not only reduces the AF4 analysis time of the egg yolk plasma, but also provides better resolution than the use of either a constant or linearly decaying cross flow rate. A combination of an exponentially decaying cross flow AF4-UV-MALS-QELS and the utilization of full retention equation was proved to be a useful method for the separation and characterization of egg yolk plasma. Copyright © 2016 Elsevier B.V. All rights reserved.

Algebraic approach to electronic spectroscopy and dynamics.

PubMed

Toutounji, Mohamad

2008-04-28

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a(+). While exp(a(+)) translates coherent states, exp(a(+)a(+)) operation on coherent states has always been a challenge, as a(+) has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(tau(1),tau(2),tau(3),tau(4)), of which the optical nonlinear response function may be procured, as evaluating F(tau(1),tau(2),tau(3),tau(4)) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.

Forecasting daily patient volumes in the emergency department.

PubMed

Jones, Spencer S; Thomas, Alun; Evans, R Scott; Welch, Shari J; Haug, Peter J; Snow, Gregory L

2008-02-01

Shifts in the supply of and demand for emergency department (ED) resources make the efficient allocation of ED resources increasingly important. Forecasting is a vital activity that guides decision-making in many areas of economic, industrial, and scientific planning, but has gained little traction in the health care industry. There are few studies that explore the use of forecasting methods to predict patient volumes in the ED. The goals of this study are to explore and evaluate the use of several statistical forecasting methods to predict daily ED patient volumes at three diverse hospital EDs and to compare the accuracy of these methods to the accuracy of a previously proposed forecasting method. Daily patient arrivals at three hospital EDs were collected for the period January 1, 2005, through March 31, 2007. The authors evaluated the use of seasonal autoregressive integrated moving average, time series regression, exponential smoothing, and artificial neural network models to forecast daily patient volumes at each facility. Forecasts were made for horizons ranging from 1 to 30 days in advance. The forecast accuracy achieved by the various forecasting methods was compared to the forecast accuracy achieved when using a benchmark forecasting method already available in the emergency medicine literature. All time series methods considered in this analysis provided improved in-sample model goodness of fit. However, post-sample analysis revealed that time series regression models that augment linear regression models by accounting for serial autocorrelation offered only small improvements in terms of post-sample forecast accuracy, relative to multiple linear regression models, while seasonal autoregressive integrated moving average, exponential smoothing, and artificial neural network forecasting models did not provide consistently accurate forecasts of daily ED volumes. This study confirms the widely held belief that daily demand for ED services is characterized by seasonal and weekly patterns. The authors compared several time series forecasting methods to a benchmark multiple linear regression model. The results suggest that the existing methodology proposed in the literature, multiple linear regression based on calendar variables, is a reasonable approach to forecasting daily patient volumes in the ED. However, the authors conclude that regression-based models that incorporate calendar variables, account for site-specific special-day effects, and allow for residual autocorrelation provide a more appropriate, informative, and consistently accurate approach to forecasting daily ED patient volumes.

Linear prediction and single-channel recording.

PubMed

Carter, A A; Oswald, R E

1995-08-01

The measurement of individual single-channel events arising from the gating of ion channels provides a detailed data set from which the kinetic mechanism of a channel can be deduced. In many cases, the pattern of dwells in the open and closed states is very complex, and the kinetic mechanism and parameters are not easily determined. Assuming a Markov model for channel kinetics, the probability density function for open and closed time dwells should consist of a sum of decaying exponentials. One method of approaching the kinetic analysis of such a system is to determine the number of exponentials and the corresponding parameters which comprise the open and closed dwell time distributions. These can then be compared to the relaxations predicted from the kinetic model to determine, where possible, the kinetic constants. We report here the use of a linear technique, linear prediction/singular value decomposition, to determine the number of exponentials and the exponential parameters. Using simulated distributions and comparing with standard maximum-likelihood analysis, the singular value decomposition techniques provide advantages in some situations and are a useful adjunct to other single-channel analysis techniques.

Exponential Correlation of IQ and the Wealth of Nations

ERIC Educational Resources Information Center

Dickerson, Richard E.

2006-01-01

Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…

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.

Exponential Sensitivity and its Cost in Quantum Physics

PubMed Central

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-01-01

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

Exponential Sensitivity and its Cost in Quantum Physics.

PubMed

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-02-10

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.

Effects of acoustic- and optical-phonon sidebands on the fundamental optical-absorption edge in crystals and disordered semiconductors

NASA Astrophysics Data System (ADS)

Grein, C. H.; John, Sajeev

1990-04-01

We present the results of a parameter-free first-principles theory for the fine structure of the Urbach optical-absorption edge in crystalline and disordered semiconductors. The dominant features are recaptured by means of a simple physical argument based on the most probable potential-well analogy. At finite temperatures, the overall linear exponential Urbach behavior of the subgap optical-absorption coefficient is a consequence of multiple LA-phonon emission and absorption sidebands that accompany the electronic transition. The fine structure of subgap absorption spectra observed in some materials is accounted for by multiple TO-, LO-, and TA-phonon absorption and emission sidebands. Good agreement is found with experimental data on crystalline silicon. The effects of nonadiabaticity in the electron-phonon interaction are calculated.

Polynomials with Restricted Coefficients and Their Applications

DTIC Science & Technology

1987-01-01

sums of exponentials of quadratics, he reduced such ýzums to exponentials of linears (geometric sums!) by simplg multiplying by their conjugates...n, the same algebraic manipulations as before lead to rn V`-~ v ie ? --8-- el4V’ .fk ts with 𔄃 = a+(2r+l)t, A = a+(2r+2m+l)t. To estimate the right...coefficients. These random polynomials represent the deviation in frequency response of a linear , equispaced antenna array cauised by coefficient

Flow Rates Measurement and Uncertainty Analysis in Multiple-Zone Water-Injection Wells from Fluid Temperature Profiles

PubMed Central

Reges, José E. O.; Salazar, A. O.; Maitelli, Carla W. S. P.; Carvalho, Lucas G.; Britto, Ursula J. B.

2016-01-01

This work is a contribution to the development of flow sensors in the oil and gas industry. It presents a methodology to measure the flow rates into multiple-zone water-injection wells from fluid temperature profiles and estimate the measurement uncertainty. First, a method to iteratively calculate the zonal flow rates using the Ramey (exponential) model was described. Next, this model was linearized to perform an uncertainty analysis. Then, a computer program to calculate the injected flow rates from experimental temperature profiles was developed. In the experimental part, a fluid temperature profile from a dual-zone water-injection well located in the Northeast Brazilian region was collected. Thus, calculated and measured flow rates were compared. The results proved that linearization error is negligible for practical purposes and the relative uncertainty increases as the flow rate decreases. The calculated values from both the Ramey and linear models were very close to the measured flow rates, presenting a difference of only 4.58 m³/d and 2.38 m³/d, respectively. Finally, the measurement uncertainties from the Ramey and linear models were equal to 1.22% and 1.40% (for injection zone 1); 10.47% and 9.88% (for injection zone 2). Therefore, the methodology was successfully validated and all objectives of this work were achieved. PMID:27420068

Exponential asymptotics of homoclinic snaking

NASA Astrophysics Data System (ADS)

Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

2011-12-01

We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

Fast radiative transfer models for retrieval of cloud properties in the back-scattering region: application to DSCOVR-EPIC sensor

NASA Astrophysics Data System (ADS)

Molina Garcia, Victor; Sasi, Sruthy; Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego

2017-04-01

In this work, the requirements for the retrieval of cloud properties in the back-scattering region are described, and their application to the measurements taken by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) is shown. Various radiative transfer models and their linearizations are implemented, and their advantages and issues are analyzed. As radiative transfer calculations in the back-scattering region are computationally time-consuming, several acceleration techniques are also studied. The radiative transfer models analyzed include the exact Discrete Ordinate method with Matrix Exponential (DOME), the Matrix Operator method with Matrix Exponential (MOME), and the approximate asymptotic and equivalent Lambertian cloud models. To reduce the computational cost of the line-by-line (LBL) calculations, the k-distribution method, the Principal Component Analysis (PCA) and a combination of the k-distribution method plus PCA are used. The linearized radiative transfer models for retrieval of cloud properties include the Linearized Discrete Ordinate method with Matrix Exponential (LDOME), the Linearized Matrix Operator method with Matrix Exponential (LMOME) and the Forward-Adjoint Discrete Ordinate method with Matrix Exponential (FADOME). These models were applied to the EPIC oxygen-A band absorption channel at 764 nm. It is shown that the approximate asymptotic and equivalent Lambertian cloud models give inaccurate results, so an offline processor for the retrieval of cloud properties in the back-scattering region requires the use of exact models such as DOME and MOME, which behave similarly. The combination of the k-distribution method plus PCA presents similar accuracy to the LBL calculations, but it is up to 360 times faster, and the relative errors for the computed radiances are less than 1.5% compared to the results when the exact phase function is used. Finally, the linearized models studied show similar behavior, with relative errors less than 1% for the radiance derivatives, but FADOME is 2 times faster than LDOME and 2.5 times faster than LMOME.

Investigation of dose characteristics in three-dimensional MAGAT-type polymer gel dosimetry with MSE MR imaging

NASA Astrophysics Data System (ADS)

Lee, Jason J. S.; Tsai, Chia-Jung; Lo, Man-Kuok; Huang, Yung-Hui; Chen, Chien-Chuan; Wu, Jay; Tyan, Yeu-Sheng; Wu, Tung-Hsin

2008-05-01

A new type of normoxic polymer gel dosimeter, named MAGAT responses well to absorbed dose even when manufacturing in the presence of normal levels of oxygen. The aim of this study was to evaluate dose response, diffusion effect and cumulated dose response under multiple fractional irradiations of the MAGAT gel dosimeter using Multiple Spin-Echo (MSE) Magnetic Resonance (MR) sequence. Dose response was performed by irradiating MAGAT-gel-filled testing vials with a 6 MV linear accelerator and a linear relationship was present with doses from 0 to 6 Gy, but gradually, a bi-exponential function result was obtained with given doses up to 20 Gy. No significant difference in dose response was present between single and cumulated doses (p > 0.05). For study of diffusion effect, edge sharpness of the R2 map imaging between two split doses was smaller than 1 cm of dose profile penumbra between 20% and 80%. In conclusion, the MAGAT polymer gel dosimeter with MSE MR imaging is a promising method for dose verification in clinical radiation therapy practice.

Saturation current and collection efficiency for ionization chambers in pulsed beams.

PubMed

DeBlois, F; Zankowski, C; Podgorsak, E B

2000-05-01

Saturation currents and collection efficiencies in ionization chambers exposed to pulsed megavoltage photon and electron beams are determined assuming a linear relationship between 1/I and 1/V in the extreme near-saturation region, with I and V the chamber current and polarizing voltage, respectively. Careful measurements of chamber current against polarizing voltage in the extreme near-saturation region reveal a current rising faster than that predicted by the linear relationship. This excess current combined with conventional "two-voltage" technique for determination of collection efficiency may result in an up to 0.7% overestimate of the saturation current for standard radiation field sizes of 10X10 cm2. The measured excess current is attributed to charge multiplication in the chamber air volume and to radiation-induced conductivity in the stem of the chamber (stem effect). These effects may be accounted for by an exponential term used in conjunction with Boag's equation for collection efficiency in pulsed beams. The semiempirical model follows the experimental data well and accounts for both the charge recombination as well as for the charge multiplication effects and the chamber stem effect.

Correlation between the change in the kinetics of the ribosomal RNA rrnB P2 promoter and the transition from lag to exponential phase with Pseudomonas fluorescens.

PubMed

McKellar, Robin C

2008-01-15

Developing accurate mathematical models to describe the pre-exponential lag phase in food-borne pathogens presents a considerable challenge to food microbiologists. While the growth rate is influenced by current environmental conditions, the lag phase is affected in addition by the history of the inoculum. A deeper understanding of physiological changes taking place during the lag phase would improve accuracy of models, and in earlier studies a strain of Pseudomonas fluorescens containing the Tn7-luxCDABE gene cassette regulated by the rRNA promoter rrnB P2 was used to measure the influence of starvation, growth temperature and sub-lethal heating on promoter expression and subsequent growth. The present study expands the models developed earlier to include a model which describes the change from exponential to linear increase in promoter expression with time when the exponential phase of growth commences. A two-phase linear model with Poisson weighting was used to estimate the lag (LPDLin) and the rate (RLin) for this linear increase in bioluminescence. The Spearman rank correlation coefficient (r=0.830) between the LPDLin and the growth lag phase (LPDOD) was extremely significant (P

PET Pharmacokinetic Modelling

NASA Astrophysics Data System (ADS)

Müller-Schauenburg, Wolfgang; Reimold, Matthias

Positron Emission Tomography is a well-established technique that allows imaging and quantification of tissue properties in-vivo. The goal of pharmacokinetic modelling is to estimate physiological parameters, e.g. perfusion or receptor density from the measured time course of a radiotracer. After a brief overview of clinical application of PET, we summarize the fundamentals of modelling: distribution volume, Fick's principle of local balancing, extraction and perfusion, and how to calculate equilibrium data from measurements after bolus injection. Three fundamental models are considered: (i) the 1-tissue compartment model, e.g. for regional cerebral blood flow (rCBF) with the short-lived tracer [15O]water, (ii) the 2-tissue compartment model accounting for trapping (one exponential + constant), e.g. for glucose metabolism with [18F]FDG, (iii) the reversible 2-tissue compartment model (two exponentials), e.g. for receptor binding. Arterial blood sampling is required for classical PET modelling, but can often be avoided by comparing regions with specific binding with so called reference regions with negligible specific uptake, e.g. in receptor imaging. To estimate the model parameters, non-linear least square fits are the standard. Various linearizations have been proposed for rapid parameter estimation, e.g. on a pixel-by-pixel basis, for the prize of a bias. Such linear approaches exist for all three models; e.g. the PATLAK-plot for trapping substances like FDG, and the LOGAN-plot to obtain distribution volumes for reversibly binding tracers. The description of receptor modelling is dedicated to the approaches of the subsequent lecture (chapter) of Millet, who works in the tradition of Delforge with multiple-injection investigations.

Gender Differences in the Effects of the Frequency of Physical Activity on the Incidence of Metabolic Syndrome: Results from a Middle-Aged Community Cohort in Taiwan.

PubMed

Chen, Sheng-Pyng; Chang, Huan-Cheng; Hsiao, Tien-Mu; Yeh, Chih-Jung; Yang, Hao-Jan

2018-06-01

Little is known about how the frequency of physical activity in adults influences the occurrence of metabolic syndrome (MetS), and whether there are gender differences within these effects. In this study, 3368 residents from the established "Landseed Cohort" underwent three waves of health examinations, and those who did not have MetS at baseline were selected and analyzed using a multiple Poisson regression model. By calculating the adjusted relative risk (ARR), the linear and nonlinear relationships between the frequency of physical activity and risk of developing MetS were examined for male and female participants. The prevalence of MetS was fairly stable across the three waves (ranging from 16.24% to 16.82%), but the incidence dropped from 7.11% to 4.52%. The risk of MetS in women was 10 times higher than that in men (ARR = 10.06; 95% CI = 6.60-15.33), and frequent exercise was shown to help prevent it. The frequency of exercise had a linear dose-response effect in females and an exponential protective effect in males on the occurrence of MetS. Exercising more than four times a week for females and twice or more a week for males effectively reduced the risk of developing MetS. The frequency of physical activity in adults was negatively related to the risk of developing MetS, and this relationship differed based on gender. The protective effect of physical activity on MetS was linear in females and exponential in males.

Memory behaviors of entropy production rates in heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2018-02-01

Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann-Gibbs-Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

Forward-backward multiplicity correlations of target fragments in nucleus-emulsion collisions at a few hundred MeV/u

NASA Astrophysics Data System (ADS)

Zhang, Dong-Hai; Chen, Yan-Ling; Wang, Guo-Rong; Li, Wang-Dong; Wang, Qing; Yao, Ji-Jie; Zhou, Jian-Guo; Li, Rong; Li, Jun-Sheng; Li, Hui-Ling

2015-01-01

The forward-backward multiplicity and correlations of a target evaporated fragment (black track particle) and target recoiled proton (grey track particle) emitted from 150 A MeV 4He, 290 A MeV 12C, 400 A MeV 12C, 400 A MeV 20Ne and 500 A MeV 56Fe induced different types of nuclear emulsion target interactions are investigated. It is found that the forward and backward averaged multiplicity of a grey, black and heavily ionized track particle increases with the increase of the target size. The averaged multiplicity of a forward black track particle, backward black track particle, and backward grey track particle do not depend on the projectile size and energy, but the averaged multiplicity of a forward grey track particle increases with an increase of projectile size and energy. The backward grey track particle multiplicity distribution follows an exponential decay law and the decay constant decreases with an increase of target size. The backward-forward multiplicity correlations follow linear law which is independent of the projectile size and energy, and the saturation effect is observed in some heavy target data sets.

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Theory, computation, and application of exponential splines

NASA Technical Reports Server (NTRS)

Mccartin, B. J.

1981-01-01

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mask patterning process using the negative tone chemically amplified resist TOK OEBR-CAN024

NASA Astrophysics Data System (ADS)

Irmscher, Mathias; Beyer, Dirk; Butschke, Joerg; Hudek, Peter; Koepernik, Corinna; Plumhoff, Jason; Rausa, Emmanuel; Sato, Mitsuru; Voehringer, Peter

2004-08-01

Optimized process parameters using the TOK OEBR-CAN024 resist for high chrome load patterning have been determined. A tight linearity tolerance for opaque and clear features, independent on the local pattern density, was the goal of our process integration work. For this purpose we evaluated a new correction method taking into account electron scattering and process influences. The method is based on matching of measured pattern geometry by iterative back-simulation using multiple Gauss and/or exponential functions. The obtained control function acts as input for the proximity correction software PROXECCO. Approaches with different pattern oversize and two Cr thicknesses were accomplished and the results have been reported. Isolated opaque and clear lines could be realized in a very tight linearity range. The increasing line width of small dense lines, induced by the etching process, could be corrected only partially.

Linear or Exponential Number Lines

ERIC Educational Resources Information Center

Stafford, Pat

2011-01-01

Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…

The matrix exponential in transient structural analysis

NASA Technical Reports Server (NTRS)

Minnetyan, Levon

1987-01-01

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Second cancer risk after 3D-CRT, IMRT and VMAT for breast cancer.

PubMed

Abo-Madyan, Yasser; Aziz, Muhammad Hammad; Aly, Moamen M O M; Schneider, Frank; Sperk, Elena; Clausen, Sven; Giordano, Frank A; Herskind, Carsten; Steil, Volker; Wenz, Frederik; Glatting, Gerhard

2014-03-01

Second cancer risk after breast conserving therapy is becoming more important due to improved long term survival rates. In this study, we estimate the risks for developing a solid second cancer after radiotherapy of breast cancer using the concept of organ equivalent dose (OED). Computer-tomography scans of 10 representative breast cancer patients were selected for this study. Three-dimensional conformal radiotherapy (3D-CRT), tangential intensity modulated radiotherapy (t-IMRT), multibeam intensity modulated radiotherapy (m-IMRT), and volumetric modulated arc therapy (VMAT) were planned to deliver a total dose of 50 Gy in 2 Gy fractions. Differential dose volume histograms (dDVHs) were created and the OEDs calculated. Second cancer risks of ipsilateral, contralateral lung and contralateral breast cancer were estimated using linear, linear-exponential and plateau models for second cancer risk. Compared to 3D-CRT, cumulative excess absolute risks (EAR) for t-IMRT, m-IMRT and VMAT were increased by 2 ± 15%, 131 ± 85%, 123 ± 66% for the linear-exponential risk model, 9 ± 22%, 82 ± 96%, 71 ± 82% for the linear and 3 ± 14%, 123 ± 78%, 113 ± 61% for the plateau model, respectively. Second cancer risk after 3D-CRT or t-IMRT is lower than for m-IMRT or VMAT by about 34% for the linear model and 50% for the linear-exponential and plateau models, respectively. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

A thorough investigation of the progressive reset dynamics in HfO{sub 2}-based resistive switching structures

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

Lorenzi, P., E-mail: lorenzi@die.uniroma1.it; Rao, R.; Irrera, F.

2015-09-14

According to previous reports, filamentary electron transport in resistive switching HfO{sub 2}-based metal-insulator-metal structures can be modeled using a diode-like conduction mechanism with a series resistance. Taking the appropriate limits, the model allows simulating the high (HRS) and low (LRS) resistance states of the devices in terms of exponential and linear current-voltage relationships, respectively. In this letter, we show that this simple equivalent circuit approach can be extended to represent the progressive reset transition between the LRS and HRS if a generalized logistic growth model for the pre-exponential diode current factor is considered. In this regard, it is demonstrated heremore » that a Verhulst logistic model does not provide accurate results. The reset dynamics is interpreted as the sequential deactivation of multiple conduction channels spanning the dielectric film. Fitting results for the current-voltage characteristics indicate that the voltage sweep rate only affects the deactivation rate of the filaments without altering the main features of the switching dynamics.« less

Smoothing Forecasting Methods for Academic Library Circulations: An Evaluation and Recommendation.

ERIC Educational Resources Information Center

Brooks, Terrence A.; Forys, John W., Jr.

1986-01-01

Circulation time-series data from 50 midwest academic libraries were used to test 110 variants of 8 smoothing forecasting methods. Data and methodologies and illustrations of two recommended methods--the single exponential smoothing method and Brown's one-parameter linear exponential smoothing method--are given. Eight references are cited. (EJS)

Distributions of Autocorrelated First-Order Kinetic Outcomes: Illness Severity

PubMed Central

Englehardt, James D.

2015-01-01

Many complex systems produce outcomes having recurring, power law-like distributions over wide ranges. However, the form necessarily breaks down at extremes, whereas the Weibull distribution has been demonstrated over the full observed range. Here the Weibull distribution is derived as the asymptotic distribution of generalized first-order kinetic processes, with convergence driven by autocorrelation, and entropy maximization subject to finite positive mean, of the incremental compounding rates. Process increments represent multiplicative causes. In particular, illness severities are modeled as such, occurring in proportion to products of, e.g., chronic toxicant fractions passed by organs along a pathway, or rates of interacting oncogenic mutations. The Weibull form is also argued theoretically and by simulation to be robust to the onset of saturation kinetics. The Weibull exponential parameter is shown to indicate the number and widths of the first-order compounding increments, the extent of rate autocorrelation, and the degree to which process increments are distributed exponential. In contrast with the Gaussian result in linear independent systems, the form is driven not by independence and multiplicity of process increments, but by increment autocorrelation and entropy. In some physical systems the form may be attracting, due to multiplicative evolution of outcome magnitudes towards extreme values potentially much larger and smaller than control mechanisms can contain. The Weibull distribution is demonstrated in preference to the lognormal and Pareto I for illness severities versus (a) toxicokinetic models, (b) biologically-based network models, (c) scholastic and psychological test score data for children with prenatal mercury exposure, and (d) time-to-tumor data of the ED01 study. PMID:26061263

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Graph Structured Program Evolution: Evolution of Loop Structures

NASA Astrophysics Data System (ADS)

Shirakawa, Shinichi; Nagao, Tomoharu

Recently, numerous automatic programming techniques have been developed and applied in various fields. A typical example is genetic programming (GP), and various extensions and representations of GP have been proposed thus far. Complex programs and hand-written programs, however, may contain several loops and handle multiple data types. In this chapter, we propose a new method called Graph Structured Program Evolution (GRAPE). The representation of GRAPE is a graph structure; therefore, it can represent branches and loops using this structure. Each programis constructed as an arbitrary directed graph of nodes and a data set. The GRAPE program handles multiple data types using the data set for each type, and the genotype of GRAPE takes the form of a linear string of integers. We apply GRAPE to three test problems, factorial, exponentiation, and list sorting, and demonstrate that the optimum solution in each problem is obtained by the GRAPE system.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Exponential stability of stochastic complex networks with multi-weights based on graph theory

NASA Astrophysics Data System (ADS)

Zhang, Chunmei; Chen, Tianrui

2018-04-01

In this paper, a novel approach to exponential stability of stochastic complex networks with multi-weights is investigated by means of the graph-theoretical method. New sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights. It is noted that our stability results are closely related with multi-weights and the intensity of stochastic disturbance. Numerical simulations are also presented to substantiate the theoretical results.

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\\infty }$ Performances.

PubMed

Choi, Hyun Duck; Ahn, Choon Ki; Karimi, Hamid Reza; Lim, Myo Taeg

2017-10-01

This paper studies delay-dependent exponential dissipative and l 2 - l ∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l 2 - l ∞ senses. The design of the desired exponential dissipative and l 2 - l ∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

Dichotomous-noise-induced pattern formation in a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Ray, Deb Shankar

2013-06-01

We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

Linearized traveling wave amplifier with hard limiter characteristics

NASA Technical Reports Server (NTRS)

Kosmahl, H. G. (Inventor)

1986-01-01

A dynamic velocity taper is provided for a traveling wave tube with increased linearity to avoid intermodulation of signals being amplified. In a traveling wave tube, the slow wave structure is a helix including a sever. A dynamic velocity taper is provided by gradually reducing the spacing between the repeating elements of the slow wave structure which are the windings of the helix. The reduction which takes place coincides with the ouput point of helix. The spacing between the repeating elements of the slow wave structure is ideally at an exponential rate because the curve increases the point of maximum efficiency and power, at an exponential rate. A coupled cavity traveling wave tube having cavities is shown. The space between apertured discs is gradually reduced from 0.1% to 5% at an exponential rate. Output power (or efficiency) versus input power for a commercial tube is shown.

Determining the Optimal Values of Exponential Smoothing Constants--Does Solver Really Work?

ERIC Educational Resources Information Center

Ravinder, Handanhal V.

2013-01-01

A key issue in exponential smoothing is the choice of the values of the smoothing constants used. One approach that is becoming increasingly popular in introductory management science and operations management textbooks is the use of Solver, an Excel-based non-linear optimizer, to identify values of the smoothing constants that minimize a measure…

First off-time treatment prostate-specific antigen kinetics predicts survival in intermittent androgen deprivation for prostate cancer.

PubMed

Sanchez-Salas, Rafael; Olivier, Fabien; Prapotnich, Dominique; Dancausa, José; Fhima, Mehdi; David, Stéphane; Secin, Fernando P; Ingels, Alexandre; Barret, Eric; Galiano, Marc; Rozet, François; Cathelineau, Xavier

2016-01-01

Prostate-specific antigen (PSA) doubling time is relying on an exponential kinetic pattern. This pattern has never been validated in the setting of intermittent androgen deprivation (IAD). Objective is to analyze the prognostic significance for PCa of recurrent patterns in PSA kinetics in patients undergoing IAD. A retrospective study was conducted on 377 patients treated with IAD. On-treatment period (ONTP) consisted of gonadotropin-releasing hormone agonist injections combined with oral androgen receptor antagonist. Off-treatment period (OFTP) began when PSA was lower than 4 ng/ml. ONTP resumed when PSA was higher than 20 ng/ml. PSA values of each OFTP were fitted with three basic patterns: exponential (PSA(t) = λ.e(αt)), linear (PSA(t) = a.t), and power law (PSA(t) = a.t(c)). Univariate and multivariate Cox regression model analyzed predictive factors for oncologic outcomes. Only 45% of the analyzed OFTPs were exponential. Linear and power law PSA kinetics represented 7.5% and 7.7%, respectively. Remaining fraction of analyzed OFTPs (40%) exhibited complex kinetics. Exponential PSA kinetics during the first OFTP was significantly associated with worse oncologic outcome. The estimated 10-year cancer-specific survival (CSS) was 46% for exponential versus 80% for nonexponential PSA kinetics patterns. The corresponding 10-year probability of castration-resistant prostate cancer (CRPC) was 69% and 31% for the two patterns, respectively. Limitations include retrospective design and mixed indications for IAD. PSA kinetic fitted with exponential pattern in approximately half of the OFTPs. First OFTP exponential PSA kinetic was associated with a shorter time to CRPC and worse CSS. © 2015 Wiley Periodicals, Inc.

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.

Exponentially convergent state estimation for delayed switched recurrent neural networks.

PubMed

Ahn, Choon Ki

2011-11-01

This paper deals with the delay-dependent exponentially convergent state estimation problem for delayed switched neural networks. A set of delay-dependent criteria is derived under which the resulting estimation error system is exponentially stable. It is shown that the gain matrix of the proposed state estimator is characterised in terms of the solution to a set of linear matrix inequalities (LMIs), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

Algebraic approach to electronic spectroscopy and dynamics

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

Toutounji, Mohamad

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponentialmore » operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a{sup +}. While exp(a{sup +}) translates coherent states, exp(a{sup +}a{sup +}) operation on coherent states has always been a challenge, as a{sup +} has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F({tau}{sub 1},{tau}{sub 2},{tau}{sub 3},{tau}{sub 4}), of which the optical nonlinear response function may be procured, as evaluating F({tau}{sub 1},{tau}{sub 2},{tau}{sub 3},{tau}{sub 4}) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.« less

Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routine

NASA Astrophysics Data System (ADS)

Wang, Jun; Endreny, Theodore A.; Hassett, James M.

2006-11-01

TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4.8 cm h-1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright

Mathematical Magnitude.

ERIC Educational Resources Information Center

Griffin, Joseph

1978-01-01

Addition, multiplication, and exponentiation form the beginning of a natural hierarchy of binary operations on the positive integers. By employing operations above exponentiation in this hierarchy, it is possible to obtain large numbers as an immediate result of combining small familiar numbers. (Author/MP)

Effects of temperature and glycerol and methanol-feeding profiles on the production of recombinant galactose oxidase in Pichia pastoris

PubMed Central

Anasontzis, George E; Salazar Penã, Margarita; Spadiut, Oliver; Brumer, Harry; Olsson, Lisbeth

2014-01-01

Optimization of protein production from methanol-induced Pichia pastoris cultures is necessary to ensure high productivity rates and high yields of recombinant proteins. We investigated the effects of temperature and different linear or exponential methanol-feeding rates on the production of recombinant Fusarium graminearum galactose oxidase (EC 1.1.3.9) in a P. pastoris Mut+ strain, under regulation of the AOX1 promoter. We found that low exponential methanol feeding led to 1.5-fold higher volumetric productivity compared to high exponential feeding rates. The duration of glycerol feeding did not affect the subsequent product yield, but longer glycerol feeding led to higher initial biomass concentration, which would reduce the oxygen demand and generate less heat during induction. A linear and a low exponential feeding profile led to productivities in the same range, but the latter was characterized by intense fluctuations in the titers of galactose oxidase and total protein. An exponential feeding profile that has been adapted to the apparent biomass concentration results in more stable cultures, but the concentration of recombinant protein is in the same range as when constant methanol feeding is employed. © 2014 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 30:728–735, 2014 PMID:24493559

A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

Effects of exogenous inosine monophosphate on growth performance, flavor compounds, enzyme activity, and gene expression of muscle tissues in chicken.

PubMed

Yan, Junshu; Liu, Peifeng; Xu, Liangmei; Huan, Hailin; Zhou, Weiren; Xu, Xiaoming; Shi, Zhendan

2018-04-01

The goal of this experiment was to examine effects of diets supplemented with exogenous inosine monophosphate (IMP) on the growth performance, flavor compounds, enzyme activity and gene expression of chicken. A total of 1,500 healthy, 1-day-old male 3-yellow chickens were used for a 52-d experimental period. Individuals were randomly divided into 5 groups (group I, II, III, IV, V) with 6 replicates per group, and fed a basal diet supplemented with 0.0, 0.05, 0.1, 0.2, and 0.3% IMP, respectively. There was no significant response to the increasing dietary IMP level in average daily feed intake (ADFI), average daily gain (ADG), and feed:gain ratio (F/G) (P ≥ 0.05). IMP content of the breast and thigh muscle showed an exponential and linear response to the increasing dietary IMP level (P < 0.05), the highest IMP content was obtained when the diet with 0.3% and 0.2% exogenous IMP was fed. There were significant effects of IMP level in diet on free amino acids (FAA) (exponential, linear and quadratic effect, P < 0.05) and delicious amino acids (DAA) (quadratic effect, P < 0.01) content in breast muscle. FAA and DAA content in thigh muscle showed an exponential and linear response (P < 0.05), and quadratic response (P < 0.01) to the increasing dietary IMP level, the highest FAA and DAA content was obtained when the diet with 0.2% exogenous IMP was fed. Dietary IMP supplementation had a quadratic effect on 5΄-NT and the alkaline phosphatase (ALP) enzyme activity in the breast muscle (P < 0.05), and the adenosine triphosphate (ATP) enzyme activity in the thigh muscles increased exponentially and linearly with increasing IMP level in diet (exponential effect, P = 0.061; linear effect, P = 0.059). Cyclohydrolase (ATIC) gene expression in thigh muscle had a quadratic response to the increasing dietary IMP level (P < 0.05), 0.2% exogenous IMP group had the highest (AMPD1) gene expression of the breast muscle and ATIC gene expression of the thigh muscle. These results indicate that dietary IMP did not affect the growth performance of chicken, the diet with 0.2 to 0.3% exogenous IMP is optimal to improve the meat flavor quality in chicken.

Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.

A statistical study of decaying kink oscillations detected using SDO/AIA

NASA Astrophysics Data System (ADS)

Goddard, C. R.; Nisticò, G.; Nakariakov, V. M.; Zimovets, I. V.

2016-01-01

Context. Despite intensive studies of kink oscillations of coronal loops in the last decade, a large-scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO). Aims: We carry out a statistical study of kink oscillations using extreme ultraviolet imaging data from a previously compiled catalogue. Methods: We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) on board SDO during its first four years of operation (2010-2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations. Results: Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck = (1330 ± 50) km s-1. The main body of the data corresponds to kink speeds in the range Ck = (800-3300) km s-1. Measurements of 52 exponential damping times were made, and it was noted that at least 21 of the damping profiles may be better approximated by a combination of non-exponential and exponential profiles rather than a purely exponential damping envelope. There are nine additional cases where the profile appears to be purely non-exponential and no damping time was measured. A scaling of the exponential damping time with the period is found, following the previously established linear scaling between these two parameters.

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

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.

Rate laws of the self-induced aggregation kinetics of Brownian particles

NASA Astrophysics Data System (ADS)

Mondal, Shrabani; Sen, Monoj Kumar; Baura, Alendu; Bag, Bidhan Chandra

2016-03-01

In this paper we have studied the self induced aggregation kinetics of Brownian particles in the presence of both multiplicative and additive noises. In addition to the drift due to the self aggregation process, the environment may induce a drift term in the presence of a multiplicative noise. Then there would be an interplay between the two drift terms. It may account qualitatively the appearance of the different laws of aggregation process. At low strength of white multiplicative noise, the cluster number decreases as a Gaussian function of time. If the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time. For additive noise driven case, the decrease of cluster number can be described by the power law. But in case of multiplicative colored driven process, cluster number decays multi exponentially. However, we have explored how the rate constant (in the mono exponentially cluster number decaying case) depends on strength of interference of the noises and their intensity. We have also explored how the structure factor at long time depends on the strength of the cross correlation (CC) between the additive and the multiplicative noises.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation.

PubMed

Negres, Raluca A; Norton, Mary A; Cross, David A; Carr, Christopher W

2010-09-13

The growth behavior of laser-induced damage sites is affected by a large number of laser parameters as well as site morphology. Here we investigate the effects of pulse duration on the growth rate of damage sites located on the exit surface of fused silica optics. Results demonstrate a significant dependence of the growth parameters on laser pulse duration at 351 nm from 1 ns to 15 ns, including the observation of a dominant exponential versus linear, multiple-shot growth behavior for long and short pulses, respectively. These salient behaviors are tied to the damage morphology and suggest a shift in the fundamental growth mechanisms for pulses in the 1-5 ns range.

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

NASA Technical Reports Server (NTRS)

Zhu, J. Jim; Liu, Yong; Hang, Rui

2010-01-01

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Exponential integration algorithms applied to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.

Linearized radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

NASA Astrophysics Data System (ADS)

Molina García, Víctor; Sasi, Sruthy; Efremenko, Dmitry S.; Doicu, Adrian; Loyola, Diego

2018-07-01

In this paper, we describe several linearized radiative transfer models which can be used for the retrieval of cloud parameters from EPIC (Earth Polychromatic Imaging Camera) measurements. The approaches under examination are (1) the linearized forward approach, represented in this paper by the linearized discrete ordinate and matrix operator methods with matrix exponential, and (2) the forward-adjoint approach based on the discrete ordinate method with matrix exponential. To enhance the performance of the radiative transfer computations, the correlated k-distribution method and the Principal Component Analysis (PCA) technique are used. We provide a compact description of the proposed methods, as well as a numerical analysis of their accuracy and efficiency when simulating EPIC measurements in the oxygen A-band channel at 764 nm. We found that the computation time of the forward-adjoint approach using the correlated k-distribution method in conjunction with PCA is approximately 13 s for simultaneously computing the derivatives with respect to cloud optical thickness and cloud top height.

Controllable excitation of higher-order rogue waves in nonautonomous systems with both varying linear and harmonic external potentials

NASA Astrophysics Data System (ADS)

Jia, Heping; Yang, Rongcao; Tian, Jinping; Zhang, Wenmei

2018-05-01

The nonautonomous nonlinear Schrödinger (NLS) equation with both varying linear and harmonic external potentials is investigated and the semirational rogue wave (RW) solution is presented by similarity transformation. Based on the solution, the interactions between Peregrine soliton and breathers, and the controllability of the semirational RWs in periodic distribution and exponential decreasing nonautonomous systems with both linear and harmonic potentials are studied. It is found that the harmonic potential only influences the constraint condition of the semirational solution, the linear potential is related to the trajectory of the semirational RWs, while dispersion and nonlinearity determine the excitation position of the higher-order RWs. The higher-order RWs can be partly, completely and biperiodically excited in periodic distribution system and the diverse excited patterns can be generated for different parameter relations in exponential decreasing system. The results reveal that the excitation of the higher-order RWs can be controlled in the nonautonomous system by choosing dispersion, nonlinearity and external potentials.

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

NASA Astrophysics Data System (ADS)

Garavaglia, Alessandro; van der Hofstad, Remco; Woeginger, Gerhard

2017-09-01

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.

Airspace Dimension Assessment with nanoparticles reflects lung density as quantified by MRI

PubMed Central

Jakobsson, Jonas K; Löndahl, Jakob; Olsson, Lars E; Diaz, Sandra; Zackrisson, Sophia; Wollmer, Per

2018-01-01

Background Airspace Dimension Assessment with inhaled nanoparticles is a novel method to determine distal airway morphology. This is the first empirical study using Airspace Dimension Assessment with nanoparticles (AiDA) to estimate distal airspace radius. The technology is relatively simple and potentially accessible in clinical outpatient settings. Method Nineteen never-smoking volunteers performed nanoparticle inhalation tests at multiple breath-hold times, and the difference in nanoparticle concentration of inhaled and exhaled gas was measured. An exponential decay curve was fitted to the concentration of recovered nanoparticles, and airspace dimensions were assessed from the half-life of the decay. Pulmonary tissue density was measured using magnetic resonance imaging (MRI). Results The distal airspace radius measured by AiDA correlated with lung tissue density as measured by MRI (ρ = −0.584; p = 0.0086). The linear intercept of the logarithm of the exponential decay curve correlated with forced expiratory volume in one second (FEV1) (ρ = 0.549; p = 0.0149). Conclusion The AiDA method shows potential to be developed into a tool to assess conditions involving changes in distal airways, eg, emphysema. The intercept may reflect airway properties; this finding should be further investigated.

Snowmelt runoff modeling in simulation and forecasting modes with the Martinec-Mango model

NASA Technical Reports Server (NTRS)

Shafer, B.; Jones, E. B.; Frick, D. M. (Principal Investigator)

1982-01-01

The Martinec-Rango snowmelt runoff model was applied to two watersheds in the Rio Grande basin, Colorado-the South Fork Rio Grande, a drainage encompassing 216 sq mi without reservoirs or diversions and the Rio Grande above Del Norte, a drainage encompassing 1,320 sq mi without major reservoirs. The model was successfully applied to both watersheds when run in a simulation mode for the period 1973-79. This period included both high and low runoff seasons. Central to the adaptation of the model to run in a forecast mode was the need to develop a technique to forecast the shape of the snow cover depletion curves between satellite data points. Four separate approaches were investigated-simple linear estimation, multiple regression, parabolic exponential, and type curve. Only the parabolic exponential and type curve methods were run on the South Fork and Rio Grande watersheds for the 1980 runoff season using satellite snow cover updates when available. Although reasonable forecasts were obtained in certain situations, neither method seemed ready for truly operational forecasts, possibly due to a large amount of estimated climatic data for one or two primary base stations during the 1980 season.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Quantifying Uncertainties in N2O Emission Due to N Fertilizer Application in Cultivated Areas

PubMed Central

Philibert, Aurore; Loyce, Chantal; Makowski, David

2012-01-01

Nitrous oxide (N2O) is a greenhouse gas with a global warming potential approximately 298 times greater than that of CO2. In 2006, the Intergovernmental Panel on Climate Change (IPCC) estimated N2O emission due to synthetic and organic nitrogen (N) fertilization at 1% of applied N. We investigated the uncertainty on this estimated value, by fitting 13 different models to a published dataset including 985 N2O measurements. These models were characterized by (i) the presence or absence of the explanatory variable “applied N”, (ii) the function relating N2O emission to applied N (exponential or linear function), (iii) fixed or random background (i.e. in the absence of N application) N2O emission and (iv) fixed or random applied N effect. We calculated ranges of uncertainty on N2O emissions from a subset of these models, and compared them with the uncertainty ranges currently used in the IPCC-Tier 1 method. The exponential models outperformed the linear models, and models including one or two random effects outperformed those including fixed effects only. The use of an exponential function rather than a linear function has an important practical consequence: the emission factor is not constant and increases as a function of applied N. Emission factors estimated using the exponential function were lower than 1% when the amount of N applied was below 160 kg N ha−1. Our uncertainty analysis shows that the uncertainty range currently used by the IPCC-Tier 1 method could be reduced. PMID:23226430

Exploiting fast detectors to enter a new dimension in room-temperature crystallography

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

Owen, Robin L., E-mail: robin.owen@diamond.ac.uk; Paterson, Neil; Axford, Danny

2014-05-01

A departure from a linear or an exponential decay in the diffracting power of macromolecular crystals is observed and accounted for through consideration of a multi-state sequential model. A departure from a linear or an exponential intensity decay in the diffracting power of protein crystals as a function of absorbed dose is reported. The observation of a lag phase raises the possibility of collecting significantly more data from crystals held at room temperature before an intolerable intensity decay is reached. A simple model accounting for the form of the intensity decay is reintroduced and is applied for the first timemore » to high frame-rate room-temperature data collection.« less

An approach to multivariable control of manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Event-driven simulations of nonlinear integrate-and-fire neurons.

PubMed

Tonnelier, Arnaud; Belmabrouk, Hana; Martinez, Dominique

2007-12-01

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

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.

Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks

NASA Astrophysics Data System (ADS)

Yang, Chun-xi; Huang, Ling-yun; Zhang, Hao; Hua, Wang

2016-01-01

The stabilisation problem for one of the clusters with bounded multiple random time delays and packet dropouts in wireless sensor and actor networks is investigated in this paper. A new multirate switching model is constructed to describe the feature of this single input multiple output linear system. According to the difficulty of controller design under multi-constraints in multirate switching model, this model can be converted to a Takagi-Sugeno fuzzy model. By designing a multirate parallel distributed compensation, a sufficient condition is established to ensure this closed-loop fuzzy control system to be globally exponentially stable. The solution of the multirate parallel distributed compensation gains can be obtained by solving an auxiliary convex optimisation problem. Finally, two numerical examples are given to show, compared with solving switching controller, multirate parallel distributed compensation can be obtained easily. Furthermore, it has stronger robust stability than arbitrary switching controller and single-rate parallel distributed compensation under the same conditions.

Writing and compiling code into biochemistry.

PubMed

Shea, Adam; Fett, Brian; Riedel, Marc D; Parhi, Keshab

2010-01-01

This paper presents a methodology for translating iterative arithmetic computation, specified as high-level programming constructs, into biochemical reactions. From an input/output specification, we generate biochemical reactions that produce output quantities of proteins as a function of input quantities performing operations such as addition, subtraction, and scalar multiplication. Iterative constructs such as "while" loops and "for" loops are implemented by transferring quantities between protein types, based on a clocking mechanism. Synthesis first is performed at a conceptual level, in terms of abstract biochemical reactions - a task analogous to high-level program compilation. Then the results are mapped onto specific biochemical reactions selected from libraries - a task analogous to machine language compilation. We demonstrate our approach through the compilation of a variety of standard iterative functions: multiplication, exponentiation, discrete logarithms, raising to a power, and linear transforms on time series. The designs are validated through transient stochastic simulation of the chemical kinetics. We are exploring DNA-based computation via strand displacement as a possible experimental chassis.

A Landsat study of water quality in Lake Okeechobee

NASA Technical Reports Server (NTRS)

Gervin, J. C.; Marshall, M. L.

1976-01-01

This paper uses multiple regression techniques to investigate the relationship between Landsat radiance values and water quality measurements. For a period of over one year, the Central and Southern Florida Flood Control District sampled the water of Lake Okeechobee for chlorophyll, carotenoids, turbidity, and various nutrients at the time of Landsat overpasses. Using an overlay map of the sampling stations, Landsat radiance values were measured from computer compatible tapes using a GE image 100 and averaging over a 22-acre area at each station. These radiance values in four bands were used to form a number of functions (powers, logarithms, exponentials, and ratios), which were then compared with the ground measurements using multiple linear regression techniques. Several dates were used to provide generality and to study possible seasonal variations. Individual correlations were presented for the various water quality parameters and best fit equations were examined for chlorophyll and turbidity. The results and their relationship to past hydrological research were discussed.

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Effect of multiple perfusion components on pseudo-diffusion coefficient in intravoxel incoherent motion imaging

NASA Astrophysics Data System (ADS)

Kuai, Zi-Xiang; Liu, Wan-Yu; Zhu, Yue-Min

2017-11-01

The aim of this work was to investigate the effect of multiple perfusion components on the pseudo-diffusion coefficient D * in the bi-exponential intravoxel incoherent motion (IVIM) model. Simulations were first performed to examine how the presence of multiple perfusion components influences D *. The real data of livers (n  =  31), spleens (n  =  31) and kidneys (n  =  31) of 31 volunteers was then acquired using DWI for in vivo study and the number of perfusion components in these tissues was determined together with their perfusion fraction and D *, using an adaptive multi-exponential IVIM model. Finally, the bi-exponential model was applied to the real data and the mean, standard variance and coefficient of variation of D * as well as the fitting residual were calculated over the 31 volunteers for each of the three tissues and compared between them. The results of both the simulations and the in vivo study showed that, for the bi-exponential IVIM model, both the variance of D * and the fitting residual tended to increase when the number of perfusion components was increased or when the difference between perfusion components became large. In addition, it was found that the kidney presented the fewest perfusion components among the three tissues. The present study demonstrated that multi-component perfusion is a main factor that causes high variance of D * and the bi-exponential model should be used only when the tissues under investigation have few perfusion components, for example the kidney.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

PubMed

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

H∞ control problem of linear periodic piecewise time-delay systems

NASA Astrophysics Data System (ADS)

Xie, Xiaochen; Lam, James; Li, Panshuo

2018-04-01

This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov-Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

Characteristics of a Linearly Tapered Slot Antenna (LTSA) Conformed Longitudinally Around a Cylinder

NASA Technical Reports Server (NTRS)

Jordan, Jennifer L.; Ponchak, George E.; Tavassolian, Negar; Tentzeris, Manos M.

2007-01-01

The family of tapered slot antennas (TSA s) is suitable for numerous applications. Their ease of fabrication, wide bandwidth, and high gain make them desirable for military and commercial systems. Fabrication on thin, flexible substrates allows the TSA to be conformed over a given body, such as an aircraft wing or a piece of clothing for wearable networks. Previously, a Double Exponentially Tapered Slot Antenna (DETSA) was conformed around an exponential curvature, which showed that the main beam skewed towards the direction of curvature. This paper presents a Linearly Tapered Slot Antenna (LTSA) conformed longitudinally around a cylinder. Measured and simulated radiation patterns and the direction of maximum H co-polarization (Hco) as a function of the cylinder radius are presented.

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

A nanostructured surface increases friction exponentially at the solid-gas interface.

PubMed

Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E; Prashanthi, Kovur; Thundat, Thomas

2016-09-06

According to Stokes' law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.

A nanostructured surface increases friction exponentially at the solid-gas interface

NASA Astrophysics Data System (ADS)

Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E.; Prashanthi, Kovur; Thundat, Thomas

2016-09-01

According to Stokes’ law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.

Model evaluation of plant metal content and biomass yield for the phytoextraction of heavy metals by switchgrass.

PubMed

Chen, Bo-Ching; Lai, Hung-Yu; Juang, Kai-Wei

2012-06-01

To better understand the ability of switchgrass (Panicum virgatum L.), a perennial grass often relegated to marginal agricultural areas with minimal inputs, to remove cadmium, chromium, and zinc by phytoextraction from contaminated sites, the relationship between plant metal content and biomass yield is expressed in different models to predict the amount of metals switchgrass can extract. These models are reliable in assessing the use of switchgrass for phytoremediation of heavy-metal-contaminated sites. In the present study, linear and exponential decay models are more suitable for presenting the relationship between plant cadmium and dry weight. The maximum extractions of cadmium using switchgrass, as predicted by the linear and exponential decay models, approached 40 and 34 μg pot(-1), respectively. The log normal model was superior in predicting the relationship between plant chromium and dry weight. The predicted maximum extraction of chromium by switchgrass was about 56 μg pot(-1). In addition, the exponential decay and log normal models were better than the linear model in predicting the relationship between plant zinc and dry weight. The maximum extractions of zinc by switchgrass, as predicted by the exponential decay and log normal models, were about 358 and 254 μg pot(-1), respectively. To meet the maximum removal of Cd, Cr, and Zn, one can adopt the optimal timing of harvest as plant Cd, Cr, and Zn approach 450 and 526 mg kg(-1), 266 mg kg(-1), and 3022 and 5000 mg kg(-1), respectively. Due to the well-known agronomic characteristics of cultivation and the high biomass production of switchgrass, it is practicable to use switchgrass for the phytoextraction of heavy metals in situ. Copyright © 2012 Elsevier Inc. All rights reserved.

Crack identification for reinforced concrete using PZT based smart rebar active sensing diagnostic network

NASA Astrophysics Data System (ADS)

Song, N. N.; Wu, F.

2016-04-01

An active sensing diagnostic system using PZT based smart rebar for SHM of RC structure has been currently under investigation. Previous test results showed that the system could detect the de-bond of concrete from reinforcement, and the diagnostic signals were increased exponentially with the de-bonding size. Previous study also showed that the smart rebar could function well like regular reinforcement to undertake tension stresses. In this study, a smart rebar network has been used to detect the crack damage of concrete based on guided waves. Experimental test has been carried out for the study. In the test, concrete beams with 2 reinforcements have been built. 8 sets of PZT elements were mounted onto the reinforcement bars in an optimized way to form an active sensing diagnostic system. A 90 kHz 5-cycle Hanning-windowed tone burst was used as input. Multiple cracks have been generated on the concrete structures. Through the guided bulk waves propagating in the structures from actuators and sensors mounted from different bars, crack damage could be detected clearly. Cases for both single and multiple cracks were tested. Different crack depths from the surface and different crack numbers have been studied. Test result shows that the amplitude of sensor output signals is deceased linearly with a propagating crack, and is decreased exponentially with increased crack numbers. From the study, the active sensing diagnostic system using PZT based smart rebar network shows a promising way to provide concrete crack damage information through the "talk" among sensors.

Comment on "Synchronization of chaotic systems with delay using intermittent linear state feedback" [Chaos 18, 033122 (2008)].

PubMed

Zhang, Yinping; Wang, Qing-Guo

2008-12-01

In the referenced paper, there is technical carelessness in the third lemma and in the main result. Hence, it is a possible failure when the result is used to design the intermittent linear state feedback controller for exponential synchronization of two chaotic delayed systems.

Threading Dislocations in InGaAs/GaAs (001) Buffer Layers for Metamorphic High Electron Mobility Transistors

NASA Astrophysics Data System (ADS)

Song, Yifei; Kujofsa, Tedi; Ayers, John E.

2018-07-01

In order to evaluate various buffer layers for metamorphic devices, threading dislocation densities have been calculated for uniform composition In x Ga1- x As device layers deposited on GaAs (001) substrates with an intermediate graded buffer layer using the L MD model, where L MD is the average length of misfit dislocations. On this basis, we compare the relative effectiveness of buffer layers with linear, exponential, and S-graded compositional profiles. In the case of a 2 μm thick buffer layer linear grading results in higher threading dislocation densities in the device layer compared to either exponential or S-grading. When exponential grading is used, lower threading dislocation densities are obtained with a smaller length constant. In the S-graded case, lower threading dislocation densities result when a smaller standard deviation parameter is used. As the buffer layer thickness is decreased from 2 μm to 0.1 μm all of the above effects are diminished, and the absolute threading dislocation densities increase.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

Compact continuous-variable entanglement distillation.

PubMed

Datta, Animesh; Zhang, Lijian; Nunn, Joshua; Langford, Nathan K; Feito, Alvaro; Plenio, Martin B; Walmsley, Ian A

2012-02-10

We introduce a new scheme for continuous-variable entanglement distillation that requires only linear temporal and constant physical or spatial resources. Distillation is the process by which high-quality entanglement may be distributed between distant nodes of a network in the unavoidable presence of decoherence. The known versions of this protocol scale exponentially in space and doubly exponentially in time. Our optimal scheme therefore provides exponential improvements over existing protocols. It uses a fixed-resource module-an entanglement distillery-comprising only four quantum memories of at most 50% storage efficiency and allowing a feasible experimental implementation. Tangible quantum advantages are obtainable by using existing off-resonant Raman quantum memories outside their conventional role of storage.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Study of the anticorrelations between ozone and UV-B radiation using linear and exponential fits in Southern Brazil

NASA Astrophysics Data System (ADS)

Guarnieri, R.; Padilha, L.; Guarnieri, F.; Echer, E.; Makita, K.; Pinheiro, D.; Schuch, A.; Boeira, L.; Schuch, N.

Ultraviolet radiation type B (UV-B 280-315nm) is well known by its damage to life on Earth, including the possibility of causing skin cancer in humans. However, the atmo- spheric ozone has absorption bands in this spectral radiation, reducing its incidence on Earth's surface. Therefore, the ozone amount is one of the parameters, besides clouds, aerosols, solar zenith angles, altitude, albedo, that determine the UV-B radia- tion intensity reaching the Earth's surface. The total ozone column, in Dobson Units, determined by TOMS spectrometer on board of a NASA satellite, and UV-B radiation measurements obtained by a UV-B radiometer model MS-210W (Eko Instruments) were correlated. The measurements were obtained at the Observatório Espacial do Sul - Instituto Nacional de Pesquisas Espaciais (OES/CRSPE/INPE-MCT) coordinates: Lat. 29.44oS, Long. 53.82oW. The correlations were made using UV-B measurements in fixed solar zenith angles and only days with clear sky were selected in a period from July 1999 to December 2001. Moreover, the mathematic behavior of correlation in dif- ferent angles was observed, and correlation coefficients were determined by linear and first order exponential fits. In both fits, high correlation coefficients values were ob- tained, and the difference between linear and exponential fit can be considered small.

Determining CDOM Absorption Spectra in Diverse Aquatic Environments Using a Multiple Pathlength, Liquid Core Waveguide System

NASA Technical Reports Server (NTRS)

Miller, Richard L.; Belz, Mathias; DelCastillo, Carlos; Trzaska, Rick

2001-01-01

We evaluated the accuracy, sensitivity and precision of a multiple pathlength, liquid core waveguide (MPLCW) system for measuring colored dissolved organic matter (CDOM) absorption in the UV-visible spectral range (370-700 nm). The MPLCW has four optical paths (2.0, 9.8, 49.3, and 204 cm) coupled to a single Teflon AF sample cell. Water samples were obtained from inland, coastal and ocean waters ranging in salinity from 0 to 36 PSU. Reference solutions for the MPLCW were made having a refractive index of the sample. CDOM absorption coefficients, aCDOM, and the slope of the log-linearized absorption spectra, S, were compared with values obtained using a dual-beam spectrophotometer. Absorption of phenol red secondary standards measured by the MPLCW at 558 nm were highly correlated with spectrophotometer values and showed a linear response across all four pathlengths. Values of aCDOM measured using the MPLCW were virtually identical to spectrophotometer values over a wide range of concentrations. The dynamic range of aCDOM for MPLCW measurements was 0.002 - 231.5 m-1. At low CDOM concentrations spectrophotometric aCDOM were slightly greater than MPLCW values and showed larger fluctuations at longer wavelengths due to limitations in instrument precision. In contrast, MPLCW spectra followed an exponential to 600 nm for all samples.

Tropisms of Avena coleoptiles: sine law for gravitropism, exponential law for photogravitropic equilibrium.

PubMed

Galland, Paul

2002-09-01

The quantitative relation between gravitropism and phototropism was analyzed for light-grown coleoptiles of Avena sativa (L.). With respect to gravitropism the coleoptiles obeyed the sine law. To study the interaction between light and gravity, coleoptiles were inclined at variable angles and irradiated for 7 h with unilateral blue light (466 nm) impinging at right angles relative to the axis of the coleoptile. The phototropic stimulus was applied from the side opposite to the direction of gravitropic bending. The fluence rate that was required to counteract the negative gravitropism increased exponentially with the sine of the inclination angle. To achieve balance, a linear increase in the gravitropic stimulus required compensation by an exponential increase in the counteracting phototropic stimulus. The establishment of photogravitropic equilibrium during continuous unilateral irradiation is thus determined by two different laws: the well-known sine law for gravitropism and a novel exponential law for phototropism described in this work.

Application of Statistical Learning Theory to Plankton Image Analysis

DTIC Science & Technology

2006-06-01

linear distance interval from 1 to 40 pixels and two directions formula (horizontal & vertical, and diagonals), EF2 is EF with 7 ex- ponential distance...and four directions formula (horizontal, vertical and two diagonals). It is clear that exponential distance inter- val works better than the linear ...PSI - PS by Vincent, linear and pseudo opening and closing spectra, each has 40 elements, total feature length of 160. PS2 - PS modified from Mei- jster

Timing of repetition suppression of event-related potentials to unattended objects.

PubMed

Stefanics, Gabor; Heinzle, Jakob; Czigler, István; Valentini, Elia; Stephan, Klaas Enno

2018-05-26

Current theories of object perception emphasize the automatic nature of perceptual inference. Repetition suppression (RS), the successive decrease of brain responses to repeated stimuli, is thought to reflect the optimization of perceptual inference through neural plasticity. While functional imaging studies revealed brain regions that show suppressed responses to the repeated presentation of an object, little is known about the intra-trial time course of repetition effects to everyday objects. Here we used event-related potentials (ERP) to task-irrelevant line-drawn objects, while participants engaged in a distractor task. We quantified changes in ERPs over repetitions using three general linear models (GLM) that modelled RS by an exponential, linear, or categorical "change detection" function in each subject. Our aim was to select the model with highest evidence and determine the within-trial time-course and scalp distribution of repetition effects using that model. Model comparison revealed the superiority of the exponential model indicating that repetition effects are observable for trials beyond the first repetition. Model parameter estimates revealed a sequence of RS effects in three time windows (86-140ms, 322-360ms, and 400-446ms) and with occipital, temporo-parietal, and fronto-temporal distribution, respectively. An interval of repetition enhancement (RE) was also observed (320-340ms) over occipito-temporal sensors. Our results show that automatic processing of task-irrelevant objects involves multiple intervals of RS with distinct scalp topographies. These sequential intervals of RS and RE might reflect the short-term plasticity required for optimization of perceptual inference and the associated changes in prediction errors (PE) and predictions, respectively, over stimulus repetitions during automatic object processing. This article is protected by copyright. All rights reserved. © 2018 The Authors European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Thermal Hall conductivity in the spin-triplet superconductor with broken time-reversal symmetry

NASA Astrophysics Data System (ADS)

Imai, Yoshiki; Wakabayashi, Katsunori; Sigrist, Manfred

2017-01-01

Motivated by the spin-triplet superconductor Sr2RuO4 , the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p -wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f -wave states as alternative candidates with d =Δ0z ̂(kx2-ky2) (kx±i ky) and Δ0z ̂kxky(kx±i ky) with gapless quasiparticle excitations, we study the temperature dependence of the thermal Hall conductivity, where for the former state the thermal Hall conductivity has a quadratic dependence on temperature, originating from the linear dispersions, in addition to linear and exponential behavior. The obtained result may enable us to distinguish between the chiral p -wave and f -wave states in Sr2RuO4 .

Simulation of the modulation transfer function dependent on the partial Fourier fraction in dynamic contrast enhancement magnetic resonance imaging.

PubMed

Takatsu, Yasuo; Ueyama, Tsuyoshi; Miyati, Tosiaki; Yamamura, Kenichirou

2016-12-01

The image characteristics in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) depend on the partial Fourier fraction and contrast medium concentration. These characteristics were assessed and the modulation transfer function (MTF) was calculated by computer simulation. A digital phantom was created from signal intensity data acquired at different contrast medium concentrations on a breast model. The frequency images [created by fast Fourier transform (FFT)] were divided into 512 parts and rearranged to form a new image. The inverse FFT of this image yielded the MTF. From the reference data, three linear models (low, medium, and high) and three exponential models (slow, medium, and rapid) of the signal intensity were created. Smaller partial Fourier fractions, and higher gradients in the linear models, corresponded to faster MTF decline. The MTF more gradually decreased in the exponential models than in the linear models. The MTF, which reflects the image characteristics in DCE-MRI, was more degraded as the partial Fourier fraction decreased.

Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Shateyi, Stanford; Marewo, Gerald T.

2018-05-01

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

PubMed

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

ParaExp Using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

NASA Astrophysics Data System (ADS)

Merkel, M.; Niyonzima, I.; Schöps, S.

2017-12-01

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

NASA Astrophysics Data System (ADS)

Raja, R.; Marshal Anthoni, S.

2011-02-01

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.

Multifactor analysis and simulation of the surface runoff and soil infiltration at different slope gradients

NASA Astrophysics Data System (ADS)

Huang, J.; Kang, Q.; Yang, J. X.; Jin, P. W.

2017-08-01

The surface runoff and soil infiltration exert significant influence on soil erosion. The effects of slope gradient/length (SG/SL), individual rainfall amount/intensity (IRA/IRI), vegetation cover (VC) and antecedent soil moisture (ASM) on the runoff depth (RD) and soil infiltration (INF) were evaluated in a series of natural rainfall experiments in the South of China. RD is found to correlate positively with IRA, IRI, and ASM factors and negatively with SG and VC. RD decreased followed by its increase with SG and ASM, it increased with a further decrease with SL, exhibited a linear growth with IRA and IRI, and exponential drop with VC. Meanwhile, INF exhibits a positive correlation with SL, IRA and IRI and VC, and a negative one with SG and ASM. INF was going up and then down with SG, linearly rising with SL, IRA and IRI, increasing by a logit function with VC, and linearly falling with ASM. The VC level above 60% can effectively lower the surface runoff and significantly enhance soil infiltration. Two RD and INF prediction models, accounting for the above six factors, were constructed using the multiple nonlinear regression method. The verification of those models disclosed a high Nash-Sutcliffe coefficient and low root-mean-square error, demonstrating good predictability of both models.

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.

Sensitivity Gains, Linearity, and Spectral Reproducibility in Nonuniformly Sampled Multidimensional MAS NMR Spectra of High Dynamic Range.

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

Suiter, Christopher L.; Paramasivam, Sivakumar; Hou, Guangjin

Recently, we have demonstrated that considerable inherent sensitivity gains are attained in MAS NMR spectra acquired by nonuniform sampling (NUS) and introduced maximum entropy interpolation (MINT) processing that assures the linearity of transformation between the time and frequency domains. In this report, we examine the utility of the NUS/MINT approach in multidimensional datasets possessing high dynamic range, such as homonuclear 13C–13C correlation spectra. We demonstrate on model compounds and on 1–73-(U-13C,15N)/74–108-(U-15N) E. coli thioredoxin reassembly, that with appropriately constructed 50 % NUS schedules inherent sensitivity gains of 1.7–2.1-fold are readily reached in such datasets. We show that both linearity andmore » line width are retained under these experimental conditions throughout the entire dynamic range of the signals. Furthermore, we demonstrate that the reproducibility of the peak intensities is excellent in the NUS/MINT approach when experiments are repeated multiple times and identical experimental and processing conditions are employed. Finally, we discuss the principles for design and implementation of random exponentially biased NUS sampling schedules for homonuclear 13C–13C MAS correlation experiments that yield high quality artifact-free datasets.« less

Sensitivity gains, linearity, and spectral reproducibility in nonuniformly sampled multidimensional MAS NMR spectra of high dynamic range

PubMed Central

Suiter, Christopher L.; Paramasivam, Sivakumar; Hou, Guangjin; Sun, Shangjin; Rice, David; Hoch, Jeffrey C.; Rovnyak, David

2014-01-01

Recently, we have demonstrated that considerable inherent sensitivity gains are attained in MAS NMR spectra acquired by nonuniform sampling (NUS) and introduced maximum entropy interpolation (MINT) processing that assures the linearity of transformation between the time and frequency domains. In this report, we examine the utility of the NUS/MINT approach in multidimensional datasets possessing high dynamic range, such as homonuclear 13C–13C correlation spectra. We demonstrate on model compounds and on 1–73-(U-13C, 15N)/74–108-(U-15N) E. coli thioredoxin reassembly, that with appropriately constructed 50 % NUS schedules inherent sensitivity gains of 1.7–2.1-fold are readily reached in such datasets. We show that both linearity and line width are retained under these experimental conditions throughout the entire dynamic range of the signals. Furthermore, we demonstrate that the reproducibility of the peak intensities is excellent in the NUS/MINT approach when experiments are repeated multiple times and identical experimental and processing conditions are employed. Finally, we discuss the principles for design and implementation of random exponentially biased NUS sampling schedules for homonuclear 13C–13C MAS correlation experiments that yield high-quality artifact-free datasets. PMID:24752819

New exponential stability criteria for stochastic BAM neural networks with impulses

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Samidurai, R.; Anthoni, S. M.

2010-10-01

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.

Penalized nonparametric scalar-on-function regression via principal coordinates

PubMed Central

Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu

2016-01-01

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. PMID:29217963

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

Compensation effect during the pyrolysis of tyres and bamboo.

PubMed

Mui, Edward L K; Cheung, W H; Lee, Vinci K C; McKay, Gordon

2010-05-01

Pyrolysis parameters (e.g. pre-exponential factor A, and activation energy E) of two waste materials, namely, tyre rubber and bamboo scaffolding, based on the Arrhenius equation were obtained from weight loss data via thermogravimetry at different heating rates. The compensation effect, which suggests that the linear variation in the pre-exponential factor and the activation energy, was observed for these materials. This can be attributed to the variety of active sites over the reactant surface in the course of decomposition. The calculated data from several revised, first-order models were compared with similar models in the literature. It has been shown that both literature and our calculated data exhibit high linearity in terms of lnA and E, revealing that the latter agree well with other researchers' work. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Reinvestigation of the relationship between the amplitude of the first heart sound to cardiac dynamics.

PubMed

Tang, Hong; Ruan, Chengjie; Qiu, Tianshuang; Park, Yongwan; Xiao, Shouzhong

2013-08-01

The relationships between the amplitude of the first heart sound (S1) and the rising rate of left ventricular pressure (LVP) concluded in previous studies were not consistent. Some researchers believed the relationship was positively linear; others stated the relationship was only positively correlated. To further investigate this relationship, this study simultaneously sampled the external phonocardiogram, electrocardiogram, and intracardiac pressure in the left ventricle in three anesthetized dogs, while invoking wide hemodynamic changes using various doses of epinephrine. The relationship between the maximum amplitude of S1 and the maximum rising rate of LVP and the relationship between the amplitude of dominant peaks/valleys and the corresponding rising rate of LVP were examined by linear, quadratic, cubic, and exponential models. The results showed that the relationships are best fit by nonlinear exponential models.

How exponential are FREDs?

NASA Astrophysics Data System (ADS)

Schaefer, Bradley E.; Dyson, Samuel E.

1996-08-01

A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.

Crime prediction modeling

NASA Technical Reports Server (NTRS)

1971-01-01

A study of techniques for the prediction of crime in the City of Los Angeles was conducted. Alternative approaches to crime prediction (causal, quasicausal, associative, extrapolative, and pattern-recognition models) are discussed, as is the environment within which predictions were desired for the immediate application. The decision was made to use time series (extrapolative) models to produce the desired predictions. The characteristics of the data and the procedure used to choose equations for the extrapolations are discussed. The usefulness of different functional forms (constant, quadratic, and exponential forms) and of different parameter estimation techniques (multiple regression and multiple exponential smoothing) are compared, and the quality of the resultant predictions is assessed.

Characterizations of linear sufficient statistics

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Reoner, R.; Decell, H. P., Jr.

1977-01-01

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.

The Use of Shrinkage Techniques in the Estimation of Attrition Rates for Large Scale Manpower Models

DTIC Science & Technology

1988-07-27

auto regressive model combined with a linear program that solves for the coefficients using MAD. But this success has diminished with time (Rowe...8217Harrison-Stevens Forcasting and the Multiprocess Dy- namic Linear Model ", The American Statistician, v.40, pp. 12 9 - 1 3 5 . 1986. 8. Box, G. E. P. and...1950. 40. McCullagh, P. and Nelder, J., Generalized Linear Models , Chapman and Hall. 1983. 41. McKenzie, E. General Exponential Smoothing and the

A decoupled approach to filter design for stochastic systems

NASA Astrophysics Data System (ADS)

Barbata, A.; Zasadzinski, M.; Ali, H. Souley; Messaoud, H.

2016-08-01

This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Seeing How Money Grows.

ERIC Educational Resources Information Center

Metz, James

2001-01-01

Describes an activity designed to help students connect the ideas of linear growth and exponential growth through graphs of the future value of accounts that earn simple interest and accounts that earn compound interest. Includes worksheets and solutions. (KHR)

An exponential model equation for thiamin loss in irradiated ground pork as a function of dose and temperature of irradiation

NASA Astrophysics Data System (ADS)

Fox, J. B.; Thayer, D. W.; Phillips, J. G.

The effect of low dose γ-irradiation on the thiamin content of ground pork was studied in the range of 0-14 kGy at 2°C and at radiation doses from 0.5 to 7 kGy at temperatures -20, 10, 0, 10 and 20°C. The detailed study at 2°C showed that loss of thiamin was exponential down to 0kGy. An exponential expression was derived for the effect of radiation dose and temperature of irradiation on thiamin loss, and compared with a previously derived general linear expression. Both models were accurate depictions of the data, but the exponential expression showed a significant decrease in the rate of loss between 0 and -10°C. This is the range over which water in meat freezes, the decrease being due to the immobolization of reactive radiolytic products of water in ice crystals.

Multi-Mode Analysis of Dual Ridged Waveguide Systems for Material Characterization

DTIC Science & Technology

2015-09-17

characterization is the process of determining the dielectric, magnetic, and magnetoelectric properties of a material. For simple (i.e., linear ...field expressions in terms of elementary functions (sines, cosines, exponentials and Bessel functions) and corresponding propagation constants of the...with material parameters 0 and µ0. • The MUT is simple ( linear , isotropic, homogeneous), and the sample has a uniform thickness. • The waveguide

Discrete-time BAM neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liu, Xin-Ge; Tang, Mei-Lan; Martin, Ralph; Liu, Xin-Bi

2007-07-01

This Letter deals with the global exponential stability of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Using a Lyapunov functional, and linear matrix inequality techniques (LMI), we derive a new delay-dependent exponential stability criterion for BAM neural networks with variable delays. As this criterion has no extra constraints on the variable delay functions, it can be applied to quite general BAM neural networks with a broad range of time delay functions. It is also easy to use in practice. An example is provided to illustrate the theoretical development.

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

Analog detection for cavity lifetime spectroscopy

DOEpatents

Zare, Richard N.; Harb, Charles C.; Paldus, Barbara A.; Spence, Thomas G.

2001-05-15

An analog detection system for determining a ring-down rate or decay rate 1/.tau. of an exponentially decaying ring-down beam issuing from a lifetime or ring-down cavity during a ring-down phase. Alternatively, the analog detection system determines a build-up rate of an exponentially growing beam issuing from the cavity during a ring-up phase. The analog system can be employed in continuous wave cavity ring-down spectroscopy (CW CRDS) and pulsed CRDS (P CRDS) arrangements utilizing any type of ring-down cavity including ring-cavities and linear cavities.

Analog detection for cavity lifetime spectroscopy

DOEpatents

Zare, Richard N.; Harb, Charles C.; Paldus, Barbara A.; Spence, Thomas G.

2003-01-01

An analog detection system for determining a ring-down rate or decay rate 1/.tau. of an exponentially decaying ring-down beam issuing from a lifetime or ring-down cavity during a ring-down phase. Alternatively, the analog detection system determines a build-up rate of an exponentially growing beam issuing from the cavity during a ring-up phase. The analog system can be employed in continuous wave cavity ring-down spectroscopy (CW CRDS) and pulsed CRDS (P CRDS) arrangements utilizing any type of ring-down cavity including ring-cavities and linear cavities.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential

NASA Astrophysics Data System (ADS)

Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola

2017-01-01

We extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer et al., Phys. Rev. D 91, 123002 (2015), 10.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Determining CDOM Absorption Spectra in Diverse Coastal Environments Using a Multiple Pathlength, Liquid Core Waveguide System. Measuring the Absorption of CDOM in the Field Using a Multiple Pathlength Liquid Waveguide System

NASA Technical Reports Server (NTRS)

Miller, Richard L.; Belz, Mathias; DelCastillo, Carlos; Trzaska, Rick

2000-01-01

We evaluated the accuracy, sensitivity and precision of a multiple pathlength, liquid core waveguide (MPLCW) system for measuring colored dissolved organic matter (CDOM) absorption in the UV-visible spectral range (370-700 nm). The MPLCW has four optical paths (2.0, 9.8, 49.3, and 204 cm) coupled to a single Teflon AF sample cell. Water samples were obtained from inland, coastal and ocean waters ranging in salinity from 0 to 36 PSU. Reference solutions for the MPLCW were made having a refractive index of the sample. CDOM absorption coefficients, a(sub CDOM), and the slope of the log-linearized absorption spectra, S, were compared with values obtained using a dual-beam spectrophotometer. Absorption of phenol red secondary standards measured by the MPLCW at 558 nm were highly correlated with spectrophotometer values (r > 0.99) and showed a linear response across all four pathlengths. Values of a(sub CDOM) measured using the MPLCW were virtually identical to spectrophotometer values over a wide range of concentrations. The dynamic range of a(sub CDOM) for MPLCW measurements was 0.002 - 231.5/m. At low CDOM concentrations (a(sub 370) < 0.1/m) spectrophotometric a(sub CDOM) were slightly greater than MPLCW values and showed larger fluctuations at longer wavelengths due to limitations in instrument precision. In contrast, MPLCW spectra followed an exponential to 600 nm for all samples. The maximum deviation in replicate MPLCW spectra was less than 0.001 absorbance units. The portability, sampling, and optical characteristics of a MPLCW system provide significant enhancements for routine CDOM absorption measurements in a broad range of natural waters.

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

Exponential approximation for daily average solar heating or photolysis. [of stratospheric ozone layer

NASA Technical Reports Server (NTRS)

Cogley, A. C.; Borucki, W. J.

1976-01-01

When incorporating formulations of instantaneous solar heating or photolytic rates as functions of altitude and sun angle into long range forecasting models, it may be desirable to replace the time integrals by daily average rates that are simple functions of latitude and season. This replacement is accomplished by approximating the integral over the solar day by a pure exponential. This gives a daily average rate as a multiplication factor times the instantaneous rate evaluated at an appropriate sun angle. The accuracy of the exponential approximation is investigated by a sample calculation using an instantaneous ozone heating formulation available in the literature.

The decline and fall of Type II error rates

Treesearch

Steve Verrill; Mark Durst

2005-01-01

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations.

Nature of the wiggle instability of galactic spiral shocks

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

Kim, Woong-Tae; Kim, Yonghwi; Kim, Jeong-Gyu, E-mail: wkim@astro.snu.ac.kr, E-mail: kimyh@astro.snu.ac.kr, E-mail: jgkim@astro.snu.ac.kr

Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence of magnetic fields and self-gravity, its physical nature has remained uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode linear stability analysis and nonlinear simulations assuming that the disk is isothermal and infinitesimally thin. We find that the WI is physical, originating from the generation of potential vorticity at a deformed shock front, rather than Kelvin-Helmholtz instabilities as previously thought. Since gasmore » in galaxy rotation periodically passes through the shocks multiple times, the potential vorticity can accumulate successively, setting up a normal mode that grows exponentially with time. Eigenfunctions of the WI decay exponentially downstream from the shock front. Both shock compression of acoustic waves and a discontinuity of shear across the shock stabilize the WI. The wavelength and growth time of the WI depend on the arm strength quite sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of the most unstable mode is about 0.07 times the arm-to-arm spacing, with the growth rate comparable to the orbital angular frequency, which is found to be in good agreement with the results of numerical simulations.« less

Breathers in a locally resonant granular chain with precompression

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-01

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computedmore » exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.« less

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet.

PubMed

Liu, Yingxiang; Liu, Junkao; Chen, Weishan; Shi, Shengjun

2012-05-01

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet was proposed in this paper. The proposed motor contains a horizontal transducer and two vertical transducers. The horizontal transducer includes two exponential shape horns located at the leading ends, and each vertical transducer contains one exponential shape horn. The horns of the horizontal transducer and the vertical transducer intersect at the tip ends where the driving feet are located. Longitudinal vibrations are superimposed in the motor and generate elliptical motions at the driving feet. The two vibration modes of the motor are discussed, and the motion trajectories of driving feet are deduced. By adjusting the structural parameters, the resonance frequencies of two vibration modes were degenerated. A prototype motor was fabricated and measured. Typical output of the prototype is no-load speed of 854 mm/s and maximum thrust force of 40 N at a voltage of 200 V(rms).

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.

[Disciplinar thematic integration in medicine: a proposal from histology and embryology].

PubMed

Bassan, N D; D'Ottavio, A E

2013-01-01

This paper intends to clarify a concept with multiple meanings and a complex reality. It starts providing varied histological and embryological examples apt to contribute the stimulation of teacher and student imaginations in favor of a crucial skill, as thematic integration is, into the present and changing curricula in Medicine in particular and Health Sciences in general. In this sense, it offers linear and branched sequences as well as consolidation graphics which focusing in both disciplines may also include other basic ones, key for clinic diagnosis, among the competences to be developed. After registering some preliminary results revealing the need of its continuous and progressive training along the complete medical career, its own integrative value and the integrative one for their teachers due to its natural link with other basic ones is outlined, its relevance for undergraduate is reaffirmed and possible future variations for them are previewed, considering the present exponential growth of science and technology.

Labeled trees and the efficient computation of derivations

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Childhood Mourning: Prospective Case Analysis of Multiple Losses

ERIC Educational Resources Information Center

Kaufman, Kenneth R.; Kaufman, Nathaniel D.

2005-01-01

Multiple losses within short time periods make one question life and can exponentially influence one's coping skills. But what are the effects on a child and what should be done when the next loss occurs? This case addresses the multiple losses suffered by a child while assessing coping skills of the child and coping strategies used by the parents…

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

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

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

Design of a novel automated methanol feed system for pilot-scale fermentation of Pichia pastoris.

PubMed

Hamaker, Kent H; Johnson, Daniel C; Bellucci, Joseph J; Apgar, Kristie R; Soslow, Sherry; Gercke, John C; Menzo, Darrin J; Ton, Christopher

2011-01-01

Large-scale fermentation of Pichia pastoris requires a large volume of methanol feed during the induction phase. However, a large volume of methanol feed is difficult to use in the processing suite because of the inconvenience of constant monitoring, manual manipulation steps, and fire and explosion hazards. To optimize and improve safety of the methanol feed process, a novel automated methanol feed system has been designed and implemented for industrial fermentation of P. pastoris. Details of the design of the methanol feed system are described. The main goals of the design were to automate the methanol feed process and to minimize the hazardous risks associated with storing and handling large quantities of methanol in the processing area. The methanol feed system is composed of two main components: a bulk feed (BF) system and up to three portable process feed (PF) systems. The BF system automatically delivers methanol from a central location to the portable PF system. The PF system provides precise flow control of linear, step, or exponential feed of methanol to the fermenter. Pilot-scale fermentations with linear and exponential methanol feeds were conducted using two Mut(+) (methanol utilization plus) strains, one expressing a recombinant therapeutic protein and the other a monoclonal antibody. Results show that the methanol feed system is accurate, safe, and efficient. The feed rates for both linear and exponential feed methods were within ± 5% of the set points, and the total amount of methanol fed was within 1% of the targeted volume. Copyright © 2011 American Institute of Chemical Engineers (AIChE).

Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?

PubMed Central

Eldon, Bjarki; Birkner, Matthias; Blath, Jochen; Freund, Fabian

2015-01-01

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular, the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple-merger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough. A normalized version of the SFS (nSFS) is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories. PMID:25575536

Rapid Acceleration of a Coronal Mass Ejection in the Low Corona and Implications of Propagation

NASA Technical Reports Server (NTRS)

Gallagher, Peter T.; Lawrence, Gareth R.; Dennis, Brian R.

2003-01-01

A high-velocity Coronal Mass Ejection (CME) associated with the 2002 April 21 X1.5 flare is studied using a unique set of observations from the Transition Region and Coronal Explorer (TRACE), the Ultraviolet Coronagraph Spectrometer (UVCS), and the Large-Angle Spectrometric Coronagraph (LASCO). The event is first observed as a rapid rise in GOES X-rays, followed by simultaneous conjugate footpoint brightenings connected by an ascending loop or flux-rope feature. While expanding, the appearance of the feature remains remarkably constant as it passes through the TRACE 195 A passband and LASCO fields-of-view, allowing its height-time behavior to be accurately determined. An analytic function, having exponential and linear components, is found to represent the height-time evolution of the CME in the range 1.05-26 R. The CME acceleration rises exponentially to approx. 900 km/sq s within approximately 20-min, peaking at approx.1400 m/sq s when the leading edge is at approx. 1.7 R. The acceleration subsequently falls off as a slowly varying exponential for approx.,90-min. At distances beyond approx. 3.4 R, the height-time profile is approximately linear with a constant velocity of approx. 2400 km/s. These results are briefly discussed in light of recent kinematic models of CMEs.

From Experiment to Theory: What Can We Learn from Growth Curves?

PubMed

Kareva, Irina; Karev, Georgy

2018-01-01

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic-exponential, exponential-linear, exponential-linear-saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.

Year-round measurements of CH4 exchange in a forested drained peatland using automated chambers

NASA Astrophysics Data System (ADS)

Korkiakoski, Mika; Koskinen, Markku; Penttilä, Timo; Arffman, Pentti; Ojanen, Paavo; Minkkinen, Kari; Laurila, Tuomas; Lohila, Annalea

2016-04-01

Pristine peatlands are usually carbon accumulating ecosystems and sources of methane (CH4). Draining peatlands for forestry increases the thickness of the oxic layer, thus enhancing CH4 oxidation which leads to decreased CH4 emissions. Closed chambers are commonly used in estimating the greenhouse gas exchange between the soil and the atmosphere. However, the closed chamber technique alters the gas concentration gradient making the concentration development against time non-linear. Selecting the correct fitting method is important as it can be the largest source of uncertainty in flux calculation. We measured CH4 exchange rates and their diurnal and seasonal variations in a nutrient-rich drained peatland located in southern Finland. The original fen was drained for forestry in 1970s and now the tree stand is a mixture of Scots pine, Norway spruce and Downy birch. Our system consisted of six transparent polycarbonate chambers and stainless steel frames, positioned on different types of field and moss layer. During winter, the frame was raised above the snowpack with extension collars and the height of the snowpack inside the chamber was measured regularly. The chambers were closed hourly and the sample gas was sucked into a cavity ring-down spectrometer and analysed for CH4, CO2 and H2O concentration with 5 second time resolution. The concentration change in time in the beginning of a closure was determined with linear and exponential fits. The results show that linear regression systematically underestimated the CH4 flux when compared to exponential regression by 20-50 %. On the other hand, the exponential regression seemed not to work reliably with small fluxes (< 3.5 μg CH4 m-2 h-1): using exponential regression in such cases typically resulted in anomalously large fluxes and high deviation. Due to these facts, we recommend first calculating the flux with the linear regression and, if the flux is high enough, calculate the flux again using the exponential regression and use this value in later analysis. The forest floor at the site (including the ground vegetation) acted as a CH4 sink most of the time. CH4 emission peaks were occasionally observed, particularly in spring during the snow melt, and during rainfall events in summer. Diurnal variation was observed mainly in summer. The net CH4 exchange for the two year measurement period in the six chambers varied from -31 to -155 mg CH4 m-2 yr-1, the average being -67 mg CH4 m-2 yr-1. However, this does not include the ditches which typically act as a significant source for CH4.

Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control.

PubMed

Li, Xiaofan; Fang, Jian-An; Li, Huiyuan

2017-09-01

This paper investigates master-slave exponential synchronization for a class of complex-valued memristor-based neural networks with time-varying delays via discontinuous impulsive control. Firstly, the master and slave complex-valued memristor-based neural networks with time-varying delays are translated to two real-valued memristor-based neural networks. Secondly, an impulsive control law is constructed and utilized to guarantee master-slave exponential synchronization of the neural networks. Thirdly, the master-slave synchronization problems are transformed into the stability problems of the master-slave error system. By employing linear matrix inequality (LMI) technique and constructing an appropriate Lyapunov-Krasovskii functional, some sufficient synchronization criteria are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Weighted Scaling in Non-growth Random Networks

NASA Astrophysics Data System (ADS)

Chen, Guang; Yang, Xu-Hua; Xu, Xin-Li

2012-09-01

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

Childhood mourning: prospective case analysis of multiple losses.

PubMed

Kaufman, Kenneth R; Kaufman, Nathaniel D

2005-04-01

Multiple losses within short time periods make one question life and can exponentially influence one's coping skills. But what are the effects on a child and what should be done when the next loss occurs? This case addresses the multiple losses suffered by a child while assessing coping skills of the child and coping strategies used by the parents to assist the child.

Optical spectroscopy of nanoscale and heterostructured oxides

NASA Astrophysics Data System (ADS)

Senty, Tess R.

Through careful analysis of a material's properties, devices are continually getting smaller, faster and more efficient each day. Without a complete scientific understanding of material properties, devices cannot continue to improve. This dissertation uses optical spectroscopy techniques to understand light-matter interactions in several oxide materials with promising uses mainly in light harvesting applications. Linear absorption, photoluminescence and transient absorption spectroscopy are primarily used on europium doped yttrium vanadate nanoparticles, copper gallium oxide delafossites doped with iron, and cadmium selenide quantum dots attached to titanium dioxide nanoparticles. Europium doped yttrium vanadate nanoparticles have promising applications for linking to biomolecules. Using Fourier-transform infrared spectroscopy, it was shown that organic ligands (benzoic acid, 3-nitro 4-chloro-benzoic acid and 3,4-dihydroxybenzoic acid) can be attached to the surface of these molecules using metal-carboxylate coordination. Photoluminescence spectroscopy display little difference in the position of the dominant photoluminescence peaks between samples with different organic ligands although there is a strong decrease in their intensity when 3,4-dihydroxybenzoic acid is attached. It is shown that this strong quenching is due to the presence of high-frequency hydroxide vibrational modes within the organic linker. Ultraviolet/visible linear absorption measurements on delafossites display that by doping copper gallium oxide with iron allows for the previously forbidden fundamental gap transition to be accessed. Using tauc plots, it is shown that doping with iron lowers the bandgap from 2.8 eV for pure copper gallium oxide, to 1.7 eV for samples with 1 -- 5% iron doping. Using terahertz transient absorption spectroscopy measurements, it was also determined that doping with iron reduces the charge mobility of the pure delafossite samples. A comparison of cadmium selenide quantum dots, both with and without capping ligands, attached to titanium dioxide nanoparticles is performed using a new transient absorption analysis technique. Multiple exponential fit models were applied to the system and compared with the new inversion analysis technique. It is shown how the new inversion analysis can map out the charge carrier dynamics, providing carrier recombination rates and lifetimes as a function of carrier concentration, where the multiple exponential fit technique is not dependent on the carrier concentration. With the inversion analysis technique it is shown that capping ligands allow for increased charge transfer due to traps being passivated on the quantum dot surface.

Method for exponentiating in cryptographic systems

DOEpatents

Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.

1994-01-01

An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.

Nonlinear observers with linearizable error dynamics

NASA Technical Reports Server (NTRS)

Krener, A. J.; Respondek, W.

1985-01-01

A new method for designing asymptotic observers for a class of nonlinear systems is presented. The error between the state of the systems and the state of the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.

Application of biological filters in water treatment systems

NASA Technical Reports Server (NTRS)

Hurley, T. L.; Bambenek, R. A.

1973-01-01

Silver chloride placed on or close to barrier kills bacteria as they arrive. Dead bacteria accumulate linearly, whereas previously, live bacteria accumulated exponentially. During continuous 30-day tests, no bacteriological contamination was found downstream of filters with silver chloride added.

Kinetics of human aging: I. Rates of senescence between ages 30 and 70 years in healthy people.

PubMed

Sehl, M E; Yates, F E

2001-05-01

A calculation of loss rates is reported for human structural and functional variables from a substantially larger data set than has been previously studied. Data were collected for healthy, nonsmoking human subjects of both sexes from a literature search of cross-sectional, longitudinal, and cross-sequential studies. The number of studies analyzed was 469, and the total number of subjects was 54,274. A linear model provided a fit of the data, for each variable, that was not significantly different from the best polynomial fit. Therefore, linear loss rates (as a percent decline per year from the reference value at age 30) were calculated for 445 variables from 13 organ systems, and additionally for 24 variables even more integrative, such as maximum oxygen consumption and exercise performance, that express effects of multiple contributing variables and systems. The frequency distribution of the 13 individual system linear loss rates (as percent loss per year) for a very healthy population has roughly a unimodal, right-skewed shape, with mean 0.65, median 0.5, and variance 0.32. (The actual underlying distribution could be a truncated Gaussian, an exponential, Poisson, gamma or some other). The linear estimates of loss rates were clustered between 0% and 2% per year for variables from most organ systems, with exceptions being the endocrine, thermoregulatory, and gastrointestinal systems, for which wider ranges (up to approximately 3% per year) of loss rates were found. We suggest that this set of linear losses over time, observed in healthy individuals between ages (approximately) 30 to 70 years, exposes the underlying kinetics of human senescence, independent of effects of substantial disease.

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

NASA Astrophysics Data System (ADS)

Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye

2016-10-01

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).

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.

Exponential Megapriming PCR (EMP) Cloning—Seamless DNA Insertion into Any Target Plasmid without Sequence Constraints

PubMed Central

Ulrich, Alexander; Andersen, Kasper R.; Schwartz, Thomas U.

2012-01-01

We present a fast, reliable and inexpensive restriction-free cloning method for seamless DNA insertion into any plasmid without sequence limitation. Exponential megapriming PCR (EMP) cloning requires two consecutive PCR steps and can be carried out in one day. We show that EMP cloning has a higher efficiency than restriction-free (RF) cloning, especially for long inserts above 2.5 kb. EMP further enables simultaneous cloning of multiple inserts. PMID:23300917

Exponential megapriming PCR (EMP) cloning--seamless DNA insertion into any target plasmid without sequence constraints.

PubMed

Ulrich, Alexander; Andersen, Kasper R; Schwartz, Thomas U

2012-01-01

We present a fast, reliable and inexpensive restriction-free cloning method for seamless DNA insertion into any plasmid without sequence limitation. Exponential megapriming PCR (EMP) cloning requires two consecutive PCR steps and can be carried out in one day. We show that EMP cloning has a higher efficiency than restriction-free (RF) cloning, especially for long inserts above 2.5 kb. EMP further enables simultaneous cloning of multiple inserts.

Exponential increase in postprandial blood-glucose exposure with increasing carbohydrate loads using a linear carbohydrate-to-insulin ratio.

PubMed

Marran, K J; Davey, B; Lang, A; Segal, D G

2013-04-10

Postprandial glucose excursions contribute significantly to average blood glucose, glycaemic variability and cardiovascular risk. Carbohydrate counting is a method of insulin dosing that balances carbohydrate load to insulin dose using a fixed ratio. Many patients and current insulin pumps calculate insulin delivery for meals based on a linear carbohydrate-to-insulin relationship. It is our hypothesis that a non-linear relationship exists between the amounts of carbohydrate consumed and the insulin required to cover it. To document blood glucose exposure in response to increasing carbohydrate loads on fixed carbohydrate-to-insulin ratios. Five type 1 diabetic subjects receiving insulin pump therapy with good control were recruited. Morning basal rates and carbohydrate- to-insulin ratios were optimised. A Medtronic glucose sensor was used for 5 days to collect data for area-under-the-curve (AUC) analysis, during which standardised meals of increasing carbohydrate loads were consumed. Increasing carbohydrate loads using a fixed carbohydrate-to-insulin ratio resulted in increasing glucose AUC. The relationship was found to be exponential rather than linear. Late postprandial hypoglycaemia followed carbohydrate loads of >60 g and this was often followed by rebound hyperglycaemia that lasted >6 hours. A non-linear relationship exists between carbohydrates consumed and the insulin required to cover them. This has implications for control of postprandial blood sugars, especially when consuming large carbohydrate loads. Further studies are required to look at the optimal ratios, duration and type of insulin boluses required to cover increasing carbohydrate loads.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

NASA Astrophysics Data System (ADS)

Graef, Federico

2017-03-01

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

Effect of water-based recovery on blood lactate removal after high-intensity exercise.

PubMed

Lucertini, Francesco; Gervasi, Marco; D'Amen, Giancarlo; Sisti, Davide; Rocchi, Marco Bruno Luigi; Stocchi, Vilberto; Benelli, Piero

2017-01-01

This study assessed the effectiveness of water immersion to the shoulders in enhancing blood lactate removal during active and passive recovery after short-duration high-intensity exercise. Seventeen cyclists underwent active water- and land-based recoveries and passive water and land-based recoveries. The recovery conditions lasted 31 minutes each and started after the identification of each cyclist's blood lactate accumulation peak, induced by a 30-second all-out sprint on a cycle ergometer. Active recoveries were performed on a cycle ergometer at 70% of the oxygen consumption corresponding to the lactate threshold (the control for the intensity was oxygen consumption), while passive recoveries were performed with subjects at rest and seated on the cycle ergometer. Blood lactate concentration was measured 8 times during each recovery condition and lactate clearance was modeled over a negative exponential function using non-linear regression. Actual active recovery intensity was compared to the target intensity (one sample t-test) and passive recovery intensities were compared between environments (paired sample t-tests). Non-linear regression parameters (coefficients of the exponential decay of lactate; predicted resting lactates; predicted delta decreases in lactate) were compared between environments (linear mixed model analyses for repeated measures) separately for the active and passive recovery modes. Active recovery intensities did not differ significantly from the target oxygen consumption, whereas passive recovery resulted in a slightly lower oxygen consumption when performed while immersed in water rather than on land. The exponential decay of blood lactate was not significantly different in water- or land-based recoveries in either active or passive recovery conditions. In conclusion, water immersion at 29°C would not appear to be an effective practice for improving post-exercise lactate removal in either the active or passive recovery modes.

Agronomic threshold of soil available phosphorus in grey desert soils in Xinjiang, China

NASA Astrophysics Data System (ADS)

Wang, B.; Liu, H.; Hao, X. Y.; Wang, X. H.; Sun, J. S.; Li, J. M.; Ma, Y. B.

2016-08-01

Based on 23 years of data, yields of maize, wheat and cotton were modelled under different fertilizer management practices and at different levels of available phosphorus (Olsen-P) in soil. Three types of threshold models were used, namely linear-linear (LL), linear- plateau (LP), and Mitscherlich type exponential (Exp). The agronomic thresholds of available phosphorus were 25.4 mgkg-1 for cotton, 14.8 mgkg-1 for wheat, 13.1 mgkg-1 for maize and 25.4 mgkg-1 for the grey desert soil regions of Xinjiang in China as a whole.

A kinetic approach to some quasi-linear laws of macroeconomics

NASA Astrophysics Data System (ADS)

Gligor, M.; Ignat, M.

2002-11-01

Some previous works have presented the data on wealth and income distributions in developed countries and have found that the great majority of population is described by an exponential distribution, which results in idea that the kinetic approach could be adequate to describe this empirical evidence. The aim of our paper is to extend this framework by developing a systematic kinetic approach of the socio-economic systems and to explain how linear laws, modelling correlations between macroeconomic variables, may arise in this context. Firstly we construct the Boltzmann kinetic equation for an idealised system composed by many individuals (workers, officers, business men, etc.), each of them getting a certain income and spending money for their needs. To each individual a certain time variable amount of money is associated this meaning him/her phase space coordinate. In this way the exponential distribution of money in a closed economy is explicitly found. The extension of this result, including states near the equilibrium, give us the possibility to take into account the regular increase of the total amount of money, according to the modern economic theories. The Kubo-Green-Onsager linear response theory leads us to a set of linear equations between some macroeconomic variables. Finally, the validity of such laws is discussed in relation with the time reversal symmetry and is tested empirically using some macroeconomic time series.

Simulating the effects of climatic variation on stem carbon accumulation of a ponderosa pine stand: comparison with annual growth increment data.

PubMed

Hunt, E R; Martin, F C; Running, S W

1991-01-01

Simulation models of ecosystem processes may be necessary to separate the long-term effects of climate change on forest productivity from the effects of year-to-year variations in climate. The objective of this study was to compare simulated annual stem growth with measured annual stem growth from 1930 to 1982 for a uniform stand of ponderosa pine (Pinus ponderosa Dougl.) in Montana, USA. The model, FOREST-BGC, was used to simulate growth assuming leaf area index (LAI) was either constant or increasing. The measured stem annual growth increased exponentially over time; the differences between the simulated and measured stem carbon accumulations were not large. Growth trends were removed from both the measured and simulated annual increments of stem carbon to enhance the year-to-year variations in growth resulting from climate. The detrended increments from the increasing LAI simulation fit the detrended increments of the stand data over time with an R(2) of 0.47; the R(2) increased to 0.65 when the previous year's simulated detrended increment was included with the current year's simulated increment to account for autocorrelation. Stepwise multiple linear regression of the detrended increments of the stand data versus monthly meteorological variables had an R(2) of 0.37, and the R(2) increased to 0.47 when the previous year's meteorological data were included to account for autocorrelation. Thus, FOREST-BGC was more sensitive to the effects of year-to-year climate variation on annual stem growth than were multiple linear regression models.

Temperature dependence of the Urbach optical absorption edge: A theory of multiple phonon absorption and emission sidebands

NASA Astrophysics Data System (ADS)

Grein, C. H.; John, Sajeev

1989-01-01

The optical absorption coefficient for subgap electronic transitions in crystalline and disordered semiconductors is calculated by first-principles means with use of a variational principle based on the Feynman path-integral representation of the transition amplitude. This incorporates the synergetic interplay of static disorder and the nonadiabatic quantum dynamics of the coupled electron-phonon system. Over photon-energy ranges of experimental interest, this method predicts accurate linear exponential Urbach behavior of the absorption coefficient. At finite temperatures the nonlinear electron-phonon interaction gives rise to multiple phonon emission and absorption sidebands which accompany the optically induced electronic transition. These sidebands dominate the absorption in the Urbach regime and account for the temperature dependence of the Urbach slope and energy gap. The physical picture which emerges is that the phonons absorbed from the heat bath are then reemitted into a dynamical polaronlike potential well which localizes the electron. At zero temperature we recover the usual polaron theory. At high temperatures the calculated tail is qualitatively similar to that of a static Gaussian random potential. This leads to a linear relationship between the Urbach slope and the downshift of the extrapolated continuum band edge as well as a temperature-independent Urbach focus. At very low temperatures, deviations from these rules are predicted arising from the true quantum dynamics of the lattice. Excellent agreement is found with experimental data on c-Si, a-Si:H, a-As2Se3, and a-As2S3. Results are compared with a simple physical argument based on the most-probable-potential-well method.

A fuzzy-logic-based model to predict biogas and methane production rates in a pilot-scale mesophilic UASB reactor treating molasses wastewater.

PubMed

Turkdogan-Aydinol, F Ilter; Yetilmezsoy, Kaan

2010-10-15

A MIMO (multiple inputs and multiple outputs) fuzzy-logic-based model was developed to predict biogas and methane production rates in a pilot-scale 90-L mesophilic up-flow anaerobic sludge blanket (UASB) reactor treating molasses wastewater. Five input variables such as volumetric organic loading rate (OLR), volumetric total chemical oxygen demand (TCOD) removal rate (R(V)), influent alkalinity, influent pH and effluent pH were fuzzified by the use of an artificial intelligence-based approach. Trapezoidal membership functions with eight levels were conducted for the fuzzy subsets, and a Mamdani-type fuzzy inference system was used to implement a total of 134 rules in the IF-THEN format. The product (prod) and the centre of gravity (COG, centroid) methods were employed as the inference operator and defuzzification methods, respectively. Fuzzy-logic predicted results were compared with the outputs of two exponential non-linear regression models derived in this study. The UASB reactor showed a remarkable performance on the treatment of molasses wastewater, with an average TCOD removal efficiency of 93 (+/-3)% and an average volumetric TCOD removal rate of 6.87 (+/-3.93) kg TCOD(removed)/m(3)-day, respectively. Findings of this study clearly indicated that, compared to non-linear regression models, the proposed MIMO fuzzy-logic-based model produced smaller deviations and exhibited a superior predictive performance on forecasting of both biogas and methane production rates with satisfactory determination coefficients over 0.98. 2010 Elsevier B.V. All rights reserved.

Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures

NASA Astrophysics Data System (ADS)

Ke, Jyh-Bin; Lee, Wen-Chiung; Wang, Kuo-Hsiung

2007-07-01

This paper presents the reliability and sensitivity analysis of a system with M primary units, W warm standby units, and R unreliable service stations where warm standby units switching to the primary state might fail. Failure times of primary and warm standby units are assumed to have exponential distributions, and service times of the failed units are exponentially distributed. In addition, breakdown times and repair times of the service stations also follow exponential distributions. Expressions for system reliability, RY(t), and mean time to system failure, MTTF are derived. Sensitivity analysis, relative sensitivity analysis of the system reliability and the mean time to failure, with respect to system parameters are also investigated.

Building an Understanding of Functions: A Series of Activities for Pre-Calculus

ERIC Educational Resources Information Center

Carducci, Olivia M.

2008-01-01

Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

Methane exchange at the peatland forest floor - automatic chamber system exposes the dynamics of small fluxes

NASA Astrophysics Data System (ADS)

Korkiakoski, Mika; Tuovinen, Juha-Pekka; Aurela, Mika; Koskinen, Markku; Minkkinen, Kari; Ojanen, Paavo; Penttilä, Timo; Rainne, Juuso; Laurila, Tuomas; Lohila, Annalea

2017-04-01

We measured methane (CH4) exchange rates with automatic chambers at the forest floor of a nutrient-rich drained peatland in 2011-2013. The fen, located in southern Finland, was drained for forestry in 1969 and the tree stand is now a mixture of Scots pine, Norway spruce, and pubescent birch. Our measurement system consisted of six transparent chambers and stainless steel frames, positioned on a number of different field and moss layer compositions. Gas concentrations were measured with an online cavity ring-down spectroscopy gas analyzer. Fluxes were calculated with both linear and exponential regression. The use of linear regression resulted in systematically smaller CH4 fluxes by 10-45 % as compared to exponential regression. However, the use of exponential regression with small fluxes ( < 2.5 µg CH4 m-2 h-1) typically resulted in anomalously large absolute fluxes and high hour-to-hour deviations. Therefore, we recommend that fluxes are initially calculated with linear regression to determine the threshold for low fluxes and that higher fluxes are then recalculated using exponential regression. The exponential flux was clearly affected by the length of the fitting period when this period was < 190 s, but stabilized with longer periods. Thus, we also recommend the use of a fitting period of several minutes to stabilize the results and decrease the flux detection limit. There were clear seasonal dynamics in the CH4 flux: the forest floor acted as a CH4 sink particularly from early summer until the end of the year, while in late winter the flux was very small and fluctuated around zero. However, the magnitude of fluxes was relatively small throughout the year, ranging mainly from -130 to +100 µg CH4 m-2 h-1. CH4 emission peaks were observed occasionally, mostly in summer during heavy rainfall events. Diurnal variation, showing a lower CH4 uptake rate during the daytime, was observed in all of the chambers, mainly in the summer and late spring, particularly in dry conditions. It was attributed more to changes in wind speed than air or soil temperature, which suggest that physical rather than biological phenomena are responsible for the observed variation. The annual net CH4 exchange varied from -104 ± 30 to -505 ± 39 mg CH4 m-2 yr-1 among the six chambers, with an average of -219 mg CH4 m-2 yr-1 over the 2-year measurement period.

Temperature and neuronal circuit function: compensation, tuning and tolerance.

PubMed

Robertson, R Meldrum; Money, Tomas G A

2012-08-01

Temperature has widespread and diverse effects on different subcellular components of neuronal circuits making it difficult to predict precisely the overall influence on output. Increases in temperature generally increase the output rate in either an exponential or a linear manner. Circuits with a slow output tend to respond exponentially with relatively high Q(10)s, whereas those with faster outputs tend to respond in a linear fashion with relatively low temperature coefficients. Different attributes of the circuit output can be compensated by virtue of opposing processes with similar temperature coefficients. At the extremes of the temperature range, differences in the temperature coefficients of circuit mechanisms cannot be compensated and the circuit fails, often with a reversible loss of ion homeostasis. Prior experience of temperature extremes activates conserved processes of phenotypic plasticity that tune neuronal circuits to be better able to withstand the effects of temperature and to recover more rapidly from failure. Copyright © 2012 Elsevier Ltd. All rights reserved.

A Long-Lived Oscillatory Space-Time Correlation Function of Two Dimensional Colloids

NASA Astrophysics Data System (ADS)

Kim, Jeongmin; Sung, Bong June

2014-03-01

Diffusion of a colloid in solution has drawn significant attention for a century. A well-known behavior of the colloid is called Brownian motion : the particle displacement probability distribution (PDPD) is Gaussian and the mean-square displacement (MSD) is linear with time. However, recent simulation and experimental studies revealed the heterogeneous dynamics of colloids near glass transitions or in complex environments such as entangled actin, PDPD exhibited the exponential tail at a large length instead of being Gaussian at all length scales. More interestingly, PDPD is still exponential even when MSD was still linear with time. It requires a refreshing insight on the colloidal diffusion in the complex environments. In this work, we study heterogeneous dynamics of two dimensional (2D) colloids using molecular dynamics simulations. Unlike in three dimensions, 2D solids do not follow the Lindemann melting criterion. The Kosterlitz-Thouless-Halperin-Nelson-Young theory predicts two-step phase transitions with an intermediate phase, the hexatic phase between isotropic liquids and solids. Near solid-hexatic transition, PDPD shows interesting oscillatory behavior between a central Gaussian part and an exponential tail. Until 12 times longer than translational relaxation time, the oscillatory behavior still persists even after entering the Fickian regime. We also show that multi-layered kinetic clusters account for heterogeneous dynamics of 2D colloids with the long-lived anomalous oscillatory PDPD.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Experimental quantum computing to solve systems of linear equations.

PubMed

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Generalized optimal design for two-arm, randomized phase II clinical trials with endpoints from the exponential dispersion family.

PubMed

Jiang, Wei; Mahnken, Jonathan D; He, Jianghua; Mayo, Matthew S

2016-11-01

For two-arm randomized phase II clinical trials, previous literature proposed an optimal design that minimizes the total sample sizes subject to multiple constraints on the standard errors of the estimated event rates and their difference. The original design is limited to trials with dichotomous endpoints. This paper extends the original approach to be applicable to phase II clinical trials with endpoints from the exponential dispersion family distributions. The proposed optimal design minimizes the total sample sizes needed to provide estimates of population means of both arms and their difference with pre-specified precision. Its applications on data from specific distribution families are discussed under multiple design considerations. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

The multiple complex exponential model and its application to EEG analysis

NASA Astrophysics Data System (ADS)

Chen, Dao-Mu; Petzold, J.

The paper presents a novel approach to the analysis of the EEG signal, which is based on a multiple complex exponential (MCE) model. Parameters of the model are estimated using a nonharmonic Fourier expansion algorithm. The central idea of the algorithm is outlined, and the results, estimated on the basis of simulated data, are presented and compared with those obtained by the conventional methods of signal analysis. Preliminary work on various application possibilities of the MCE model in EEG data analysis is described. It is shown that the parameters of the MCE model reflect the essential information contained in an EEG segment. These parameters characterize the EEG signal in a more objective way because they are closer to the recent supposition of the nonlinear character of the brain's dynamic behavior.

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

Nonlinear Dynamics and the Growth of Literature.

ERIC Educational Resources Information Center

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Wu, Wei; Cui, Bao-Tong

2007-07-01

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Simultaneous estimation of multiple phases in digital holographic interferometry using state space analysis

NASA Astrophysics Data System (ADS)

Kulkarni, Rishikesh; Rastogi, Pramod

2018-05-01

A new approach is proposed for the multiple phase estimation from a multicomponent exponential phase signal recorded in multi-beam digital holographic interferometry. It is capable of providing multidimensional measurements in a simultaneous manner from a single recording of the exponential phase signal encoding multiple phases. Each phase within a small window around each pixel is appproximated with a first order polynomial function of spatial coordinates. The problem of accurate estimation of polynomial coefficients, and in turn the unwrapped phases, is formulated as a state space analysis wherein the coefficients and signal amplitudes are set as the elements of a state vector. The state estimation is performed using the extended Kalman filter. An amplitude discrimination criterion is utilized in order to unambiguously estimate the coefficients associated with the individual signal components. The performance of proposed method is stable over a wide range of the ratio of signal amplitudes. The pixelwise phase estimation approach of the proposed method allows it to handle the fringe patterns that may contain invalid regions.

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

NASA Astrophysics Data System (ADS)

Jemseena, V.; Gopalakrishnan, Manoj

2015-05-01

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M. K. Gardner et al., Cell 147, 1092 (2011), 10.1016/j.cell.2011.10.037] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here we investigate, via numerical simulations and mathematical calculations, some of the consequences of the age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically, and purely linear growth. The boundary demarcating the steady-state and non-steady-state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to nonexponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that the age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

Bayesian Travel Time Inversion adopting Gaussian Process Regression

NASA Astrophysics Data System (ADS)

Mauerberger, S.; Holschneider, M.

2017-12-01

A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

Group Velocity for Leaky Waves

NASA Astrophysics Data System (ADS)

Rzeznik, Andrew; Chumakova, Lyubov; Rosales, Rodolfo

2017-11-01

In many linear dispersive/conservative wave problems one considers solutions in an infinite medium which is uniform everywhere except for a bounded region. In general, localized inhomogeneities of the medium cause partial internal reflection, and some waves leak out of the domain. Often one only desires the solution in the inhomogeneous region, with the exterior accounted for by radiation boundary conditions. Formulating such conditions requires definition of the direction of energy propagation for leaky waves in multiple dimensions. In uniform media such waves have the form exp (d . x + st) where d and s are complex and related by a dispersion relation. A complex s is required since these waves decay via radiation to infinity, even though the medium is conservative. We present a modified form of Whitham's Averaged Lagrangian Theory along with modulation theory to extend the classical idea of group velocity to leaky waves. This allows for solving on the bounded region by representing the waves as a linear combination of leaky modes, each exponentially decaying in time. This presentation is part of a joint project, and applications of these results to example GFD problems will be presented by L. Chumakova in the talk ``Leaky GFD Problems''. This work is partially supported by NSF Grants DMS-1614043, DMS-1719637, and 1122374, and by the Hertz Foundation.

Linear and non-linear contributions to oxygen transport and utilization during moderate random exercise in humans.

PubMed

Beltrame, T; Hughson, R L

2017-05-01

What is the central question of this study? The pulmonary oxygen uptake (pV̇O2) data used to study the muscle aerobic system dynamics during moderate-exercise transitions is classically described as a mono-exponential function controlled by a complex interaction of the oxygen delivery-utilization balance. This elevated complexity complicates the acquisition of relevant information regarding aerobic system dynamics based on pV̇O2 data during a varying exercise stimulus. What is the main finding and its importance? The elevated complexity of pV̇O2 dynamics is a consequence of a multiple-order interaction between muscle oxygen uptake and circulatory distortion. Our findings challenge the use of a first-order function to study the influences of the oxygen delivery-utilization balance over the pV̇O2 dynamics. The assumption of aerobic system linearity implies that the pulmonary oxygen uptake (pV̇O2) dynamics during exercise transitions present a first-order characteristic. The main objective of this study was to test the linearity of the oxygen delivery-utilization balance during random moderate exercise. The cardiac output (Q̇) and deoxygenated haemoglobin concentration ([HHb]) were measured to infer the central and local O 2 availability, respectively. Thirteen healthy men performed two consecutive pseudorandom binary sequence cycling exercises followed by an incremental protocol. The system input and the outputs pV̇O2, [HHb] and Q̇ were submitted to frequency-domain analysis. The linearity of the variables was tested by computing the ability of the response at a specific frequency to predict the response at another frequency. The predictability levels were assessed by the coefficient of determination. In a first-order system, a participant who presents faster dynamics at a specific frequency should also present faster dynamics at any other frequency. All experimentally obtained variables (pV̇O2, [HHb] and Q̇) presented a certainly degree of non-linearity. The local O 2 availability, evaluated by the ratio pV̇O2/[HHb], presented the most irregular behaviour. The overall [HHb] kinetics were faster than pV̇O2 and Q̇ kinetics. In conclusion, the oxygen delivery-utilization balance behaved as a non-linear phenomenon. Therefore, the elevated complexity of the pulmonary oxygen uptake dynamics is governed by a complex multiple-order interaction between the oxygen delivery and utilization systems. © 2017 The Authors. Experimental Physiology © 2017 The Physiological Society.

Large-scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability

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

Bhat, Pallavi; Ebrahimi, Fatima; Blackman, Eric G.

Here, we study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x–y) averaging, we also demonstrate the presence of large-scale fields when vertical (y–z) averaging is employed instead. By computing space–time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase – a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumbermore » fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode–mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.« less

Modeling of thermal degradation kinetics of the C-glucosyl xanthone mangiferin in an aqueous model solution as a function of pH and temperature and protective effect of honeybush extract matrix.

PubMed

Beelders, Theresa; de Beer, Dalene; Kidd, Martin; Joubert, Elizabeth

2018-01-01

Mangiferin, a C-glucosyl xanthone, abundant in mango and honeybush, is increasingly targeted for its bioactive properties and thus to enhance functional properties of food. The thermal degradation kinetics of mangiferin at pH3, 4, 5, 6 and 7 were each modeled at five temperatures ranging between 60 and 140°C. First-order reaction models were fitted to the data using non-linear regression to determine the reaction rate constant at each pH-temperature combination. The reaction rate constant increased with increasing temperature and pH. Comparison of the reaction rate constants at 100°C revealed an exponential relationship between the reaction rate constant and pH. The data for each pH were also modeled with the Arrhenius equation using non-linear and linear regression to determine the activation energy and pre-exponential factor. Activation energies decreased slightly with increasing pH. Finally, a multi-linear model taking into account both temperature and pH was developed for mangiferin degradation. Sterilization (121°C for 4min) of honeybush extracts dissolved at pH4, 5 and 7 did not cause noticeable degradation of mangiferin, although the multi-linear model predicted 34% degradation at pH7. The extract matrix is postulated to exert a protective effect as changes in potential precursor content could not fully explain the stability of mangiferin. Copyright © 2017 Elsevier Ltd. All rights reserved.

Large-scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability

DOE PAGES

Bhat, Pallavi; Ebrahimi, Fatima; Blackman, Eric G.

2016-07-06

Here, we study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x–y) averaging, we also demonstrate the presence of large-scale fields when vertical (y–z) averaging is employed instead. By computing space–time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase – a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumbermore » fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode–mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.« less

Photoluminescence study of MBE grown InGaN with intentional indium segregation

NASA Astrophysics Data System (ADS)

Cheung, Maurice C.; Namkoong, Gon; Chen, Fei; Furis, Madalina; Pudavar, Haridas E.; Cartwright, Alexander N.; Doolittle, W. Alan

2005-05-01

Proper control of MBE growth conditions has yielded an In0.13Ga0.87N thin film sample with emission consistent with In-segregation. The photoluminescence (PL) from this epilayer showed multiple emission components. Moreover, temperature and power dependent studies of the PL demonstrated that two of the components were excitonic in nature and consistent with indium phase separation. At 15 K, time resolved PL showed a non-exponential PL decay that was well fitted with the stretched exponential solution expected for disordered systems. Consistent with the assumed carrier hopping mechanism of this model, the effective lifetime, , and the stretched exponential parameter, , decrease with increasing emission energy. Finally, room temperature micro-PL using a confocal microscope showed spatial clustering of low energy emission.

M. Riesz-Schur-type inequalities for entire functions of exponential type

NASA Astrophysics Data System (ADS)

Ganzburg, M. I.; Nevai, P.; Erdélyi, T.

2015-01-01

We prove a general M. Riesz-Schur-type inequality for entire functions of exponential type. If f and Q are two functions of exponential types σ > 0 and τ ≥ 0, respectively, and if Q is real-valued and the real zeros of Q, not counting multiplicities, are bounded away from each other, then \\displaystyle \\vert f(x)\\vert≤ (σ+τ) (Aσ+τ(Q))-1/2\\Vert Q f\\Vert C( R),\\qquad x\\in R, where \\displaystyle A_s(Q) \\stackrel{{def}}{=}\\infx\\in R \\bigl( \\lbrack Q'(x) \\rbrack ^2+s2 [Q(x)]^2\\bigr). We apply this inequality to the weights Q(x)\\stackrel{{def}}{=} \\sin (τ x) and Q(x) \\stackrel{{def}}{=} x and describe the extremal functions in the corresponding inequalities. Bibliography: 7 titles.

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Determining the Kinetic Parameters Characteristic of Microalgal Growth.

ERIC Educational Resources Information Center

Martinez Sancho, Maria Eugenie; And Others

1991-01-01

An activity in which students obtain a growth curve for algae, identify the exponential and linear growth phases, and calculate the parameters which characterize both phases is described. The procedure, a list of required materials, experimental conditions, analytical technique, and a discussion of the interpretations of individual results are…

Individual Differences in a Positional Learning Task across the Adult Lifespan

ERIC Educational Resources Information Center

Rast, Philippe; Zimprich, Daniel

2010-01-01

This study aimed at modeling individual and average non-linear trajectories of positional learning using a structured latent growth curve approach. The model is based on an exponential function which encompasses three parameters: Initial performance, learning rate, and asymptotic performance. These learning parameters were compared in a positional…

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Population-based absolute risk estimation with survey data

PubMed Central

Kovalchik, Stephanie A.; Pfeiffer, Ruth M.

2013-01-01

Absolute risk is the probability that a cause-specific event occurs in a given time interval in the presence of competing events. We present methods to estimate population-based absolute risk from a complex survey cohort that can accommodate multiple exposure-specific competing risks. The hazard function for each event type consists of an individualized relative risk multiplied by a baseline hazard function, which is modeled nonparametrically or parametrically with a piecewise exponential model. An influence method is used to derive a Taylor-linearized variance estimate for the absolute risk estimates. We introduce novel measures of the cause-specific influences that can guide modeling choices for the competing event components of the model. To illustrate our methodology, we build and validate cause-specific absolute risk models for cardiovascular and cancer deaths using data from the National Health and Nutrition Examination Survey. Our applications demonstrate the usefulness of survey-based risk prediction models for predicting health outcomes and quantifying the potential impact of disease prevention programs at the population level. PMID:23686614

Diffusive dynamics of nanoparticles in ultra-confined media

DOE PAGES

Jacob, Jack Deodato; Conrad, Jacinta; Krishnamoorti, Ramanan; ...

2015-08-10

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200 400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3 5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accountedmore » for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Altogether, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.« less

Ultrasonic Study of Dislocation Dynamics in Lithium -

NASA Astrophysics Data System (ADS)

Han, Myeong-Deok

1987-09-01

Experimental studies of dislocation dynamics in LiF single crystals, using ultrasonic techniques combined with dynamic loading, were performed to investigate the time evolution of the plastic deformation process under a short stress pulse at room temperature, and the temperature dependence of the dislocation damping mechanism in the temperature range 25 - 300(DEGREES)K. From the former, the time dependence of the ultrasonic attenuation was understood as resulting from dislocation multiplication followed by the evolution of mobile dislocations to immobile ones under large stress. From the latter, the temperature dependence of the ultrasonic attenuation was interpreted as due to the motion of the dislocation loops overcoming the periodic Peierls potential barrier in a manner analogous to the motion of a thermalized sine-Gordon chain under a small stress. The Peierls stress obtained from the experimental results by application of Seeger's relaxation model with exponential dislocation length distribution was 4.26MPa, which is consistent with the lowest stress for the linear relation between the dislocation velocity and stress observed by Flinn and Tinder.

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen

2018-06-01

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Growth and mortality of larval Myctophum affine (Myctophidae, Teleostei).

PubMed

Namiki, C; Katsuragawa, M; Zani-Teixeira, M L

2015-04-01

The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south-eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L(S)). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird-Gompertz model. The exponential model best fitted the data, and L(0) values from exponential and Laird-Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L(S)). The average growth rate (0·33 mm day(-1)) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area. © 2015 The Fisheries Society of the British Isles.

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

NASA Astrophysics Data System (ADS)

Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.

2016-06-01

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite-Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

Long-run growth rate in a random multiplicative model

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

Pirjol, Dan

2014-08-01

We consider the long-run growth rate of the average value of a random multiplicative process x{sub i+1} = a{sub i}x{sub i} where the multipliers a{sub i}=1+ρexp(σW{sub i}₋1/2 σ²t{sub i}) have Markovian dependence given by the exponential of a standard Brownian motion W{sub i}. The average value (x{sub n}) is given by the grand partition function of a one-dimensional lattice gas with two-body linear attractive interactions placed in a uniform field. We study the Lyapunov exponent λ=lim{sub n→∞}1/n log(x{sub n}), at fixed β=1/2 σ²t{sub n}n, and show that it is given by the equation of state of the lattice gas inmore » thermodynamical equilibrium. The Lyapunov exponent has discontinuous partial derivatives along a curve in the (ρ, β) plane ending at a critical point (ρ{sub C}, β{sub C}) which is related to a phase transition in the equivalent lattice gas. Using the equivalence of the lattice gas with a bosonic system, we obtain the exact solution for the equation of state in the thermodynamical limit n → ∞.« less

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

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

Diwaker, E-mail: diwakerphysics@gmail.com; Chakraborty, Aniruddha

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

Algebraic Generalization Strategies Used by Kuwaiti Pre-Service Teachers

ERIC Educational Resources Information Center

Alajmi, Amal Hussain

2016-01-01

This study reports on the algebraic generalization strategies used by elementary and middle/high school pre-service mathematics teachers in Kuwait. They were presented with 9 tasks that involved linear, exponential, and quadratic situations. The results showed that these pre-service teachers had difficulty in generalizing algebraic rules in all 3…

Using Spreadsheets to Discover Meaning for Parameters in Nonlinear Models

ERIC Educational Resources Information Center

Green, Kris H.

2008-01-01

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…

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

AlHallak, M.; Chamoun, N.; Physikalisches Institut der Universität Bonn,Nußalle 12, D-53115 Bonn

We present a model of power law inflation generated by variation of the strong coupling constant. We then extend the model to two varying coupling constants which leads to a potential consisting of a linear combination of exponential terms. Some variants of the latter may be self-consistent and can accommodate the experimental data of the Planck 2015 and other recent experiments.

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Characterization of plasma current quench during disruptions at HL-2A

NASA Astrophysics Data System (ADS)

Zhu, Jinxia; Zhang, Yipo; Dong, Yunbo; HL-2A Team

2017-05-01

The most essential assumptions of physics for the evaluation of electromagnetic forces on the plasma-facing components due to a disruption-induced eddy current are characteristics of plasma current quenches including the current quench rate or its waveforms. The characteristics of plasma current quenches at HL-2A have been analyzed during spontaneous disruptions. Both linear decay and exponential decay are found in the disruptions with the fastest current quenches. However, there are two stages of current quench in the slow current quench case. The first stage with an exponential decay and the second stage followed by a rapid linear decay. The faster current quench rate corresponds to the faster movement of plasma displacement. The parameter regimes on the current quench time and the current quench rates have been obtained from disruption statistics at HL-2A. There exists no remarkable difference for distributions obtained between the limiter and the divertor configuration. This data from HL-2A provides basic data of the derivation of design criteria for a large-sized machine during the current decay phase of the disruptions.

Linear diffusion into a Faraday cage.

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

Warne, Larry Kevin; Lin, Yau Tang; Merewether, Kimball O.

2011-11-01

Linear lightning diffusion into a Faraday cage is studied. An early-time integral valid for large ratios of enclosure size to enclosure thickness and small relative permeability ({mu}/{mu}{sub 0} {le} 10) is used for this study. Existing solutions for nearby lightning impulse responses of electrically thick-wall enclosures are refined and extended to calculate the nearby lightning magnetic field (H) and time-derivative magnetic field (HDOT) inside enclosures of varying thickness caused by a decaying exponential excitation. For a direct strike scenario, the early-time integral for a worst-case line source outside the enclosure caused by an impulse is simplified and numerically integrated tomore » give the interior H and HDOT at the location closest to the source as well as a function of distance from the source. H and HDOT enclosure response functions for decaying exponentials are considered for an enclosure wall of any thickness. Simple formulas are derived to provide a description of enclosure interior H and HDOT as well. Direct strike voltage and current bounds for a single-turn optimally-coupled loop for all three waveforms are also given.« less

Improving Strategies via SMT Solving

NASA Astrophysics Data System (ADS)

Gawlitza, Thomas Martin; Monniaux, David

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of Gawlitza and Seidl [17]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Π2 P -complete.

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

NASA Astrophysics Data System (ADS)

Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

2018-04-01

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

Pattern analysis of total item score and item response of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative sample of US adults

PubMed Central

Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Yutaka, Ono; Furukawa, Toshiaki A.

2017-01-01

Background Several recent studies have shown that total scores on depressive symptom measures in a general population approximate an exponential pattern except for the lower end of the distribution. Furthermore, we confirmed that the exponential pattern is present for the individual item responses on the Center for Epidemiologic Studies Depression Scale (CES-D). To confirm the reproducibility of such findings, we investigated the total score distribution and item responses of the Kessler Screening Scale for Psychological Distress (K6) in a nationally representative study. Methods Data were drawn from the National Survey of Midlife Development in the United States (MIDUS), which comprises four subsamples: (1) a national random digit dialing (RDD) sample, (2) oversamples from five metropolitan areas, (3) siblings of individuals from the RDD sample, and (4) a national RDD sample of twin pairs. K6 items are scored using a 5-point scale: “none of the time,” “a little of the time,” “some of the time,” “most of the time,” and “all of the time.” The pattern of total score distribution and item responses were analyzed using graphical analysis and exponential regression model. Results The total score distributions of the four subsamples exhibited an exponential pattern with similar rate parameters. The item responses of the K6 approximated a linear pattern from “a little of the time” to “all of the time” on log-normal scales, while “none of the time” response was not related to this exponential pattern. Discussion The total score distribution and item responses of the K6 showed exponential patterns, consistent with other depressive symptom scales. PMID:28289560

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Are infant mortality rate declines exponential? The general pattern of 20th century infant mortality rate decline

PubMed Central

Bishai, David; Opuni, Marjorie

2009-01-01

Background Time trends in infant mortality for the 20th century show a curvilinear pattern that most demographers have assumed to be approximately exponential. Virtually all cross-country comparisons and time series analyses of infant mortality have studied the logarithm of infant mortality to account for the curvilinear time trend. However, there is no evidence that the log transform is the best fit for infant mortality time trends. Methods We use maximum likelihood methods to determine the best transformation to fit time trends in infant mortality reduction in the 20th century and to assess the importance of the proper transformation in identifying the relationship between infant mortality and gross domestic product (GDP) per capita. We apply the Box Cox transform to infant mortality rate (IMR) time series from 18 countries to identify the best fitting value of lambda for each country and for the pooled sample. For each country, we test the value of λ against the null that λ = 0 (logarithmic model) and against the null that λ = 1 (linear model). We then demonstrate the importance of selecting the proper transformation by comparing regressions of ln(IMR) on same year GDP per capita against Box Cox transformed models. Results Based on chi-squared test statistics, infant mortality decline is best described as an exponential decline only for the United States. For the remaining 17 countries we study, IMR decline is neither best modelled as logarithmic nor as a linear process. Imposing a logarithmic transform on IMR can lead to bias in fitting the relationship between IMR and GDP per capita. Conclusion The assumption that IMR declines are exponential is enshrined in the Preston curve and in nearly all cross-country as well as time series analyses of IMR data since Preston's 1975 paper, but this assumption is seldom correct. Statistical analyses of IMR trends should assess the robustness of findings to transformations other than the log transform. PMID:19698144

Initial mass function of planetesimals formed by the streaming instability

NASA Astrophysics Data System (ADS)

Schäfer, Urs; Yang, Chao-Chin; Johansen, Anders

2017-01-01

The streaming instability is a mechanism to concentrate solid particles into overdense filaments that undergo gravitational collapse and form planetesimals. However, it remains unclear how the initial mass function of these planetesimals depends on the box dimensions of numerical simulations. To resolve this, we perform simulations of planetesimal formation with the largest box dimensions to date, allowing planetesimals to form simultaneously in multiple filaments that can only emerge within such large simulation boxes. In our simulations, planetesimals with sizes between 80 km and several hundred kilometers form. We find that a power law with a rather shallow exponential cutoff at the high-mass end represents the cumulative birth mass function better than an integrated power law. The steepness of the exponential cutoff is largely independent of box dimensions and resolution, while the exponent of the power law is not constrained at the resolutions we employ. Moreover, we find that the characteristic mass scale of the exponential cutoff correlates with the mass budget in each filament. Together with previous studies of high-resolution simulations with small box domains, our results therefore imply that the cumulative birth mass function of planetesimals is consistent with an exponentially tapered power law with a power-law exponent of approximately -1.6 and a steepness of the exponential cutoff in the range of 0.3-0.4.

Quantification of the Effects of Salt Stress and Physiological State on Thermotolerance of Bacillus cereus ATCC 10987 and ATCC 14579

PubMed Central

den Besten, Heidy M. W.; Mataragas, Marios; Moezelaar, Roy; Abee, Tjakko; Zwietering, Marcel H.

2006-01-01

The food-borne pathogen Bacillus cereus can acquire enhanced thermal resistance through multiple mechanisms. Two Bacillus cereus strains, ATCC 10987 and ATCC 14579, were used to quantify the effects of salt stress and physiological state on thermotolerance. Cultures were exposed to increasing concentrations of sodium chloride for 30 min, after which their thermotolerance was assessed at 50°C. Linear and nonlinear microbial survival models, which cover a wide range of known inactivation curvatures for vegetative cells, were fitted to the inactivation data and evaluated. Based on statistical indices and model characteristics, biphasic models with a shoulder were selected and used for quantification. Each model parameter reflected a survival characteristic, and both models were flexible, allowing a reduction of parameters when certain phenomena were not present. Both strains showed enhanced thermotolerance after preexposure to (non)lethal salt stress conditions in the exponential phase. The maximum adaptive stress response due to salt preexposure demonstrated for exponential-phase cells was comparable to the effect of physiological state on thermotolerance in both strains. However, the adaptive salt stress response was less pronounced for transition- and stationary-phase cells. The distinct tailing of strain ATCC 10987 was attributed to the presence of a subpopulation of spores. The existence of a stable heat-resistant subpopulation of vegetative cells could not be demonstrated for either of the strains. Quantification of the adaptive stress response might be instrumental in understanding adaptation mechanisms and will allow the food industry to develop more accurate and reliable stress-integrated predictive modeling to optimize minimal processing conditions. PMID:16957208

Multiple-beam propagation in an Anderson localized optical fiber.

PubMed

Karbasi, Salman; Koch, Karl W; Mafi, Arash

2013-01-14

We investigate the simultaneous propagation of multiple beams in a disordered Anderson localized optical fiber. The profiles of each beam fall off exponentially, enabling multiple channels at high-density. We examine the influence of fiber bends on the movement of the beam positions, which we refer to as drift. We investigate the extent of the drift of localized beams induced by macro-bending and show that it is possible to design Anderson localized optical fibers that can be used for practical beam-multiplexing applications.

Multiple Beam Optical Processing

DTIC Science & Technology

1989-12-01

the interference of multiple reflections between the two mirrors. The most promising optical bistable devices, at present, are very thin, solid Fabry...MEDIUM b) R - Ir ,, PMASE SHIFTr Figure 1.3 (a) Nonlinear Fabry-Perot etalon consisting of solid material with parallel surfaces with coatings of...instead of the solid planar structure [2.10]. Voids between columns cause an Inhomogeneous broadening and an exponential extension (Urbach tail) of the

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

q Breathers in Finite Lattices: Nonlinearity and Weak Disorder

NASA Astrophysics Data System (ADS)

Ivanchenko, M. V.

2009-05-01

Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

NASA Astrophysics Data System (ADS)

Wienkers, A. F.; Ogilvie, G. I.

2018-07-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalizes the often-used Cartesian shearing box model. The numerical method is an overall second-order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localize the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of 'bursty' dynamics such as the superhump phenomenon.

Do Vampires Exist? Using Spreadsheets To Investigate a Common Folktale.

ERIC Educational Resources Information Center

Drier, Hollylynne Stohl

1999-01-01

Describes the use of spreadsheets in a third grade class to teach basic mathematical concepts by investigating the existence of vampires. Incorporates addition and multiplication skills, patterning, variables, formulas, exponential growth, and proof by contradiction. (LRW)

Fluid particles only separate exponentially in the dissipation range of turbulence after extremely long times

NASA Astrophysics Data System (ADS)

Dhariwal, Rohit; Bragg, Andrew D.

2018-03-01

In this paper, we consider how the statistical moments of the separation between two fluid particles grow with time when their separation lies in the dissipation range of turbulence. In this range, the fluid velocity field varies smoothly and the relative velocity of two fluid particles depends linearly upon their separation. While this may suggest that the rate at which fluid particles separate is exponential in time, this is not guaranteed because the strain rate governing their separation is a strongly fluctuating quantity in turbulence. Indeed, Afik and Steinberg [Nat. Commun. 8, 468 (2017), 10.1038/s41467-017-00389-8] argue that there is no convincing evidence that the moments of the separation between fluid particles grow exponentially with time in the dissipation range of turbulence. Motivated by this, we use direct numerical simulations (DNS) to compute the moments of particle separation over very long periods of time in a statistically stationary, isotropic turbulent flow to see if we ever observe evidence for exponential separation. Our results show that if the initial separation between the particles is infinitesimal, the moments of the particle separation first grow as power laws in time, but we then observe convincing evidence that at sufficiently long times the moments do grow exponentially. However, this exponential growth is only observed after extremely long times ≳200 τη , where τη is the Kolmogorov time scale. This is due to fluctuations in the strain rate about its mean value measured along the particle trajectories, the effect of which on the moments of the particle separation persists for very long times. We also consider the backward-in-time (BIT) moments of the article separation, and observe that they too grow exponentially in the long-time regime. However, a dramatic consequence of the exponential separation is that at long times the difference between the rate of the particle separation forward in time (FIT) and BIT grows exponentially in time, leading to incredibly strong irreversibility in the dispersion. This is in striking contrast to the irreversibility of their relative dispersion in the inertial range, where the difference between FIT and BIT is constant in time according to Richardson's phenomenology.

Firing patterns in the adaptive exponential integrate-and-fire model.

PubMed

Naud, Richard; Marcille, Nicolas; Clopath, Claudia; Gerstner, Wulfram

2008-11-01

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.

How extreme are extremes?

NASA Astrophysics Data System (ADS)

Cucchi, Marco; Petitta, Marcello; Calmanti, Sandro

2016-04-01

High temperatures have an impact on the energy balance of any living organism and on the operational capabilities of critical infrastructures. Heat-wave indicators have been mainly developed with the aim of capturing the potential impacts on specific sectors (agriculture, health, wildfires, transport, power generation and distribution). However, the ability to capture the occurrence of extreme temperature events is an essential property of a multi-hazard extreme climate indicator. Aim of this study is to develop a standardized heat-wave indicator, that can be combined with other indices in order to describe multiple hazards in a single indicator. The proposed approach can be used in order to have a quantified indicator of the strenght of a certain extreme. As a matter of fact, extremes are usually distributed in exponential or exponential-exponential functions and it is difficult to quickly asses how strong was an extreme events considering only its magnitude. The proposed approach simplify the quantitative and qualitative communication of extreme magnitude

The effects of temperature and humidity on formaldehyde emission from UF-bonded boards : a literature critique

Treesearch

George E. Myers

1985-01-01

An analysis has been conducted on available data related to temperature and humidity effects on formaldehyde concentrations that are produced by emission from particleboard and hardwood plywood paneling. Temperature changes are described by an exponential relation while a linear relation suffices for humidity effects. Large variations exist in the results from...

Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2012-01-01

Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…

A Fluid-driven Earthquake Cycle, Omori's Law, and Fluid-driven Aftershocks

NASA Astrophysics Data System (ADS)

Miller, S. A.

2015-12-01

Few models exist that predict the Omori's Law of aftershock rate decay, with rate-state friction the only physically-based model. ETAS is a probabilistic model of cascading failures, and is sometimes used to infer rate-state frictional properties. However, the (perhaps dominant) role of fluids in the earthquake process is being increasingly realised, so a fluid-based physical model for Omori's Law should be available. In this talk, I present an hypothesis for a fluid-driven earthquake cycle where dehydration and decarbonization at depth provides continuous sources of buoyant high pressure fluids that must eventually make their way back to the surface. The natural pathway for fluid escape is along plate boundaries, where in the ductile regime high pressure fluids likely play an integral role in episodic tremor and slow slip earthquakes. At shallower levels, high pressure fluids pool at the base of seismogenic zones, with the reservoir expanding in scale through the earthquake cycle. Late in the cycle, these fluids can invade and degrade the strength of the brittle crust and contribute to earthquake nucleation. The mainshock opens permeable networks that provide escape pathways for high pressure fluids and generate aftershocks along these flow paths, while creating new pathways by the aftershocks themselves. Thermally activated precipitation then seals up these pathways, returning the system to a low-permeability environment and effective seal during the subsequent tectonic stress buildup. I find that the multiplicative effect of an exponential dependence of permeability on the effective normal stress coupled with an Arrhenius-type, thermally activated exponential reduction in permeability results in Omori's Law. I simulate this scenario using a very simple model that combines non-linear diffusion and a step-wise increase in permeability when a Mohr Coulomb failure condition is met, and allow permeability to decrease as an exponential function in time. I show very strong spatial correlations of the simulated evolved permeability and fluid pressure field with aftershock hypocenters from this 1992 Landers and 1994 Northridge aftershock sequences, and reproduce the observed aftershock decay rates. Controls on the decay rates (p-value) will also be discussed.

Dissociative Identity Disorder

ERIC Educational Resources Information Center

Schmidt, Tom

2007-01-01

Few psychological disorders in the Diagnostic Statistical Manual have generated as much controversy as Dissociative Identity Disorder (DID). For the past 35 years diagnoses of DID, previously referred to as Multiple Personality Disorder (MPD), have increased exponentially, causing various psychological researchers and clinicians to question the…

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

NASA Astrophysics Data System (ADS)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Exponential H(infinity) synchronization of general discrete-time chaotic neural networks with or without time delays.

PubMed

Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin

2010-08-01

This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Olsen, Lars Folke; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi

2003-02-01

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits.

PubMed

Lu, Chao-Yang; Browne, Daniel E; Yang, Tao; Pan, Jian-Wei

2007-12-21

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period r=2 and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents an essential step toward full realization of Shor's algorithm and scalable linear optics quantum computation.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Diffusion-weighted MR imaging of pancreatic cancer: A comparison of mono-exponential, bi-exponential and non-Gaussian kurtosis models.

PubMed

Kartalis, Nikolaos; Manikis, Georgios C; Loizou, Louiza; Albiin, Nils; Zöllner, Frank G; Del Chiaro, Marco; Marias, Kostas; Papanikolaou, Nikolaos

2016-01-01

To compare two Gaussian diffusion-weighted MRI (DWI) models including mono-exponential and bi-exponential, with the non-Gaussian kurtosis model in patients with pancreatic ductal adenocarcinoma. After written informed consent, 15 consecutive patients with pancreatic ductal adenocarcinoma underwent free-breathing DWI (1.5T, b-values: 0, 50, 150, 200, 300, 600 and 1000 s/mm 2 ). Mean values of DWI-derived metrics ADC, D, D*, f, K and D K were calculated from multiple regions of interest in all tumours and non-tumorous parenchyma and compared. Area under the curve was determined for all metrics. Mean ADC and D K showed significant differences between tumours and non-tumorous parenchyma (both P  < 0.001). Area under the curve for ADC, D, D*, f, K, and D K were 0.77, 0.52, 0.53, 0.62, 0.42, and 0.84, respectively. ADC and D K could differentiate tumours from non-tumorous parenchyma with the latter showing a higher diagnostic accuracy. Correction for kurtosis effects has the potential to increase the diagnostic accuracy of DWI in patients with pancreatic ductal adenocarcinoma.

An efficient and accurate technique to compute the absorption, emission, and transmission of radiation by the Martian atmosphere

NASA Technical Reports Server (NTRS)

Lindner, Bernhard Lee; Ackerman, Thomas P.; Pollack, James B.

1990-01-01

CO2 comprises 95 pct. of the composition of the Martian atmosphere. However, the Martian atmosphere also has a high aerosol content. Dust particles vary from less than 0.2 to greater than 3.0. CO2 is an active absorber and emitter in near IR and IR wavelengths; the near IR absorption bands of CO2 provide significant heating of the atmosphere, and the 15 micron band provides rapid cooling. Including both CO2 and aerosol radiative transfer simultaneously in a model is difficult. Aerosol radiative transfer requires a multiple scattering code, while CO2 radiative transfer must deal with complex wavelength structure. As an alternative to the pure atmosphere treatment in most models which causes inaccuracies, a treatment was developed called the exponential sum or k distribution approximation. The chief advantage of the exponential sum approach is that the integration over k space of f(k) can be computed more quickly than the integration of k sub upsilon over frequency. The exponential sum approach is superior to the photon path distribution and emissivity techniques for dusty conditions. This study was the first application of the exponential sum approach to Martian conditions.

The Arrhenius equation revisited.

PubMed

Peleg, Micha; Normand, Mark D; Corradini, Maria G

2012-01-01

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.

Exponentiation: A New Basic?

ERIC Educational Resources Information Center

Davis, Brent

2015-01-01

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Quantum Neural Nets

NASA Technical Reports Server (NTRS)

Zak, Michail; Williams, Colin P.

1997-01-01

The capacity of classical neurocomputers is limited by the number of classical degrees of freedom which is roughly proportional to the size of the computer. By Contrast, a Hypothetical quantum neurocomputer can implement an exponentially large number of the degrees of freedom within the same size. In this paper an attempt is made to reconcile linear reversible structure of quantum evolution with nonlinear irreversible dynamics for neural nets.

The Exponential Growth of Mathematics and Technology at the University of Portsmouth

ERIC Educational Resources Information Center

McCabe, Michael

2009-01-01

The number of students studying university mathematics in the UK has been increasing gradually and linearly since 2002. At the University of Portsmouth, number of students studying mathematics doubled from 30 to 60 between 2002 and 2007, then increased by 240% in just 1 year to over 140 in 2008. This article explains how learning technology has…

Modelling the Dynamics of Bodies Self-Propelled by Exponential Mass Exhaustion

ERIC Educational Resources Information Center

Rodrigues, Hilario; Pinho, Marcos Oliveira; Portes, Dirceu, Jr.; Santiago, Arnaldo Jose

2008-01-01

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing…

Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

Properties of one-dimensional anharmonic lattice solitons

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

2000-12-01

The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

Fresh and Dry Mass Estimates of Hermetia illucens (Linnaeus, 1758) (Diptera: Stratiomyidae) Larvae Associated with Swine Decomposition in Urban Area of Central Amazonia.

PubMed

Barros, L M; Martins, R T; Ferreira-Keppler, R L; Gutjahr, A L N

2017-08-04

Information on biomass is substantial for calculating growth rates and may be employed in the medicolegal and economic importance of Hermetia illucens (Linnaeus, 1758). Although biomass is essential to understanding many ecological processes, it is not easily measured. Biomass may be determined by directly weighing or indirectly through regression models of fresh/dry mass versus body dimensions. In this study, we evaluated the association between morphometry and fresh/dry mass of immature H. illucens using linear, exponential, and power regression models. We measured width and length of the cephalic capsule, overall body length, and width of the largest abdominal segment of 280 larvae. Overall body length and width of the largest abdominal segment were the best predictors for biomass. Exponential models best fitted body dimensions and biomass (both fresh and dry), followed by power and linear models. In all models, fresh and dry biomass were strongly correlated (>75%). Values estimated by the models did not differ from observed ones, and prediction power varied from 27 to 79%. Accordingly, the correspondence between biomass and body dimensions should facilitate and motivate the development of applied studies involving H. illucens in the Amazon region.

A new look at atmospheric carbon dioxide

NASA Astrophysics Data System (ADS)

Hofmann, David J.; Butler, James H.; Tans, Pieter P.

Carbon dioxide is increasing in the atmosphere and is of considerable concern in global climate change because of its greenhouse gas warming potential. The rate of increase has accelerated since measurements began at Mauna Loa Observatory in 1958 where carbon dioxide increased from less than 1 part per million per year (ppm yr -1) prior to 1970 to more than 2 ppm yr -1 in recent years. Here we show that the anthropogenic component (atmospheric value reduced by the pre-industrial value of 280 ppm) of atmospheric carbon dioxide has been increasing exponentially with a doubling time of about 30 years since the beginning of the industrial revolution (˜1800). Even during the 1970s, when fossil fuel emissions dropped sharply in response to the "oil crisis" of 1973, the anthropogenic atmospheric carbon dioxide level continued increasing exponentially at Mauna Loa Observatory. Since the growth rate (time derivative) of an exponential has the same characteristic lifetime as the function itself, the carbon dioxide growth rate is also doubling at the same rate. This explains the observation that the linear growth rate of carbon dioxide has more than doubled in the past 40 years. The accelerating growth rate is simply the outcome of exponential growth in carbon dioxide with a nearly constant doubling time of about 30 years (about 2%/yr) and appears to have tracked human population since the pre-industrial era.

Life prediction for high temperature low cycle fatigue of two kinds of titanium alloys based on exponential function

NASA Astrophysics Data System (ADS)

Mu, G. Y.; Mi, X. Z.; Wang, F.

2018-01-01

The high temperature low cycle fatigue tests of TC4 titanium alloy and TC11 titanium alloy are carried out under strain controlled. The relationships between cyclic stress-life and strain-life are analyzed. The high temperature low cycle fatigue life prediction model of two kinds of titanium alloys is established by using Manson-Coffin method. The relationship between failure inverse number and plastic strain range presents nonlinear in the double logarithmic coordinates. Manson-Coffin method assumes that they have linear relation. Therefore, there is bound to be a certain prediction error by using the Manson-Coffin method. In order to solve this problem, a new method based on exponential function is proposed. The results show that the fatigue life of the two kinds of titanium alloys can be predicted accurately and effectively by using these two methods. Prediction accuracy is within ±1.83 times scatter zone. The life prediction capability of new methods based on exponential function proves more effective and accurate than Manson-Coffin method for two kinds of titanium alloys. The new method based on exponential function can give better fatigue life prediction results with the smaller standard deviation and scatter zone than Manson-Coffin method. The life prediction results of two methods for TC4 titanium alloy prove better than TC11 titanium alloy.

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.

Application of artificial neural networks to identify equilibration in computer simulations

NASA Astrophysics Data System (ADS)

Leibowitz, Mitchell H.; Miller, Evan D.; Henry, Michael M.; Jankowski, Eric

2017-11-01

Determining which microstates generated by a thermodynamic simulation are representative of the ensemble for which sampling is desired is a ubiquitous, underspecified problem. Artificial neural networks are one type of machine learning algorithm that can provide a reproducible way to apply pattern recognition heuristics to underspecified problems. Here we use the open-source TensorFlow machine learning library and apply it to the problem of identifying which hypothetical observation sequences from a computer simulation are “equilibrated” and which are not. We generate training populations and test populations of observation sequences with embedded linear and exponential correlations. We train a two-neuron artificial network to distinguish the correlated and uncorrelated sequences. We find that this simple network is good enough for > 98% accuracy in identifying exponentially-decaying energy trajectories from molecular simulations.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2012-09-01

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Optimal estimation for the satellite attitude using star tracker measurements

NASA Technical Reports Server (NTRS)

Lo, J. T.-H.

1986-01-01

An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.

A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

NASA Astrophysics Data System (ADS)

Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

2018-04-01

In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

Assembly of multiple cell gradients directed by three-dimensional microfluidic channels.

PubMed

Li, Yiwei; Feng, Xiaojun; Wang, Yachao; Du, Wei; Chen, Peng; Liu, Chao; Liu, Bi-Feng

2015-08-07

Active control over the cell gradient is essential for understanding biological systems and the reconstitution of the functionality of many types of tissues, particularly for organ-on-a-chip. Here, we propose a three-dimensional (3D) microfluidic strategy for generating controllable cell gradients. In this approach, a homogeneous cell suspension is loaded into a 3D stair-shaped PDMS microchannel to generate a cell gradient within 10 min by sedimentation. We demonstrate that cell gradients of various profiles (exponential and piecewise linear) can be achieved by precisely controlling the height of each layer during the fabrication. With sequential seeding, we further demonstrate the generation of two overlapping cell gradients on the same glass substrate with pre-defined designs. The cell gradient-based QD cytotoxicity assay also demonstrated that cell behaviors and resistances were regulated by the changes in cell density. These results reveal that the proposed 3D microfluidic strategy provides a simple and versatile means for establishing controllable gradients in cell density, opening up a new avenue for reconstructing functional tissues.

Coherent instability in wall-bounded turbulence

NASA Astrophysics Data System (ADS)

Hack, M. J. Philipp

2017-11-01

Hairpin vortices are commonly considered one of the major classes of coherent fluid motions in shear layers, even as their significance in the grand scheme of turbulence has remained an openly debated question. The statistical prevalence of the dynamic process that gives rise to the hairpins across different types of flows suggests an origin in a robust common mechanism triggered by conditions widespread in wall-bounded shear layers. This study seeks to shed light on the physical process which drives the generation of hairpin vortices. It is primarily facilitated through an algorithm based on concepts developed in the field of computer vision which allows the topological identification and analysis of coherent flow processes across multiple scales. Application to direct numerical simulations of boundary layers enables the time-resolved sampling and exploration of the hairpin process in natural flow. The analysis yields rich statistical results which lead to a refined characterization of the hairpin process. Linear stability theory offers further insight into the flow physics and especially into the connection between the hairpin and exponential amplification mechanisms. The results also provide a sharpened understanding of the underlying causality of events.

Multi-objective reverse logistics model for integrated computer waste management.

PubMed

Ahluwalia, Poonam Khanijo; Nema, Arvind K

2006-12-01

This study aimed to address the issues involved in the planning and design of a computer waste management system in an integrated manner. A decision-support tool is presented for selecting an optimum configuration of computer waste management facilities (segregation, storage, treatment/processing, reuse/recycle and disposal) and allocation of waste to these facilities. The model is based on an integer linear programming method with the objectives of minimizing environmental risk as well as cost. The issue of uncertainty in the estimated waste quantities from multiple sources is addressed using the Monte Carlo simulation technique. An illustrated example of computer waste management in Delhi, India is presented to demonstrate the usefulness of the proposed model and to study tradeoffs between cost and risk. The results of the example problem show that it is possible to reduce the environmental risk significantly by a marginal increase in the available cost. The proposed model can serve as a powerful tool to address the environmental problems associated with exponentially growing quantities of computer waste which are presently being managed using rudimentary methods of reuse, recovery and disposal by various small-scale vendors.

Improvement of the Mair scoring system using structural equations modeling for classifying the diagnostic adequacy of cytology material from thyroid lesions.

PubMed

Kulkarni, H R; Kamal, M M; Arjune, D G

1999-12-01

The scoring system developed by Mair et al. (Acta Cytol 1989;33:809-813) is frequently used to grade the quality of cytology smears. Using a one-factor analytic structural equations model, we demonstrate that the errors in measurement of the parameters used in the Mair scoring system are highly and significantly correlated. We recommend the use of either a multiplicative scoring system, using linear scores, or an additive scoring system, using exponential scores, to correct for the correlated errors. We suggest that the 0, 1, and 2 points used in the Mair scoring system be replaced by 1, 2, and 4, respectively. Using data on fine-needle biopsies of 200 thyroid lesions by both fine-needle aspiration (FNA) and fine-needle capillary sampling (FNC), we demonstrate that our modification of the Mair scoring system is more sensitive and more consistent with the structural equations model. Therefore, we recommend that the modified Mair scoring system be used for classifying the diagnostic adequacy of cytology smears. Diagn. Cytopathol. 1999;21:387-393. Copyright 1999 Wiley-Liss, Inc.

Kinetics of the pyrolysis of arundo, sawdust, corn stover and switch grass biomass by thermogravimetric analysis using a multi-stage model.

PubMed

Biney, Paul O; Gyamerah, Michael; Shen, Jiacheng; Menezes, Bruna

2015-03-01

A new multi-stage kinetic model has been developed for TGA pyrolysis of arundo, corn stover, sawdust and switch grass that accounts for the initial biomass weight (W0). The biomass were decomposed in a nitrogen atmosphere from 23°C to 900°C in a TGA at a single 20°C/min ramp rate in contrast with the isoconversion technique. The decomposition was divided into multiple stages based on the absolute local minimum values of conversion derivative, (dx/dT), obtained from DTG curves. This resulted in three decomposition stages for arundo, corn stover and sawdust and four stages for switch grass. A linearized multi-stage model was applied to the TGA data for each stage to determine the pre-exponential factor, activation energy, and reaction order. The activation energies ranged from 54.7 to 60.9 kJ/mol, 62.9 to 108.7 kJ/mol, and 18.4 to 257.9 kJ/mol for the first, second and the third decomposition stages respectively. Copyright © 2014 Elsevier Ltd. All rights reserved.

The potential of non-invasive pre- and post-mortem carcass measurements to predict the contribution of carcass components to slaughter yield of guinea pigs.

PubMed

Barba, Lida; Sánchez-Macías, Davinia; Barba, Iván; Rodríguez, Nibaldo

2018-06-01

Guinea pig meat consumption is increasing exponentially worldwide. The evaluation of the contribution of carcass components to carcass quality potentially can allow for the estimation of the value added to food animal origin and make research in guinea pigs more practicable. The aim of this study was to propose a methodology for modelling the contribution of different carcass components to the overall carcass quality of guinea pigs by using non-invasive pre- and post mortem carcass measurements. The selection of predictors was developed through correlation analysis and statistical significance; whereas the prediction models were based on Multiple Linear Regression. The prediction results showed higher accuracy in the prediction of carcass component contribution expressed in grams, compared to when expressed as a percentage of carcass quality components. The proposed prediction models can be useful for the guinea pig meat industry and research institutions by using non-invasive and time- and cost-efficient carcass component measuring techniques. Copyright © 2018 Elsevier Ltd. All rights reserved.

The rational parameterization theorem for multisite post-translational modification systems.

PubMed

Thomson, Matthew; Gunawardena, Jeremy

2009-12-21

Post-translational modification of proteins plays a central role in cellular regulation but its study has been hampered by the exponential increase in substrate modification forms ("modforms") with increasing numbers of sites. We consider here biochemical networks arising from post-translational modification under mass-action kinetics, allowing for multiple substrates, having different types of modification (phosphorylation, methylation, acetylation, etc.) on multiple sites, acted upon by multiple forward and reverse enzymes (in total number L), using general enzymatic mechanisms. These assumptions are substantially more general than in previous studies. We show that the steady-state modform concentrations constitute an algebraic variety that can be parameterized by rational functions of the L free enzyme concentrations, with coefficients which are rational functions of the rate constants. The parameterization allows steady states to be calculated by solving L algebraic equations, a dramatic reduction compared to simulating an exponentially large number of differential equations. This complexity collapse enables analysis in contexts that were previously intractable and leads to biological predictions that we review. Our results lay a foundation for the systems biology of post-translational modification and suggest deeper connections between biochemical networks and algebraic geometry.

Experimental research of iterated dynamics for the complex exponentials with linear term

NASA Astrophysics Data System (ADS)

Matyushkin, Igor V.; Zapletina, Maria A.

2018-03-01

The research of the orbit of the point zero, fixed points, Julia and Fatou sets for the iterated complex-valued exponential is carried by means of computer experiment. The object of study is three one-parameter families based on exp (iz): f : z → (1 + μ) exp (iz), g : z → (1 + μ|z ‑ z*|) exp (iz), h : z → (1 + μ (z ‑ z*)) exp (iz). Here. For the first family 17- and 2-periodic regimes are detected when passing near the bifurcation value μ ≈ 2.475i, while the multiplicator equals 1. The second family shows a more interesting behavior: (i) three-valley structure of isolines of the convergence rate near fixpoint z* at μ = 0 + 1 + i; (ii) saddle-node transition when the parameter moves along a straight line Reμ = 0, leading to the appearance of a second fixpoint and loss of stability by the old fixpoint at Imμ = 2.1682; (iii) the nontrivial nature of the orbits of points in the vicinity of the new fixpoint and the presence of false fixpoints in the portrait of the Julia set; (iv) second phase transition leading to a radical change in the form of the Julia and Fatou sets at μ ≃ 2.5i. The dynamics of the third family during movement at Reμ = 0 is similar to the first case, but 17th and 2nd periodic modes are replaced by 39th and 3rd modes. Transitions 17 → 2 and 39 → 3 seem to be rapid and discreet while their geometric interpretation matches the ratios 17=1+2*8, 39=13*3. At μ = |z*|‑1 for the h- family Julia set fills the entire complex plane.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

PubMed Central

Chylek, Lily A.; Harris, Leonard A.; Tung, Chang-Shung; Faeder, James R.; Lopez, Carlos F.

2013-01-01

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and post-translational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation). PMID:24123887

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.

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

PubMed Central

Fernandez, Fernando R.; Malerba, Paola; White, John A.

2015-01-01

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na+ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances. PMID:25909971

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations.

PubMed

Fernandez, Fernando R; Malerba, Paola; White, John A

2015-04-01

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na+ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Exploring the Biotic Pump Hypothesis along Non-linear Transects in Tropical South America

NASA Astrophysics Data System (ADS)

Molina, R.; Bettin, D. M.; Salazar, J. F.; Villegas, J. C.

2014-12-01

Forests might actively transport atmospheric moisture from the oceans, according to the biotic pump of atmospheric moisture (BiPAM) hypothesis. The BiPAM hypothesis appears to be supported by the fact that precipitation drops exponentially with distance from ocean along non-forested land transects, but not on their forested counterparts. Yet researchers have discussed the difficulty in defining proper transects for BiPAM studies. Previous studies calculate precipitation gradients either along linear transects maximizing distance to the ocean, or along polylines following specific atmospheric pathways (e.g., aerial rivers). In this study we analyzed precipitation gradients along curvilinear streamlines of wind in tropical South America. Wind streamlines were computed using long-term quarterly averages of meridional and zonal wind components from the ERA-Interim and NCEP/NCAR reanalyses. Total precipitation along streamlines was obtained from four data sources: TRMM, UDEL, ERA-Interim, and NCEP/NCAR. Precipitation on land versus distance from the ocean was analyzed along selected streamlines for each data source. As predicted by BiPAM, precipitation gradients did not decrease exponentially along streamlines in the vicinity of the Amazon forest, but dropped rapidly as distance from the forest increased. Remarkably, precipitation along streamlines in some areas outside the Amazon forest did not decrease exponentially either. This was possibly owing to convergence of moisture conveyed by low level jets (LLJs) in those areas (e.g., streamlines driven by the Caribbean and CHOCO jets on the Pacific coast of Colombia). Significantly, BiPAM held true even along long transects displaying strong sinuosity. In fact, the general conclusions of previous studies remain valid. Yet effects of LLJs on precipitation gradients need to be thoroughly considered in future BiPAM studies.

Determining the turnover time of groundwater systems with the aid of environmental tracers. 1. Models and their applicability

NASA Astrophysics Data System (ADS)

Małoszewski, P.; Zuber, A.

1982-06-01

Three new lumped-parameter models have been developed for the interpretation of environmental radioisotope data in groundwater systems. Two of these models combine other simpler models, i.e. the piston flow model is combined either with the exponential model (exponential distribution of transit times) or with the linear model (linear distribution of transit times). The third model is based on a new solution to the dispersion equation which more adequately represents the real systems than the conventional solution generally applied so far. The applicability of models was tested by the reinterpretation of several known case studies (Modry Dul, Cheju Island, Rasche Spring and Grafendorf). It has been shown that two of these models, i.e. the exponential-piston flow model and the dispersive model give better fitting than other simpler models. Thus, the obtained values of turnover times are more reliable, whereas the additional fitting parameter gives some information about the structure of the system. In the examples considered, in spite of a lower number of fitting parameters, the new models gave practically the same fitting as the multiparameter finite state mixing-cell models. It has been shown that in the case of a constant tracer input a prior physical knowledge of the groundwater system is indispensable for determining the turnover time. The piston flow model commonly used for age determinations by the 14C method is an approximation applicable only in the cases of low dispersion. In some cases the stable-isotope method aids in the interpretation of systems containing mixed waters of different ages. However, when 14C method is used for mixed-water systems a serious mistake may arise by neglecting the different bicarbonate contents in particular water components.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

NASA Astrophysics Data System (ADS)

Brown, J. S.; Shaheen, S. E.

2018-04-01

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics.

PubMed

Brown, J S; Shaheen, S E

2018-04-04

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique.

PubMed

Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan

2009-01-01

The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.

Universal patterns of inequality

NASA Astrophysics Data System (ADS)

Banerjee, Anand; Yakovenko, Victor M.

2010-07-01

Probability distributions of money, income and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures between different systems generates net fluxes of money and population. To describe income distribution, a stochastic process with additive and multiplicative components is introduced. The resultant distribution interpolates between exponential at the low end and power law at the high end, in agreement with the empirical data for the USA. We show that the increase in income inequality in the USA originates primarily from the increase in the income fraction going to the upper tail, which now exceeds 20% of the total income. Analyzing the data from the World Resources Institute, we find that the distribution of energy consumption per capita around the world can be approximately described by the exponential function. Comparing the data for 1990, 2000 and 2005, we discuss the effect of globalization on the inequality of energy consumption.

Properties of branching exponential flights in bounded domains

NASA Astrophysics Data System (ADS)

Zoia, A.; Dumonteil, E.; Mazzolo, A.

2012-11-01

In a series of recent works, important results have been reported concerning the statistical properties of exponential flights evolving in bounded domains, a widely adopted model for finite-speed transport phenomena (Blanco S. and Fournier R., Europhys. Lett., 61 (2003) 168; Mazzolo A., Europhys. Lett., 68 (2004) 350; Bénichou O. et al., Europhys. Lett., 70 (2005) 42). Motivated by physical and biological systems where random spatial displacements are coupled with Galton-Watson birth-death mechanisms, such as neutron multiplication, diffusion of reproducing bacteria or spread of epidemics, in this letter we extend those results in two directions, via a Feynman-Kac formalism. First, we characterize the occupation statistics of exponential flights in the presence of absorption and branching, and give explicit moment formulas for the total length travelled by the walker and the number of performed collisions in a given domain. Then, we show that the survival and escape probability can be derived as well by resorting to a similar approach.

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

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of thismore » object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.« less

Linear Time Algorithms to Restrict Insider Access using Multi-Policy Access Control Systems

PubMed Central

Mell, Peter; Shook, James; Harang, Richard; Gavrila, Serban

2017-01-01

An important way to limit malicious insiders from distributing sensitive information is to as tightly as possible limit their access to information. This has always been the goal of access control mechanisms, but individual approaches have been shown to be inadequate. Ensemble approaches of multiple methods instantiated simultaneously have been shown to more tightly restrict access, but approaches to do so have had limited scalability (resulting in exponential calculations in some cases). In this work, we take the Next Generation Access Control (NGAC) approach standardized by the American National Standards Institute (ANSI) and demonstrate its scalability. The existing publicly available reference implementations all use cubic algorithms and thus NGAC was widely viewed as not scalable. The primary NGAC reference implementation took, for example, several minutes to simply display the set of files accessible to a user on a moderately sized system. In our approach, we take these cubic algorithms and make them linear. We do this by reformulating the set theoretic approach of the NGAC standard into a graph theoretic approach and then apply standard graph algorithms. We thus can answer important access control decision questions (e.g., which files are available to a user and which users can access a file) using linear time graph algorithms. We also provide a default linear time mechanism to visualize and review user access rights for an ensemble of access control mechanisms. Our visualization appears to be a simple file directory hierarchy but in reality is an automatically generated structure abstracted from the underlying access control graph that works with any set of simultaneously instantiated access control policies. It also provide an implicit mechanism for symbolic linking that provides a powerful access capability. Our work thus provides the first efficient implementation of NGAC while enabling user privilege review through a novel visualization approach. This may help transition from concept to reality the idea of using ensembles of simultaneously instantiated access control methodologies, thereby limiting insider threat. PMID:28758045

Determinism in synthesized chaotic waveforms.

PubMed

Corron, Ned J; Blakely, Jonathan N; Hayes, Scott T; Pethel, Shawn D

2008-03-01

The output of a linear filter driven by a randomly polarized square wave, when viewed backward in time, is shown to exhibit determinism at all times when embedded in a three-dimensional state space. Combined with previous results establishing exponential divergence equivalent to a positive Lyapunov exponent, this result rigorously shows that such reverse-time synthesized waveforms appear equally to have been produced by a deterministic chaotic system.

A scaling theory for linear systems

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Krishnaprasad, P. S.

1980-01-01

A theory of scaling for rational (transfer) functions in terms of transformation groups is developed. Two different four-parameter scaling groups which play natural roles in studying linear systems are identified and the effect of scaling on Fisher information and related statistical measures in system identification are studied. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied is tied to the geometry of transfer functions in a rather strong way as becomes apparent in the examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.

Multiple types of synchronization analysis for discontinuous Cohen-Grossberg neural networks with time-varying delays.

PubMed

Li, Jiarong; Jiang, Haijun; Hu, Cheng; Yu, Zhiyong

2018-03-01

This paper is devoted to the exponential synchronization, finite time synchronization, and fixed-time synchronization of Cohen-Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Discontinuous feedback controller and Novel adaptive feedback controller are designed to realize global exponential synchronization, finite time synchronization and fixed-time synchronization by adjusting the values of the parameters ω in the controller. Furthermore, the settling time of the fixed-time synchronization derived in this paper is less conservative and more accurate. Finally, some numerical examples are provided to show the effectiveness and flexibility of the results derived in this paper. Copyright © 2018 Elsevier Ltd. All rights reserved.

Mathematical modeling of drying of pretreated and untreated pumpkin.

PubMed

Tunde-Akintunde, T Y; Ogunlakin, G O

2013-08-01

In this study, drying characteristics of pretreated and untreated pumpkin were examined in a hot-air dryer at air temperatures within a range of 40-80 °C and a constant air velocity of 1.5 m/s. The drying was observed to be in the falling-rate drying period and thus liquid diffusion is the main mechanism of moisture movement from the internal regions to the product surface. The experimental drying data for the pumpkin fruits were used to fit Exponential, General exponential, Logarithmic, Page, Midilli-Kucuk and Parabolic model and the statistical validity of models tested were determined by non-linear regression analysis. The Parabolic model had the highest R(2) and lowest χ(2) and RMSE values. This indicates that the Parabolic model is appropriate to describe the dehydration behavior for the pumpkin.

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

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

Apalara, Tijani A., E-mail: tijani@kfupm.edu.sa; Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in themore » presence of a small delay is an open question.« less

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Gradient-based stochastic estimation of the density matrix

NASA Astrophysics Data System (ADS)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

NASA Astrophysics Data System (ADS)

Zhang, Ruimei; Zeng, Deqiang; Zhong, Shouming; Shi, Kaibo

2017-09-01

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

n-Iterative Exponential Forgetting Factor for EEG Signals Parameter Estimation

PubMed Central

Palma Orozco, Rosaura

2018-01-01

Electroencephalograms (EEG) signals are of interest because of their relationship with physiological activities, allowing a description of motion, speaking, or thinking. Important research has been developed to take advantage of EEG using classification or predictor algorithms based on parameters that help to describe the signal behavior. Thus, great importance should be taken to feature extraction which is complicated for the Parameter Estimation (PE)–System Identification (SI) process. When based on an average approximation, nonstationary characteristics are presented. For PE the comparison of three forms of iterative-recursive uses of the Exponential Forgetting Factor (EFF) combined with a linear function to identify a synthetic stochastic signal is presented. The one with best results seen through the functional error is applied to approximate an EEG signal for a simple classification example, showing the effectiveness of our proposal. PMID:29568310

AITRAC: Augmented Interactive Transient Radiation Analysis by Computer. User's information manual

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

Not Available

1977-10-01

AITRAC is a program designed for on-line, interactive, DC, and transient analysis of electronic circuits. The program solves linear and nonlinear simultaneous equations which characterize the mathematical models used to predict circuit response. The program features 100 external node--200 branch capability; conversional, free-format input language; built-in junction, FET, MOS, and switch models; sparse matrix algorithm with extended-precision H matrix and T vector calculations, for fast and accurate execution; linear transconductances: beta, GM, MU, ZM; accurate and fast radiation effects analysis; special interface for user-defined equations; selective control of multiple outputs; graphical outputs in wide and narrow formats; and on-line parametermore » modification capability. The user describes the problem by entering the circuit topology and part parameters. The program then automatically generates and solves the circuit equations, providing the user with printed or plotted output. The circuit topology and/or part values may then be changed by the user, and a new analysis, requested. Circuit descriptions may be saved on disk files for storage and later use. The program contains built-in standard models for resistors, voltage and current sources, capacitors, inductors including mutual couplings, switches, junction diodes and transistors, FETS, and MOS devices. Nonstandard models may be constructed from standard models or by using the special equations interface. Time functions may be described by straight-line segments or by sine, damped sine, and exponential functions. 42 figures, 1 table. (RWR)« less

Recurrence formulas for fully exponentially correlated four-body wave functions

NASA Astrophysics Data System (ADS)

Harris, Frank E.

2009-03-01

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (≥-1) of all the interparticle distances rij , multiplied by an exponential containing an arbitrary linear combination of all the rij . These integrals are generalizations of those encountered using Hylleraas basis functions and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill plus some easily evaluated three-body “boundary” integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.

Proportional Feedback Control of Energy Intake During Obesity Pharmacotherapy.

PubMed

Hall, Kevin D; Sanghvi, Arjun; Göbel, Britta

2017-12-01

Obesity pharmacotherapies result in an exponential time course for energy intake whereby large early decreases dissipate over time. This pattern of declining drug efficacy to decrease energy intake results in a weight loss plateau within approximately 1 year. This study aimed to elucidate the physiology underlying the exponential decay of drug effects on energy intake. Placebo-subtracted energy intake time courses were examined during long-term obesity pharmacotherapy trials for 14 different drugs or drug combinations within the theoretical framework of a proportional feedback control system regulating human body weight. Assuming each obesity drug had a relatively constant effect on average energy intake and did not affect other model parameters, our model correctly predicted that long-term placebo-subtracted energy intake was linearly related to early reductions in energy intake according to a prespecified equation with no free parameters. The simple model explained about 70% of the variance between drug studies with respect to the long-term effects on energy intake, although a significant proportional bias was evident. The exponential decay over time of obesity pharmacotherapies to suppress energy intake can be interpreted as a relatively constant effect of each drug superimposed on a physiological feedback control system regulating body weight. © 2017 The Obesity Society.

Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

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

Peng, Bo; Kowalski, Karol

In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CCmore » self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.« less

Enhanced Response Time of Electrowetting Lenses with Shaped Input Voltage Functions.

PubMed

Supekar, Omkar D; Zohrabi, Mo; Gopinath, Juliet T; Bright, Victor M

2017-05-16

Adaptive optical lenses based on the electrowetting principle are being rapidly implemented in many applications, such as microscopy, remote sensing, displays, and optical communication. To characterize the response of these electrowetting lenses, the dependence upon direct current (DC) driving voltage functions was investigated in a low-viscosity liquid system. Cylindrical lenses with inner diameters of 2.45 and 3.95 mm were used to characterize the dynamic behavior of the liquids under DC voltage electrowetting actuation. With the increase of the rise time of the input exponential driving voltage, the originally underdamped system response can be damped, enabling a smooth response from the lens. We experimentally determined the optimal rise times for the fastest response from the lenses. We have also performed numerical simulations of the lens actuation with input exponential driving voltage to understand the variation in the dynamics of the liquid-liquid interface with various input rise times. We further enhanced the response time of the devices by shaping the input voltage function with multiple exponential rise times. For the 3.95 mm inner diameter lens, we achieved a response time improvement of 29% when compared to the fastest response obtained using single-exponential driving voltage. The technique shows great promise for applications that require fast response times.

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

Correlation of conformational heterogeneity of the tryptophyl side chain and time-resolved fluorescence intensity decay kinetics

NASA Astrophysics Data System (ADS)

Laws, William R.; Ross, J. B. Alexander

1992-04-01

The time-resolved fluorescence properties of a tryptophan residue should be useful for probing protein structure, function, and dynamics. To date, however, the non-single exponential fluorescence intensity decay kinetics for numerous peptides and proteins having a single tryptophan residue have not been adequately explained. Many possibilities have been considered and include: (1) contributions from the 1La and 1Lb states of indole; (2) excited-state hydrogen exchange; and (3) environmental heterogeneity from (chi) 1 and (chi) 2 rotamers. In addition, it has been suggested that generally many factors contribute to the decay and a distribution of probabilities may be more appropriate. Two recent results support multiple species due to conformational heterogeneity as the major contributor to complex kinetics. First, a rotationally constrained tryptophan analogue has fluorescence intensity decay kinetics that can be described by the sum of two exponentials with amplitudes comparable to the relative populations of the two rotational isomers. Second, the multiple exponentials observed for tyrosine-containing model compounds and peptides correlate with the (chi) 1 rotamer populations independently determined by 1H NMR. We now report similar correlations between rotamer populations and fluorescence intensity decay kinetics for a tryptophan analogue of oxytocin. It appears for this compound that either (chi) 2 rotations do not appreciably alter the indole environment, (chi) 2 rotations are rapid enough to average the observed dependence, or only one of two possible (chi) 2 populations is associated with each (chi) 1 rotamer.

Analysis of Multiple Cracks in an Infinite Functionally Graded Plate

NASA Technical Reports Server (NTRS)

Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.

1999-01-01

A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.

Continuous Acoustic Sensing With an Unmanned Aerial Vehicle System for Anti-Submarine Warfare in a High-Threat Area

DTIC Science & Technology

2015-12-01

strive in multiple warfare areas. This research benefits not only the Navy, through enhancement of offensive warfighting by testing the next...multiple warfare areas. This research benefits not only the Navy, through enhancement of offensive warfighting by testing the next generation of...produce and definitely worth the research and testing to be a positive asset for the Navy. It not only can stay on station for an exponential amount of

A secure distributed logistic regression protocol for the detection of rare adverse drug events

PubMed Central

El Emam, Khaled; Samet, Saeed; Arbuckle, Luk; Tamblyn, Robyn; Earle, Craig; Kantarcioglu, Murat

2013-01-01

Background There is limited capacity to assess the comparative risks of medications after they enter the market. For rare adverse events, the pooling of data from multiple sources is necessary to have the power and sufficient population heterogeneity to detect differences in safety and effectiveness in genetic, ethnic and clinically defined subpopulations. However, combining datasets from different data custodians or jurisdictions to perform an analysis on the pooled data creates significant privacy concerns that would need to be addressed. Existing protocols for addressing these concerns can result in reduced analysis accuracy and can allow sensitive information to leak. Objective To develop a secure distributed multi-party computation protocol for logistic regression that provides strong privacy guarantees. Methods We developed a secure distributed logistic regression protocol using a single analysis center with multiple sites providing data. A theoretical security analysis demonstrates that the protocol is robust to plausible collusion attacks and does not allow the parties to gain new information from the data that are exchanged among them. The computational performance and accuracy of the protocol were evaluated on simulated datasets. Results The computational performance scales linearly as the dataset sizes increase. The addition of sites results in an exponential growth in computation time. However, for up to five sites, the time is still short and would not affect practical applications. The model parameters are the same as the results on pooled raw data analyzed in SAS, demonstrating high model accuracy. Conclusion The proposed protocol and prototype system would allow the development of logistic regression models in a secure manner without requiring the sharing of personal health information. This can alleviate one of the key barriers to the establishment of large-scale post-marketing surveillance programs. We extended the secure protocol to account for correlations among patients within sites through generalized estimating equations, and to accommodate other link functions by extending it to generalized linear models. PMID:22871397

A secure distributed logistic regression protocol for the detection of rare adverse drug events.

PubMed

El Emam, Khaled; Samet, Saeed; Arbuckle, Luk; Tamblyn, Robyn; Earle, Craig; Kantarcioglu, Murat

2013-05-01

There is limited capacity to assess the comparative risks of medications after they enter the market. For rare adverse events, the pooling of data from multiple sources is necessary to have the power and sufficient population heterogeneity to detect differences in safety and effectiveness in genetic, ethnic and clinically defined subpopulations. However, combining datasets from different data custodians or jurisdictions to perform an analysis on the pooled data creates significant privacy concerns that would need to be addressed. Existing protocols for addressing these concerns can result in reduced analysis accuracy and can allow sensitive information to leak. To develop a secure distributed multi-party computation protocol for logistic regression that provides strong privacy guarantees. We developed a secure distributed logistic regression protocol using a single analysis center with multiple sites providing data. A theoretical security analysis demonstrates that the protocol is robust to plausible collusion attacks and does not allow the parties to gain new information from the data that are exchanged among them. The computational performance and accuracy of the protocol were evaluated on simulated datasets. The computational performance scales linearly as the dataset sizes increase. The addition of sites results in an exponential growth in computation time. However, for up to five sites, the time is still short and would not affect practical applications. The model parameters are the same as the results on pooled raw data analyzed in SAS, demonstrating high model accuracy. The proposed protocol and prototype system would allow the development of logistic regression models in a secure manner without requiring the sharing of personal health information. This can alleviate one of the key barriers to the establishment of large-scale post-marketing surveillance programs. We extended the secure protocol to account for correlations among patients within sites through generalized estimating equations, and to accommodate other link functions by extending it to generalized linear models.

Split exponential track length estimator for Monte-Carlo simulations of small-animal radiation therapy

NASA Astrophysics Data System (ADS)

Smekens, F.; Létang, J. M.; Noblet, C.; Chiavassa, S.; Delpon, G.; Freud, N.; Rit, S.; Sarrut, D.

2014-12-01

We propose the split exponential track length estimator (seTLE), a new kerma-based method combining the exponential variant of the TLE and a splitting strategy to speed up Monte Carlo (MC) dose computation for low energy photon beams. The splitting strategy is applied to both the primary and the secondary emitted photons, triggered by either the MC events generator for primaries or the photon interactions generator for secondaries. Split photons are replaced by virtual particles for fast dose calculation using the exponential TLE. Virtual particles are propagated by ray-tracing in voxelized volumes and by conventional MC navigation elsewhere. Hence, the contribution of volumes such as collimators, treatment couch and holding devices can be taken into account in the dose calculation. We evaluated and analysed the seTLE method for two realistic small animal radiotherapy treatment plans. The effect of the kerma approximation, i.e. the complete deactivation of electron transport, was investigated. The efficiency of seTLE against splitting multiplicities was also studied. A benchmark with analog MC and TLE was carried out in terms of dose convergence and efficiency. The results showed that the deactivation of electrons impacts the dose at the water/bone interface in high dose regions. The maximum and mean dose differences normalized to the dose at the isocenter were, respectively of 14% and 2% . Optimal splitting multiplicities were found to be around 300. In all situations, discrepancies in integral dose were below 0.5% and 99.8% of the voxels fulfilled a 1%/0.3 mm gamma index criterion. Efficiency gains of seTLE varied from 3.2 × 105 to 7.7 × 105 compared to analog MC and from 13 to 15 compared to conventional TLE. In conclusion, seTLE provides results similar to the TLE while increasing the efficiency by a factor between 13 and 15, which makes it particularly well-suited to typical small animal radiation therapy applications.

Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Kang, Moon-Jin; Morales, Javier

2018-03-01

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

Factors Influencing Army Accessions.

DTIC Science & Technology

1982-12-01

partial autocorrelations were examined for significant lags or a recognizable pattern such as a damped exponential or a sine wave. The TSP prugrams...decreasing function indicating nonstation- *arity or a very long sine wave where only a small portion of the wave is plotted. The partial...plot of the raw data appeared (Appendix E-1) to be either the middle of a long sine wave or a linearly decreasing function. This pattern is recognized

Topics in the Sequential Design of Experiments

DTIC Science & Technology

1992-03-01

decision , unless so designated by other documentation. 12a. DISTRIBUTION /AVAILABIIUTY STATEMENT 12b. DISTRIBUTION CODE Approved for public release...3 0 1992 D 14. SUBJECT TERMS 15. NUMBER OF PAGES12 Design of Experiments, Renewal Theory , Sequential Testing 1 2. PRICE CODE Limit Theory , Local...distributions for one parameter exponential families," by Michael Woodroofe. Stntca, 2 (1991), 91-112. [6] "A non linear renewal theory for a functional of

Comparison of remote sensing algorithms for retrieval of suspended particulate matter concentration from reflectance in coastal waters

NASA Astrophysics Data System (ADS)

Freeman, Lauren A.; Ackleson, Steven G.; Rhea, William Joseph

2017-10-01

Suspended particulate matter (SPM) is a key environmental indicator for rivers, estuaries, and coastal waters, which can be calculated from remote sensing reflectance obtained by an airborne or satellite imager. Here, algorithms from prior studies are applied to a dataset of in-situ at surface hyperspectral remote sensing reflectance, collected in three geographic regions representing different water types. These data show the optically inherent exponential nature of the relationship between reflectance and sediment concentration. However, linear models are also shown to provide a reasonable estimate of sediment concentration when utilized with care in similar conditions to those under which the algorithms were developed, particularly at lower SPM values (0 to 20 mg/L). Fifteen published SPM algorithms are tested, returning strong correlations of R2>0.7, and in most cases, R2>0.8. Very low SPM values show weaker correlation with algorithm calculated SPM that is not wavelength dependent. None of the tested algorithms performs well for high SPM values (>30 mg/L), with most algorithms underestimating SPM. A shift toward a smaller number of simple exponential or linear models relating satellite remote sensing reflectance to suspended sediment concentration with regional consideration will greatly aid larger spatiotemporal studies of suspended sediment trends.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

PubMed

Rakkiyappan, R; Sakthivel, N; Cao, Jinde

2015-06-01

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

Large decline in injecting drug use in Amsterdam, 1986-1998: explanatory mechanisms and determinants of injecting transitions.

PubMed

van Ameijden, E J; Coutinho, R A

2001-05-01

To study community wide trends in injecting prevalence and trends in injecting transitions, and determinants. Open cohort study with follow up every four months (Amsterdam Cohort Study). Generalised estimating equations were used for statistical analysis. Amsterdam has adopted a harm reduction approach as drug policy. 996 drug users who were recruited from 1986 to 1998, mainly at methadone programmes, who paid 13620 cohort visits. The prevalence of injecting decreased exponentially (66% to 36% in four to six monthly periods). Selective mortality and migration could maximally explain 33% of this decline. Instead, injecting initiation linearly decreased (4.1% to 0.7% per visit), cessation exponentially increased (10.0% to 17.1%), and relapse linearly decreased (21.3% to 11.8%). Non-injecting cocaine use (mainly pre-cooked, comparable to crack) and heroin use strongly increased. Trends were not attributable to changes in the study sample. Harm reduction, including large scale needle exchange programmes, does not lead to an increase in injecting drug use. The injecting decline seems mainly attributable to ecological factors (for example, drug culture and market). Prevention of injecting is possible and peer-based interventions may be effective. The consequences of the recent upsurge in crack use requires further study.

Prediction of infarction volume and infarction growth rate in acute ischemic stroke.

PubMed

Kamran, Saadat; Akhtar, Naveed; Alboudi, Ayman; Kamran, Kainat; Ahmad, Arsalan; Inshasi, Jihad; Salam, Abdul; Shuaib, Ashfaq; Qidwai, Uvais

2017-08-08

The prediction of infarction volume after stroke onset depends on the shape of the growth dynamics of the infarction. To understand growth patterns that predict lesion volume changes, we studied currently available models described in literature and compared the models with Adaptive Neuro-Fuzzy Inference System [ANFIS], a method previously unused in the prediction of infarction growth and infarction volume (IV). We included 67 patients with malignant middle cerebral artery [MMCA] stroke who underwent decompressive hemicraniectomy. All patients had at least three cranial CT scans prior to the surgery. The rate of growth and volume of infarction measured on the third CT was predicted with ANFIS without statistically significant difference compared to the ground truth [P = 0.489]. This was not possible with linear, logarithmic or exponential methods. ANFIS was able to predict infarction volume [IV3] over a wide range of volume [163.7-600 cm 3 ] and time [22-110 hours]. The cross correlation [CRR] indicated similarity between the ANFIS-predicted IV3 and original data of 82% for ANFIS, followed by logarithmic 70%, exponential 63% and linear 48% respectively. Our study shows that ANFIS is superior to previously defined methods in the prediction of infarction growth rate (IGR) with reasonable accuracy, over wide time and volume range.

The Trend Odds Model for Ordinal Data‡

PubMed Central

Capuano, Ana W.; Dawson, Jeffrey D.

2013-01-01

Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values (Peterson and Harrell, 1990). We consider a trend odds version of this constrained model, where the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc Nlmixed, and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical dataset is used to illustrate the interpretation of the trend odds model, and we apply this model to a Swine Influenza example where the proportional odds assumption appears to be violated. PMID:23225520

The trend odds model for ordinal data.

PubMed

Capuano, Ana W; Dawson, Jeffrey D

2013-06-15

Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values. We consider a trend odds version of this constrained model, wherein the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc NLMIXED and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical data set is used to illustrate the interpretation of the trend odds model, and we apply this model to a swine influenza example wherein the proportional odds assumption appears to be violated. Copyright © 2012 John Wiley & Sons, Ltd.

Towards enhancing and delaying disturbances in free shear flows

NASA Technical Reports Server (NTRS)

Criminale, W. O.; Jackson, T. L.; Lasseigne, D. G.

1994-01-01

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Quantitative Study of the Effects of Dehydration on the Viscoelastic Parameters in the Vocal Fold Mucosa.

PubMed

Yang, Shuai; Zhang, Yu; Mills, Randal D; Jiang, Jack J

2017-05-01

The goal of this study was to quantify the viscoelastic parameters of the vocal fold mucosa at varying dehydration levels. Healthy canine larynges were obtained postmortem, and the samples were separated from the subglottal wall. The samples were dehydrated in a vacuum dryer. According to the total dehydration time per sample, dehydration levels were divided into four degrees: 0%, 40%, 60%, and 80%. The stepper was set to stretch the sample to a level of 35% strain at the same rate (0.5 mm/s). Data collection was repeated five times under each dehydration condition. The compression resilience, RC% = S'/S*100%, and the hysteresis area were measured according to the stress-strain curves. The varying properties of the samples under different dehydration levels were investigated by fitting the curves. The area of the hysteresis loops observed in the stress-strain curves increased exponentially with dehydration levels, whereas the RC% decreased linearly. For all curves, low-strain stages can be explained by Hooke's law (σ = E 0 *ε). With increasing levels of dehydration, E 0 was shown to increase, whereas the linear range was shortened. High-strain stages resembled exponential rather than the linear curves. And the nonlinear stage of the curve became increasingly apparent in the stress-strain curves of increased dehydration levels. The quantitative results in this study not only provide a numerical reference for future experimental measurements, but also can be used to verify the biphasic model in future studies. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Changes in copper sulfate crystal habit during cooling crystallization

NASA Astrophysics Data System (ADS)

Giulietti, M.; Seckler, M. M.; Derenzo, S.; Valarelli, J. V.

1996-09-01

The morphology of technical grade copper(II) sulfate pentahydrate crystals produced from batch cooling experiments in the temperature range of 70 to 30°C is described and correlated with the process conditions. A slow linear cooling rate (batch time of 90 min) predominantly caused the appearance of well-formed crystals. Exponential cooling (120 min) resulted in the additional formation of agglomerates and twins. The presence of seeds for both cooling modes led to round crystals, agglomerates and twins. Fast linear cooling (15 min) gave rise to a mixture of the former types. Broken crystals and adhering fragments were often found. Growth zoning was pronounced in seeded and linear cooling experiments. Fluid inclusions were always found and were more pronounced for larger particles. The occurrence of twinning, zoning and fluid inclusions was qualitatively explained in terms of fundamental principles.

Essays on the statistical mechanics of the labor market and implications for the distribution of earned income

NASA Astrophysics Data System (ADS)

Schneider, Markus P. A.

This dissertation contributes to two areas in economics: the understanding of the distribution of earned income and to Bayesian analysis of distributional data. Recently, physicists claimed that the distribution of earned income is exponential (see Yakovenko, 2009). The first chapter explores the perspective that the economy is a statistical mechanical system and the implication for labor market outcomes is considered critically. The robustness of the empirical results that lead to the physicists' claims, the significance of the exponential distribution in statistical mechanics, and the case for a conservation law in economics are discussed. The conclusion reached is that physicists' conception of the economy is too narrow even within their chosen framework, but that their overall approach is insightful. The dual labor market theory of segmented labor markets is invoked to understand why the observed distribution may be a mixture of distributional components, corresponding to different generating mechanisms described in Reich et al. (1973). The application of informational entropy in chapter II connects this work to Bayesian analysis and maximum entropy econometrics. The analysis follows E. T. Jaynes's treatment of Wolf's dice data, but is applied to the distribution of earned income based on CPS data. The results are calibrated to account for rounded survey responses using a simple simulation, and answer the graphical analyses by physicists. The results indicate that neither the income distribution of all respondents nor of the subpopulation used by physicists appears to be exponential. The empirics do support the claim that a mixture with exponential and log-normal distributional components ts the data. In the final chapter, a log-linear model is used to fit the exponential to the earned income distribution. Separating the CPS data by gender and marital status reveals that the exponential is only an appropriate model for a limited number of subpopulations, namely the never married and women. The estimated parameter for never-married men's incomes is significantly different from the parameter estimated for never-married women, implying that either the combined distribution is not exponential or that the individual distributions are not exponential. However, it substantiates the existence of a persistent gender income gap among the never-married. References: Reich, M., D. M. Gordon, and R. C. Edwards (1973). A Theory of Labor Market Segmentation. Quarterly Journal of Economics 63, 359-365. Yakovenko, V. M. (2009). Econophysics, Statistical Mechanics Approach to. In R. A. Meyers (Ed.), Encyclopedia of Complexity and System Science. Springer.

The inverse resonance problem for CMV operators

NASA Astrophysics Data System (ADS)

Weikard, Rudi; Zinchenko, Maxim

2010-05-01

We consider the class of CMV operators with super-exponentially decaying Verblunsky coefficients. For these we define the concept of a resonance. Then we prove the existence of Jost solutions and a uniqueness theorem for the inverse resonance problem: given the location of all resonances, taking multiplicities into account, the Verblunsky coefficients are uniquely determined.

Why Are There Developmental Stages in Language Learning? A Developmental Robotics Model of Language Development

ERIC Educational Resources Information Center

Morse, Anthony F.; Cangelosi, Angelo

2017-01-01

Most theories of learning would predict a gradual acquisition and refinement of skills as learning progresses, and while some highlight exponential growth, this fails to explain why natural cognitive development typically progresses in stages. Models that do span multiple developmental stages typically have parameters to "switch" between…

Continuous Toxicological Dose-Response Relationships Are Pretty Homogeneous (Society for Risk Analysis Annual Meeting)

EPA Science Inventory

Dose-response relationships for a wide range of in vivo and in vitro continuous datasets are well-described by a four-parameter exponential or Hill model, based on a recent analysis of multiple historical dose-response datasets, mostly with more than five dose groups (Slob and Se...

Inclusive particle production in e/sup +/e- interactions at 3. 8 and 4. 8 GeV. Technical report No. 77-040. [Cross sections, Feynman and Bjorken scaling

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

Atwood, T.L.

1976-01-01

This dissertation describes an experiment which measured the inclusive momentum spectra for hadrons and muons produced in e/sup +/e/sup -/ interactions at total center of mass energies of 3.8 and 4.8 GeV. The experiment was performed at the SPEAR electron-positron storage ring at the Stanford Linear Accelerator Center. It consisted of a single-arm spectrometer, with additional apparatus to measure charged multiplicities and to tag collinear muon and electron pairs. The Lorentz-invariant cross section for hadrons is found to exhibit Feynman scaling at all measured momenta. The invariant cross sections for pions, kaons and protons fell along the same exponential energymore » curve, exhibiting a characteristic hadron temperature of kT = 0.19 GeV. Bjorken scaling was found to hold separately for pions and for kaons for x = 2E/..sqrt..s > 0.4; however, the x-dependence of the two cross sections are significantly different. Results are also presented for the inclusive momentum distributions of the hadron charged multiplicity. An examination of inclusive muon production found the presence of a small anomalous muon signal for two-prong events noncoplanar by more than 20/sup 0/ and with p/sub ..mu../ > 1.05 GeV/c; dsigma/domega/sub 90/sup 0// = 17/sup +12//sub -9/ pb/sr. Known processes accounted for the observed muon events having charged multiplicity greater than 2, giving an upper limit at the 95% confidence level of dsigma/domega/sub 90/sup 0// < 7.5 pb/sr for any new process.« less

Radiation Risks of Leukemia, Lymphoma and Multiple Myeloma Incidence in the Mayak Cohort: 1948–2004

PubMed Central

Kuznetsova, Irina S.; Labutina, Elena V.; Hunter, Nezahat

2016-01-01

Incidence of all types of lymphatic and hematopoietic cancers, including Hodgkin’s lymphoma, non-Hodgkin's lymphoma, multiple myeloma, acute and chronic myeloid leukemia (AML and CML respectively), chronic lymphocytic leukemia (CLL) and other forms of leukemia have been studied in a cohort of 22,373 workers employed at the Mayak Production Association (PA) main facilities during 536,126 person-years of follow-up from the start of employment between 1948 and 1982 to the end of 2004. Risk assessment was performed for both external gamma-radiation and internal alpha-exposure of red bone marrow due to incorporated Pu-239 using Mayak Workers Dosimetry System 2008 taking into account non-radiation factors. The incidence of leukemia excluding CLL showed a non-linear dose response relationship for external gamma exposure with exponential effect modifiers based on time since exposure and age at exposure. Among the major subtypes of leukemia, the excess risk of AML was the highest within the first 2–5 years of external exposure (ERR per Gy: 38.40; 90% CI: 13.92–121.4) and decreased substantially thereafter, but the risks remained statistically significant (ERR per Gy: 2.63; 90% CI: 0.07–12.55). In comparison, excess CML first occurred 5 years after exposure and decreased about 10 years after exposure, although the association was not statistically significant (ERR per Gy: 1.39; 90% CI: -0.22–7.32). The study found no evidence of an association between leukemia and occupational exposure to internal plutonium ERR per Gy 2.13; 90% CI: <0–9.45). There was also no indication of any relationship with either external gamma or internal plutonium radiation exposure for either incidence of Hodgkin or non-Hodgkin lymphoma or multiple myeloma. PMID:27631102

Model-based analysis of multi-shell diffusion MR data for tractography: How to get over fitting problems

PubMed Central

Jbabdi, Saad; Sotiropoulos, Stamatios N; Savio, Alexander M; Graña, Manuel; Behrens, Timothy EJ

2012-01-01

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-mono-exponential decay, commonly observed in experimental data, is shown to induce over-fitting in the distribution of fibre orientations when not considered in the model. Extra fibre orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous Gamma distribution of diffusivities, which significantly improves the fitting and reduces the over-fitting. Using in-vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-mono-exponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fibre orientations in white matter and near the cortex. PMID:22334356

Study on the application of NASA energy management techniques for control of a terrestrial solar water heating system

NASA Technical Reports Server (NTRS)

Swanson, T. D.; Ollendorf, S.

1979-01-01

This paper addresses the potential for enhanced solar system performance through sophisticated control of the collector loop flow rate. Computer simulations utilizing the TRNSYS solar energy program were performed to study the relative effect on system performance of eight specific control algorithms. Six of these control algorithms are of the proportional type: two are concave exponentials, two are simple linear functions, and two are convex exponentials. These six functions are typical of what might be expected from future, more advanced, controllers. The other two algorithms are of the on/off type and are thus typical of existing control devices. Results of extensive computer simulations utilizing actual weather data indicate that proportional control does not significantly improve system performance. However, it is shown that thermal stratification in the liquid storage tank may significantly improve performance.

Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

PubMed

Shehla, Romana; Khan, Athar Ali

2016-01-01

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.

Phosphorus-zinc interactive effects on growth by Selenastrum capricornutum (chlorophyta)

USGS Publications Warehouse

Kuwabara, J.S.

1985-01-01

Culturing experiments in chemically defined growth media were conducted to observe possible Zn and P interactions on Selenastrum capricornutum Printz growth indexes. Elevated Zn concentrations (7.5 ?? 10-8 and 1.5 ?? 10-7 M [Zn2+]) were highly detrimental to algal growth, affecting lag, exponential, and stationary growth phases. P behaved as a yield-limiting nutrient with maximum cell densities increasing linearly with total P. This yield limitation was intensified at elevated Zn concentrations. Although calculated cellular phosphorus concentrations increased markedly with Zn ion activity, elevated Zn concentrations had no apparent effect on rates of phosphorus uptake estimated for Selenastrum during exponential growth. Results indicated that P-Zn interactions were significant in describing Selenastrum cell yield results and are consistent with previous Zn studies on chlorophytes. These P-Zn interactions and the observed inhibitory growth effects of submicromolar Zn concentrations suggest that in nature an apparent P yield-limiting condition may result from elevated Zn concentrations.

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Constraining generalized non-local cosmology from Noether symmetries.

PubMed

Bahamonde, Sebastian; Capozziello, Salvatore; Dialektopoulos, Konstantinos F

2017-01-01

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Constraining generalized non-local cosmology from Noether symmetries

NASA Astrophysics Data System (ADS)

Bahamonde, Sebastian; Capozziello, Salvatore; Dialektopoulos, Konstantinos F.

2017-11-01

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods.

PubMed

Gómez Pueyo, Adrián; Marques, Miguel A L; Rubio, Angel; Castro, Alberto

2018-05-09

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm

PubMed Central

Hsiao, Feng-Hsiag

2015-01-01

This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

Kinetics of microstructure formation of high-pressure induced gel from a whey protein isolate

NASA Astrophysics Data System (ADS)

He, Jin-Song; Yang, Hongwei; Zhu, Wanpeng; Mu, Tai-Hua

2010-03-01

The kinetic process of pressure-induced gelation of whey protein isolate (WPI) solutions was studied using in situ light scattering. The relationship of the logarithm of scattered light intensity (I) versus time (t) was linear after the induced time and could be described by the Cahn-Hilliard linear theory. With increasing time, the scattered intensity deviated from the exponential relationship, and the time evolution of the scattered light intensity maximum Im and the corresponding wavenumber qm could be described in terms of the power-law relationship as Im~fβ and qm~f-α, respectively. These results indicated that phase separation occurred during the gelation of WPI solutions under high pressure.

Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

PubMed

Sumner, Jeremy G

2017-03-01

We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.

Instability of the cored barotropic disc: the linear eigenvalue formulation

NASA Astrophysics Data System (ADS)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

Joint inversion of multiple geophysical and petrophysical data using generalized fuzzy clustering algorithms

NASA Astrophysics Data System (ADS)

Sun, Jiajia; Li, Yaoguo

2017-02-01

Joint inversion that simultaneously inverts multiple geophysical data sets to recover a common Earth model is increasingly being applied to exploration problems. Petrophysical data can serve as an effective constraint to link different physical property models in such inversions. There are two challenges, among others, associated with the petrophysical approach to joint inversion. One is related to the multimodality of petrophysical data because there often exist more than one relationship between different physical properties in a region of study. The other challenge arises from the fact that petrophysical relationships have different characteristics and can exhibit point, linear, quadratic, or exponential forms in a crossplot. The fuzzy c-means (FCM) clustering technique is effective in tackling the first challenge and has been applied successfully. We focus on the second challenge in this paper and develop a joint inversion method based on variations of the FCM clustering technique. To account for the specific shapes of petrophysical relationships, we introduce several different fuzzy clustering algorithms that are capable of handling different shapes of petrophysical relationships. We present two synthetic and one field data examples and demonstrate that, by choosing appropriate distance measures for the clustering component in the joint inversion algorithm, the proposed joint inversion method provides an effective means of handling common petrophysical situations we encounter in practice. The jointly inverted models have both enhanced structural similarity and increased petrophysical correlation, and better represent the subsurface in the spatial domain and the parameter domain of physical properties.

Optimized "detectors" for dynamics analysis in solid-state NMR

NASA Astrophysics Data System (ADS)

Smith, Albert A.; Ernst, Matthias; Meier, Beat H.

2018-01-01

Relaxation in nuclear magnetic resonance (NMR) results from stochastic motions that modulate anisotropic NMR interactions. Therefore, measurement of relaxation-rate constants can be used to characterize molecular-dynamic processes. The motion is often characterized by Markov processes using an auto-correlation function, which is assumed to be a sum of multiple decaying exponentials. We have recently shown that such a model can lead to severe misrepresentation of the real motion, when the real correlation function is more complex than the model. Furthermore, multiple distributions of motion may yield the same set of dynamics data. Therefore, we introduce optimized dynamics "detectors" to characterize motions which are linear combinations of relaxation-rate constants. A detector estimates the average or total amplitude of motion for a range of motional correlation times. The information obtained through the detectors is less specific than information obtained using an explicit model, but this is necessary because the information contained in the relaxation data is ambiguous, if one does not know the correct motional model. On the other hand, if one has a molecular dynamics trajectory, one may calculate the corresponding detector responses, allowing direct comparison to experimental NMR dynamics analysis. We describe how to construct a set of optimized detectors for a given set of relaxation measurements. We then investigate the properties of detectors for a number of different data sets, thus gaining an insight into the actual information content of the NMR data. Finally, we show an example analysis of ubiquitin dynamics data using detectors, using the DIFRATE software.

Modular multiplication in GF(p) for public-key cryptography

NASA Astrophysics Data System (ADS)

Olszyna, Jakub

Modular multiplication forms the basis of modular exponentiation which is the core operation of the RSA cryptosystem. It is also present in many other cryptographic algorithms including those based on ECC and HECC. Hence, an efficient implementation of PKC relies on efficient implementation of modular multiplication. The paper presents a survey of most common algorithms for modular multiplication along with hardware architectures especially suitable for cryptographic applications in energy constrained environments. The motivation for studying low-power and areaefficient modular multiplication algorithms comes from enabling public-key security for ultra-low power devices that can perform under constrained environments like wireless sensor networks. Serial architectures for GF(p) are analyzed and presented. Finally proposed architectures are verified and compared according to the amount of power dissipated throughout the operation.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Control logic to track the outputs of a command generator or randomly forced target

NASA Technical Reports Server (NTRS)

Trankle, T. L.; Bryson, A. E., Jr.

1977-01-01

A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).

Quantum Linear System Algorithm for Dense Matrices.

PubMed

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-02

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that Ax=b. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O(κ^{2}sqrt[n]polylog(n)/ε) for an n×n dimensional A with bounded spectral norm, where κ denotes the condition number of A, and ε is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A.

Tunnel current across linear homocatenated germanium chains

NASA Astrophysics Data System (ADS)

Matsuura, Yukihito

2014-01-01

The electronic transport properties of germanium oligomers catenating into linear chains (linear Ge chains) have been theoretically studied using first principle methods. The conduction mechanism of a Ge chain sandwiched between gold electrodes was analyzed based on the density of states and the eigenstates of the molecule in a two-probe environment. Like that of silicon chains (Si chains), the highest occupied molecular orbital of Ge chains contains the extended σ-conjugation of Ge 4p orbitals at energy levels close to the Fermi level; this is in contrast to the electronic properties of linear carbon chains. Furthermore, the conductance of a Ge chain is expected to decrease exponentially with molecular length L. The decay constant β, which is defined as e-βL, of a Ge chain is similar to that of a Si chain, whereas the conductance of the Ge chains is higher than that of Si chains even though the Ge-Ge bond length is longer than the Si-Si bond length.

Existence and energy decay of a nonuniform Timoshenko system with second sound

NASA Astrophysics Data System (ADS)

Hamadouche, Taklit; Messaoudi, Salim A.

2018-02-01

In this paper, we consider a linear thermoelastic Timoshenko system with variable physical parameters, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We discuss the well-posedness and the regularity of solution using the semigroup theory. Moreover, we establish the exponential decay result provided that the stability function χ r(x)=0. Otherwise, we show that the solution decays polynomially.

INCREASED NUMBER OF COFFEE BEANS PRODUCED FROM IRRADIATED SEEDS (in Spanish)

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

Monge, F.

1962-10-01

A genetic analysis of coffee plants from neutron and x-irradiated seed reveals that peaberry percent increased with radiation dose applied. The response for neutron irradiated plants was linear whereas for the x ray treatments it was exponential. This suggests that the high frequency of peaberries obtained from irradiated plants is due to chromosomal aberration; that cause gamete elimination and thus, a high production of one-seeded fruits. (auth)

Disassembling the clockwork mechanism

NASA Astrophysics Data System (ADS)

Craig, Nathaniel; Garcia Garcia, Isabel; Sutherland, Dave

2017-10-01

The clockwork mechanism is a means of naturally generating exponential hierarchies in theories without significant hierarchies among fundamental parameters. We emphasize the role of interactions in the clockwork mechanism, demonstrating that clockwork is an intrinsically abelian phenomenon precluded in non-abelian theories such as Yang-Mills, non-linear sigma models, and gravity. We also show that clockwork is not realized in extra-dimensional theories through purely geometric effects, but may be generated by appropriate localization of zero modes.

Study of Equatorial Ionospheric irregularities and Mapping of Electron Density Profiles and Ionograms

DTIC Science & Technology

2012-03-09

equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the...wave function arguments from complex scalars to complex vectors . This conversion allows us to separate the electric field vector and the imaginary...magnetic field vector , because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while ex- ponentials of imaginary

Application of linear logic to simulation

NASA Astrophysics Data System (ADS)

Clarke, Thomas L.

1998-08-01

Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

Dynamic Latent Trait Models with Mixed Hidden Markov Structure for Mixed Longitudinal Outcomes.

PubMed

Zhang, Yue; Berhane, Kiros

2016-01-01

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMM). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study (CHS) to jointly model questionnaire based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

Evolutionary inference via the Poisson Indel Process.

PubMed

Bouchard-Côté, Alexandre; Jordan, Michael I

2013-01-22

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

Evolutionary inference via the Poisson Indel Process

PubMed Central

Bouchard-Côté, Alexandre; Jordan, Michael I.

2013-01-01

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114–124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments. PMID:23275296

Seismic signatures of carbonate caves affected by near-surface absorptions

NASA Astrophysics Data System (ADS)

Rao, Ying; Wang, Yanghua

2015-12-01

The near-surface absorption within a low-velocity zone generally has an exponential attenuation effect on seismic waves. But how does this absorption affect seismic signatures of karstic caves in deep carbonate reservoirs? Seismic simulation and analysis reveals that, although this near-surface absorption attenuates the wave energy of a continuous reflection, it does not alter the basic kinematic shape of bead-string reflections, a special seismic characteristic associated with carbonate caves in the Tarim Basin, China. Therefore, the bead-strings in seismic profiles can be utilized, with a great certainty, for interpreting the existence of caves within the deep carbonate reservoirs and for evaluating their pore spaces. Nevertheless, the difference between the central frequency and the peak frequency is increased along with the increment in the absorption. While the wave energy of bead-string reflections remains strong, due to the interference of seismic multiples generated by big impedance contrast between the infill materials of a cave and the surrounding carbonate rocks, the central frequency is shifted linearly with respect to the near-surface absorption. These two features can be exploited simultaneously, for a stable attenuation analysis of field seismic data.

Factors affecting the dissipation of pharmaceuticals in freshwater sediments.

PubMed

Al-Khazrajy, Omar S A; Bergström, Ed; Boxall, Alistair B A

2018-03-01

Degradation is one of the key processes governing the impact of pharmaceuticals in the aquatic environment. Most studies on the degradation of pharmaceuticals have focused on soil and sludge, with fewer exploring persistence in aquatic sediments. We investigated the dissipation of 6 pharmaceuticals from different therapeutic classes in a range of sediment types. Dissipation of each pharmaceutical was found to follow first-order exponential decay. Half-lives in the sediments ranged from 9.5 (atenolol) to 78.8 (amitriptyline) d. Under sterile conditions, the persistence of pharmaceuticals was considerably longer. Stepwise multiple linear regression analysis was performed to explore the relationships between half-lives of the pharmaceuticals, sediment physicochemical properties, and sorption coefficients for the compounds. Sediment clay, silt, and organic carbon content and microbial activity were the predominant factors related to the degradation rates of diltiazem, cimetidine, and ranitidine. Regression analysis failed to highlight a key property which may be responsible for observed differences in the degradation of the other pharmaceuticals. The present results suggest that the degradation rate of pharmaceuticals in sediments is determined by different factors and processes and does not exclusively depend on a single sediment parameter. Environ Toxicol Chem 2018;37:829-838. © 2017 SETAC. © 2017 SETAC.

Fishing Quotas, Induced Allee Effect, and Fluctuation-Driven Extinction.

PubMed

Hastings, Harold M; Radin, Michael; Wiandt, Tamas

2017-01-01

We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level). In the presence of environmental noise, fish population dynamics is similar to a random walk with (non-linear) drift. The expected survival time (first passage time to collapse) is shown to depend sensitively upon the amount of environmental noise and size of the 'safe zone' between the deterministic steady state population and the critical population level at which the system collapses; more precisely it is exponential in the cube of the size of the safe zone divided by the variance of the noise process. Similar scaling can be expected for more survival in more general systems with multiple steady states. Our calculations imply an amplification effect under which small increases in harvest yield large decreases in expected survival time, and one should be cautious in changes in harvesting, especially in fisheries with poor or limited data and fisheries affected by climate change.

Highly sensitive and selective microRNA detection based on DNA-bio-bar-code and enzyme-assisted strand cycle exponential signal amplification.

PubMed

Dong, Haifeng; Meng, Xiangdan; Dai, Wenhao; Cao, Yu; Lu, Huiting; Zhou, Shufeng; Zhang, Xueji

2015-04-21

Herein, a highly sensitive and selective microRNA (miRNA) detection strategy using DNA-bio-bar-code amplification (BCA) and Nb·BbvCI nicking enzyme-assisted strand cycle for exponential signal amplification was designed. The DNA-BCA system contains a locked nucleic acid (LNA) modified DNA probe for improving hybridization efficiency, while a signal reported molecular beacon (MB) with an endonuclease recognition site was designed for strand cycle amplification. In the presence of target miRNA, the oligonucleotides functionalized magnetic nanoprobe (MNP-DNA) and gold nanoprobe (AuNP-DNA) with numerous reported probes (RP) can hybridize with target miRNA, respectively, to form a sandwich structure. After sandwich structures were separated from the solution by the magnetic field, the RP were released under high temperature to recognize the MB and cleaved the hairpin DNA to induce the dissociation of RP. The dissociated RP then triggered the next strand cycle to produce exponential fluorescent signal amplification for miRNA detection. Under optimized conditions, the exponential signal amplification system shows a good linear range of 6 orders of magnitude (from 0.3 pM to 3 aM) with limit of detection (LOD) down to 52.5 zM, while the sandwich structure renders the system with high selectivity. Meanwhile, the feasibility of the proposed strategy for cell miRNA detection was confirmed by analyzing miRNA-21 in HeLa lysates. Given the high-performance for miRNA analysis, the strategy has a promising application in biological detection and in clinical diagnosis.

Trends analysis of PM source contributions and chemical tracers in NE Spain during 2004-2014: a multi-exponential approach

NASA Astrophysics Data System (ADS)

Pandolfi, Marco; Alastuey, Andrés; Pérez, Noemi; Reche, Cristina; Castro, Iria; Shatalov, Victor; Querol, Xavier

2016-09-01

In this work for the first time data from two twin stations (Barcelona, urban background, and Montseny, regional background), located in the northeast (NE) of Spain, were used to study the trends of the concentrations of different chemical species in PM10 and PM2.5 along with the trends of the PM10 source contributions from the positive matrix factorization (PMF) model. Eleven years of chemical data (2004-2014) were used for this study. Trends of both species concentrations and source contributions were studied using the Mann-Kendall test for linear trends and a new approach based on multi-exponential fit of the data. Despite the fact that different PM fractions (PM2.5, PM10) showed linear decreasing trends at both stations, the contributions of specific sources of pollutants and of their chemical tracers showed exponential decreasing trends. The different types of trends observed reflected the different effectiveness and/or time of implementation of the measures taken to reduce the concentrations of atmospheric pollutants. Moreover, the trends of the contributions of specific sources such as those related with industrial activities and with primary energy consumption mirrored the effect of the financial crisis in Spain from 2008. The sources that showed statistically significant downward trends at both Barcelona (BCN) and Montseny (MSY) during 2004-2014 were secondary sulfate, secondary nitrate, and V-Ni-bearing source. The contributions from these sources decreased exponentially during the considered period, indicating that the observed reductions were not gradual and consistent over time. Conversely, the trends were less steep at the end of the period compared to the beginning, thus likely indicating the attainment of a lower limit. Moreover, statistically significant decreasing trends were observed for the contributions to PM from the industrial/traffic source at MSY (mixed metallurgy and road traffic) and from the industrial (metallurgy mainly) source at BCN. These sources were clearly linked with anthropogenic activities, and the observed decreasing trends confirmed the effectiveness of pollution control measures implemented at European or regional/local levels. Conversely, at regional level, the contributions from sources mostly linked with natural processes, such as aged marine and aged organics, did not show statistically significant trends. The trends observed for the PM10 source contributions reflected the trends observed for the chemical tracers of these pollutant sources well.

ISC-GEM: Global Instrumental Earthquake Catalogue (1900-2009), III. Re-computed MS and mb, proxy MW, final magnitude composition and completeness assessment

NASA Astrophysics Data System (ADS)

Di Giacomo, Domenico; Bondár, István; Storchak, Dmitry A.; Engdahl, E. Robert; Bormann, Peter; Harris, James

2015-02-01

This paper outlines the re-computation and compilation of the magnitudes now contained in the final ISC-GEM Reference Global Instrumental Earthquake Catalogue (1900-2009). The catalogue is available via the ISC website (http://www.isc.ac.uk/iscgem/). The available re-computed MS and mb provided an ideal basis for deriving new conversion relationships to moment magnitude MW. Therefore, rather than using previously published regression models, we derived new empirical relationships using both generalized orthogonal linear and exponential non-linear models to obtain MW proxies from MS and mb. The new models were tested against true values of MW, and the newly derived exponential models were then preferred to the linear ones in computing MW proxies. For the final magnitude composition of the ISC-GEM catalogue, we preferred directly measured MW values as published by the Global CMT project for the period 1976-2009 (plus intermediate-depth earthquakes between 1962 and 1975). In addition, over 1000 publications have been examined to obtain direct seismic moment M0 and, therefore, also MW estimates for 967 large earthquakes during 1900-1978 (Lee and Engdahl, 2015) by various alternative methods to the current GCMT procedure. In all other instances we computed MW proxy values by converting our re-computed MS and mb values into MW, using the newly derived non-linear regression models. The final magnitude composition is an improvement in terms of magnitude homogeneity compared to previous catalogues. The magnitude completeness is not homogeneous over the 110 years covered by the ISC-GEM catalogue. Therefore, seismicity rate estimates may be strongly affected without a careful time window selection. In particular, the ISC-GEM catalogue appears to be complete down to MW 5.6 starting from 1964, whereas for the early instrumental period the completeness varies from ∼7.5 to 6.2. Further time and resources would be necessary to homogenize the magnitude of completeness over the entire catalogue length.

Increased rates of authorship in radiology publications: a bibliometric analysis of 142,576 articles published worldwide by radiologists between 1991 and 2012.

PubMed

Chow, Daniel S; Ha, Richard; Filippi, Christopher G

2015-01-01

OBJECTIVE; There is evidence in academic medicine that the number of authors per paper has increased over time. The goal of this study was to quantitatively analyze authorship trends in the field of radiology over 20 years. A search of the National Library of Medicine MEDLINE database was conducted to identify articles published by radiology departments between 1991 and 2012. Country of origin, article study design, and journal impact factor were recorded. The increase in number of authors per paper was assessed by linear and nonlinear regression. Pearson correlation was used to assess the relation between journal impact factor and number of authors. A total of 142,576 articles and 699,257 authors were identified during the study period. The mean number of authors per paper displayed linear growth from 3.9 to 5.7 (p < 0.0001). The proportion of single authors declined from 11% in 1991 to 4.4% in 2012. The number of clinical trials increased in a linear pattern, review articles in an exponential pattern, and case reports in a logistic pattern (p < 0.0001 for each). Countries with the highest number of authors per paper were Japan, Italy, and Germany. The number of articles funded by the U.S. National Institutes of Health (NIH) displayed exponential growth and of non-NIH-funded articles displayed linear growth (p < 0.0001 for each). A negligible relation was observed between journal impact factor and number of authors (Pearson r = 0.1066). Radiology has had a steady increase in mean number of authors per paper since the early 1990s that has varied by study design. The increase is probably multi-factorial and includes components of author inflation and increasing complexity of research. Findings support the need for reemphasis of authorship criteria to preserve authorship value and accountability.

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

PubMed Central

Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

2014-01-01

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches. PMID:24626049

Loss of EGF binding and cation transport response during differentiation of mouse neuroblastoma cells.

PubMed

Mummery, C L; van der Saag, P T; de Laat, S W

1983-01-01

Mouse neuroblastoma cells (clone N1E-115) differentiate in culture upon withdrawal of serum growth factors and acquire the characteristics of neurons. We have shown tht exponentially growing N1E-115 cells possess functional epidermal growth factor (EGF) receptors but that the capacity for binding EGF and for stimulation of DNA synthesis is lost as the cells differentiate. Furthermore, in exponentially growing cells, EGF induces a rapid increase in amiloride-sensitive Na+ influx, followed by stimulation of the (Na+-K+)ATPase, indicating that activation of the Na+/H+ exchange mechanism in N1E-115 cells [1] may be induced by EGF. The ionic response is also lost during differentiation, but we have shown that the stimulation of both Na+ and K+ influx is directly proportional to the number of occupied receptors in all cells whether exponentially growing or differentiating, thus only indirectly dependent on the external EGF concentration. The linearity of the relationships indicates that there is no rate-limiting step between EGF binding and the ionic response. Our data would suggest that as neuroblastoma cells differentiate and acquire neuronal properties, their ability to respond to mitogens, both biologically and in the activation of cation transport processes, progressively decreases owing to the loss of the appropriate receptors.

Application of the compensated Arrhenius formalism to self-diffusion: implications for ionic conductivity and dielectric relaxation.

PubMed

Petrowsky, Matt; Frech, Roger

2010-07-08

Self-diffusion coefficients are measured from -5 to 80 degrees C in a series of linear alcohols using pulsed field gradient NMR. The temperature dependence of these data is studied using a compensated Arrhenius formalism that assumes an Arrhenius-like expression for the diffusion coefficient; however, this expression includes a dielectric constant dependence in the exponential prefactor. Scaling temperature-dependent diffusion coefficients to isothermal diffusion coefficients so that the exponential prefactors cancel results in calculated energies of activation E(a). The exponential prefactor is determined by dividing the temperature-dependent diffusion coefficients by the Boltzmann term exp(-E(a)/RT). Plotting the prefactors versus the dielectric constant places the data on a single master curve. This procedure is identical to that previously used to study the temperature dependence of ionic conductivities and dielectric relaxation rate constants. The energies of activation determined from self-diffusion coefficients in the series of alcohols are strikingly similar to those calculated for the same series of alcohols from both dielectric relaxation rate constants and ionic conductivities of dilute electrolytes. The experimental results are described in terms of an activated transport mechanism that is mediated by relaxation of the solution molecules. This microscopic picture of transport is postulated to be common to diffusion, dielectric relaxation, and ionic transport.

β-NMR measurements of molecular-scale lithium-ion dynamics in poly(ethylene oxide)-lithium-salt thin films

NASA Astrophysics Data System (ADS)

McKenzie, Iain; Cortie, David L.; Harada, Masashi; Kiefl, Robert F.; Levy, C. D. Philip; MacFarlane, W. Andrew; McFadden, Ryan M. L.; Morris, Gerald D.; Ogata, Shin-Ichi; Pearson, Matthew R.; Sugiyama, Jun

2017-06-01

β -detected NMR (β -NMR) has been used to study the molecular-scale dynamics of lithium ions in thin films of poly(ethylene oxide) (PEO) containing either lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) or lithium trifluoroacetate (LiTFA) salts at monomer-to-salt ratios (EO/Li) of 8.3. The results are compared with previous β -NMR measurements on pure PEO and PEO with lithium triflate (LiOTf) at the same loading [McKenzie et al., J. Am. Chem. Soc. 136, 7833 (2014)]. Activated hopping of 8Li+ was observed in all of the films above ˜250 K, with the hopping parameters strongly correlated with the ionicity of the lithium salt rather than the polymer glass transition temperature. The pre-exponential factor increases exponentially with ionicity, while the activation energy for hopping increases approximately linearly, going from 6.3 ±0.2 kJ mol-1 in PEO:LiTFA to 17.8 ±0.2 kJ mol-1 in PEO:LiTFSI. The more rapid increase in the pre-exponential factor outweighs the effect of the larger activation energy and results in 8Li+ hopping being fastest in PEO followed by PEO:LiTFSI, PEO:LiOTf, and PEO:LiTFA.

β-NMR measurements of molecular-scale lithium-ion dynamics in poly(ethylene oxide)-lithium-salt thin films.

PubMed

McKenzie, Iain; Cortie, David L; Harada, Masashi; Kiefl, Robert F; Levy, C D Philip; MacFarlane, W Andrew; McFadden, Ryan M L; Morris, Gerald D; Ogata, Shin-Ichi; Pearson, Matthew R; Sugiyama, Jun

2017-06-28

β-detected NMR (β-NMR) has been used to study the molecular-scale dynamics of lithium ions in thin films of poly(ethylene oxide) (PEO) containing either lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) or lithium trifluoroacetate (LiTFA) salts at monomer-to-salt ratios (EO/Li) of 8.3. The results are compared with previous β-NMR measurements on pure PEO and PEO with lithium triflate (LiOTf) at the same loading [McKenzie et al., J. Am. Chem. Soc. 136, 7833 (2014)]. Activated hopping of 8 Li + was observed in all of the films above ∼250 K, with the hopping parameters strongly correlated with the ionicity of the lithium salt rather than the polymer glass transition temperature. The pre-exponential factor increases exponentially with ionicity, while the activation energy for hopping increases approximately linearly, going from 6.3±0.2 kJ mol -1 in PEO:LiTFA to 17.8±0.2 kJ mol -1 in PEO:LiTFSI. The more rapid increase in the pre-exponential factor outweighs the effect of the larger activation energy and results in 8 Li + hopping being fastest in PEO followed by PEO:LiTFSI, PEO:LiOTf, and PEO:LiTFA.

A model of canopy photosynthesis incorporating protein distribution through the canopy and its acclimation to light, temperature and CO2

PubMed Central

Johnson, Ian R.; Thornley, John H. M.; Frantz, Jonathan M.; Bugbee, Bruce

2010-01-01

Background and Aims The distribution of photosynthetic enzymes, or nitrogen, through the canopy affects canopy photosynthesis, as well as plant quality and nitrogen demand. Most canopy photosynthesis models assume an exponential distribution of nitrogen, or protein, through the canopy, although this is rarely consistent with experimental observation. Previous optimization schemes to derive the nitrogen distribution through the canopy generally focus on the distribution of a fixed amount of total nitrogen, which fails to account for the variation in both the actual quantity of nitrogen in response to environmental conditions and the interaction of photosynthesis and respiration at similar levels of complexity. Model A model of canopy photosynthesis is presented for C3 and C4 canopies that considers a balanced approach between photosynthesis and respiration as well as plant carbon partitioning. Protein distribution is related to irradiance in the canopy by a flexible equation for which the exponential distribution is a special case. The model is designed to be simple to parameterize for crop, pasture and ecosystem studies. The amount and distribution of protein that maximizes canopy net photosynthesis is calculated. Key Results The optimum protein distribution is not exponential, but is quite linear near the top of the canopy, which is consistent with experimental observations. The overall concentration within the canopy is dependent on environmental conditions, including the distribution of direct and diffuse components of irradiance. Conclusions The widely used exponential distribution of nitrogen or protein through the canopy is generally inappropriate. The model derives the optimum distribution with characteristics that are consistent with observation, so overcoming limitations of using the exponential distribution. Although canopies may not always operate at an optimum, optimization analysis provides valuable insight into plant acclimation to environmental conditions. Protein distribution has implications for the prediction of carbon assimilation, plant quality and nitrogen demand. PMID:20861273

Evo-SETI SCALE to measure Life on Exoplanets

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2016-04-01

Darwinian Evolution over the last 3.5 billion years was an increase in the number of living species from 1 (RNA?) to the current 50 million. This increasing trend in time looks like being exponential, but one may not assume an exactly exponential curve since many species went extinct in the past, even in mass extinctions. Thus, the simple exponential curve must be replaced by a stochastic process having an exponential mean value. Borrowing from financial mathematics (;Black-Scholes models;), this ;exponential; stochastic process is called Geometric Brownian Motion (GBM), and its probability density function (pdf) is a lognormal (not a Gaussian) (Proof: see ref. Maccone [3], Chapter 30, and ref. Maccone [4]). Lognormal also is the pdf of the statistical number of communicating ExtraTerrestrial (ET) civilizations in the Galaxy at a certain fixed time, like a snapshot: this result was found in 2008 by this author as his solution to the Statistical Drake Equation of SETI (Proof: see ref. Maccone [1]). Thus, the GBM of Darwinian Evolution may also be regarded as the extension in time of the Statistical Drake equation (Proof: see ref. Maccone [4]). But the key step ahead made by this author in his Evo-SETI (Evolution and SETI) mathematical model was to realize that LIFE also is just a b-lognormal in time: every living organism (a cell, a human, a civilization, even an ET civilization) is born at a certain time b (;birth;), grows up to a peak p (with an ascending inflexion point in between, a for adolescence), then declines from p to s (senility, i.e. descending inflexion point) and finally declines linearly and dies at a final instant d (death). In other words, the infinite tail of the b-lognormal was cut away and replaced by just a straight line between s and d, leading to simple mathematical formulae (;History Formulae;) allowing one to find this ;finite b-lognormal; when the three instants b, s, and d are assigned. Next the crucial Peak-Locus Theorem comes. It means that the GBM exponential may be regarded as the geometric locus of all the peaks of a one-parameter (i.e. the peak time p) family of b-lognormals. Since b-lognormals are pdf-s, the area under each of them always equals 1 (normalization condition) and so, going from left to right on the time axis, the b-lognormals become more and more ;peaky;, and so they last less and less in time. This is precisely what happened in human history: civilizations that lasted millennia (like Ancient Greece and Rome) lasted just centuries (like the Italian Renaissance and Portuguese, Spanish, French, British and USA Empires) but they were more and more advanced in the ;level of civilization;. This ;level of civilization; is what physicists call ENTROPY. Also, in refs. Maccone [3] and [4], this author proved that, for all GBMs, the (Shannon) Entropy of the b-lognormals in his Peak-Locus Theorem grows LINEARLY in time. The Molecular Clock, well known to geneticists since 50 years, shows that the DNA base-substitutions occur LINEARLY in time since they are neutral with respect to Darwinian selection. In simple words: DNA evolved by obeying the laws of quantum physics only (microscopic laws) and not by obeying assumed ;Darwinian selection laws; (macroscopic laws). This is Kimura's neutral theory of molecular evolution. The conclusion is that the Molecular Clock and the b-lognormal Entropy are the same thing. At last, we reach the new, original result justifying the publication of this paper. On exoplanets, molecular evolution is proceeding at about the same rate as it did proceed on Earth: rather independently of the physical conditions of the exoplanet, if the DNA had the possibility to evolve in water initially. Thus, Evo-Entropy, i.e. the (Shannon) Entropy of the generic b-lognormal of the Peak-Locus Theorem, provides the Evo-SETI SCALE to measure the evolution of life on exoplanets.

Comparing Multiple-Group Multinomial Log-Linear Models for Multidimensional Skill Distributions in the General Diagnostic Model. Research Report. ETS RR-08-35

ERIC Educational Resources Information Center

Xu, Xueli; von Davier, Matthias

2008-01-01

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

DOE PAGES

Prathama, Aditya Heru; Pantano, Carlos

2017-08-09

Here, we study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interfacemore » is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.« less

The vortex as a clock

NASA Astrophysics Data System (ADS)

Breidenthal, Robert

2003-11-01

Using heuristic arguments, the fundamental effect of acceleration on dissipation in self-similar turbulence is explored. If the ratio of the next vortex rotation period to the last one is always constant, a flow is temporally self-similar. This implies that the vortex rotation period is a linear function of time. For ordinary, unforced turbulence, the period increases linearly in time. However, by imposing an external e-folding time scale on the flow that decreases linearly in time, the dissipation rate is changed from that of the corresponding unforced flow. The dissipation rate depends on the time rate of change of the rotation period as well as the dimensions of the dynamic quantity controlling the flow. For almost all canonical laboratory flows, acceleration reduces the dissipation and entrainment rates. An example is the exponential jet, where the flame length increases by about 20conventional jet. An exception is Rayleigh-Taylor flow, where acceleration increases the dissipation rate.

Effects of entanglement in an ideal optical amplifier

NASA Astrophysics Data System (ADS)

Franson, J. D.; Brewster, R. A.

2018-04-01

In an ideal linear amplifier, the output signal is linearly related to the input signal with an additive noise that is independent of the input. The decoherence of a quantum-mechanical state as a result of optical amplification is usually assumed to be due to the addition of quantum noise. Here we show that entanglement between the input signal and the amplifying medium can produce an exponentially-large amount of decoherence in an ideal optical amplifier even when the gain is arbitrarily close to unity and the added noise is negligible. These effects occur for macroscopic superposition states, where even a small amount of gain can leave a significant amount of which-path information in the environment. Our results show that the usual input/output relation of a linear amplifier does not provide a complete description of the output state when post-selection is used.

A consistent two-mutation model of bone cancer for two data sets of radium-injected beagles.

PubMed

Bijwaard, H; Brugmans, M J P; Leenhouts, H P

2002-09-01

A two-mutation carcinogenesis model has been applied to model osteosarcoma incidence in two data sets of beagles injected with 226Ra. Taking age-specific retention into account, the following results have been obtained: (1) a consistent and well-fitting solution for all age and dose groups, (2) mutation rates that are linearly dependent on dose rate, with an exponential decrease for the second mutation at high dose rates, (3) a linear-quadratic dose-effect relationship, which indicates that care should be taken when extrapolating linearly, (4) highest cumulative incidences for injection at young adult age, and highest risks for injection doses of a few kBq kg(-1) at these ages, and (5) when scaled appropriately, the beagle model compares fairly well with a description for radium dial painters, suggesting that a consistent model description of bone cancer induction in beagles and humans may be possible.

Optimal mode transformations for linear-optical cluster-state generation

DOE PAGES

Uskov, Dmitry B.; Lougovski, Pavel; Alsing, Paul M.; ...

2015-06-15

In this paper, we analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (CZ) gate with success rate of 1/9 per operation. The question of optimality of the CZ gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. Finally,more » we show that the maximal success rate of postselected entangling n photonic qubits or m Bell pairs into a cluster is (1/2) n-1 and (1/4) m-1, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.« less

Performance improvements of wavelength-shifting-fiber neutron detectors using high-resolution positioning algorithms

DOE PAGES

Wang, C. L.

2016-05-17

On the basis of FluoroBancroft linear-algebraic method [S.B. Andersson, Opt. Exp. 16, 18714 (2008)] three highly-resolved positioning methods were proposed for wavelength-shifting fiber (WLSF) neutron detectors. Using a Gaussian or exponential-decay light-response function (LRF), the non-linear relation of photon-number profiles vs. x-pixels was linearized and neutron positions were determined. The proposed algorithms give an average 0.03-0.08 pixel position error, much smaller than that (0.29 pixel) from a traditional maximum photon algorithm (MPA). The new algorithms result in better detector uniformity, less position misassignment (ghosting), better spatial resolution, and an equivalent or better instrument resolution in powder diffraction than the MPA.more » Moreover, these characters will facilitate broader applications of WLSF detectors at time-of-flight neutron powder diffraction beamlines, including single-crystal diffraction and texture analysis.« less

Integrating Apps with the Core Arts Standards in the 21st-Century Elementary Music Classroom

ERIC Educational Resources Information Center

Heath-Reynolds, Julia; VanWeelden, Kimberly

2015-01-01

The implementation of the National Core Arts Standards has amplified the need for multiple approaches and opportunities for student responses and may compel music educators to use new tools. There are currently over one million available apps, and with the popularity of smart devices, student access to technology is increasing exponentially. Music…

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

Jiang, Yunshan; DeVore, Peter T. S.; Jalali, Bahram

Optical computing accelerators help alleviate bandwidth and power consumption bottlenecks in electronics. In this paper, we show an approach to implementing logarithmic-type analog co-processors in silicon photonics and use it to perform the exponentiation operation and the recovery of a signal in the presence of multiplicative distortion. Finally, the function is realized by exploiting nonlinear-absorption-enhanced Raman amplification saturation in a silicon waveguide.

Higgsplosion: Solving the hierarchy problem via rapid decays of heavy states into multiple Higgs bosons

NASA Astrophysics Data System (ADS)

Khoze, Valentin V.; Spannowsky, Michael

2018-01-01

We introduce and discuss two inter-related mechanisms operative in the electroweak sector of the Standard Model at high energies. Higgsplosion, the first mechanism, occurs at some critical energy in the 25 to 103 TeV range, and leads to an exponentially growing decay rate of highly energetic particles into multiple Higgs bosons. We argue that this is a well-controlled non-perturbative phenomenon in the Higgs-sector which involves the final state Higgs multiplicities n in the regime nλ ≫ 1 where λ is the Higgs self-coupling. If this mechanism is realised in nature, the cross-sections for producing ultra-high multiplicities of Higgs bosons are likely to become observable and even dominant in this energy range. At the same time, however, the apparent exponential growth of these cross-sections at even higher energies will be tamed and automatically cut-off by a related Higgspersion mechanism. As a result, and in contrast to previous studies, multi-Higgs production does not violate perturbative unitarity. Building on this approach, we then argue that the effects of Higgsplosion alter quantum corrections from very heavy states to the Higgs boson mass. Above a certain energy, which is much smaller than their masses, these states would rapidly decay into multiple Higgs bosons. The heavy states become unrealised as they decay much faster than they are formed. The loop integrals contributing to the Higgs mass will be cut off not by the masses of the heavy states, but by the characteristic loop momenta where their decay widths become comparable to their masses. Hence, the cut-off scale would be many orders of magnitude lower than the heavy mass scales themselves, thus suppressing their quantum corrections to the Higgs boson mass.

The effect of breed and parity on curves of body condition during lactation estimated using a non-linear function.

PubMed

Friggens, N C; Badsberg, J H

2007-05-01

The objectives of this study were to see if the body condition score curve during lactation could be described using a model amenable to biological interpretation, a non-linear function assuming exponential rates of change in body condition with time, and to quantify the effect of breed and parity on curves of body condition during lactation. Three breeds were represented: Danish Holstein (n = 112), Danish Red (n = 97) and Jerseys (n = 8). Cows entered the experiment at the start of first lactation and were studied during consecutive lactations (average number of lactations 2, minimum 1, maximum 3). They remained on the same dietary treatment throughout. Body condition was scored to the nearest half unit on the Danish scale (see Kristensen (1986); derived from the Lowman et al. (1976) system) from 1 to 5 on days: 2, 14, 28, 42, 56, 84, 112, 168, 224 after calving. Additionally, condition score was recorded on the day of drying off the cow, 35, 21, and 7 days before expected calving and finally on the day of calving. All condition scores were made by the trained personal on the research farm, where the same person made 92% of the scores. The temporal patterns in condition score were modelled as consisting of two underlying processes, one related to days from calving, referred to as lactation only, the other to days from (subsequent) conception, referred to as pregnancy. Both processes were assumed to be exponential functions of time. Each process was modelled separately using exponential functions, i.e. one model for lactation only and one for pregnancy, and then a combined model for both lactation only and pregnancy was fitted. The data set contained 467 lactation periods and 378 pregnancy periods. The temporal patterns in condition score of cows kept under stable and sufficient nutritional conditions were successfully described using a two component non-linear function. First lactation cows had shallower curves, they had greater condition scores at the nadir of the curve. Danish Holstein and Jersey were thinner at the end of the mobilisation period having lost more body condition than the Danish Red breed. Although the dairy breeds ended up being thinner there were no significant differences in the rate at which they lost body condition.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population.

PubMed

Tomitaka, Shinichiro; Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A; Ono, Yutaka

2016-01-01

Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population

PubMed Central

Kawasaki, Yohei; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A.; Ono, Yutaka

2016-01-01

Background Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Methods Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. Results The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. Discussion The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern. PMID:27761346

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Heavy ion-induced DNA double-strand breaks in yeast.

PubMed

Kiefer, Jürgen; Egenolf, Ralf; Ikpeme, Samuel

2002-02-01

Induction of DSBs in the diploid yeast, Saccharomyces cerevisiae, was measured by pulsed-field gel electrophoresis (PFGE) after the cells had been exposed on membrane filters to a variety of energetic heavy ions with values of linear energy transfer (LET) ranging from about 2 to 11,500 keV/microm, (241)Am alpha particles, and 80 keV X rays. After irradiation, the cells were lysed, and the chromosomes were separated by PFGE. The gels were stained with ethidium bromide, placed on a UV transilluminator, and analyzed using a computer-coupled camera. The fluorescence intensities of the larger bands were found to decrease exponentially with dose or particle fluence. The slope of this line corresponds to the cross section for at least one double-strand break (DSB), but closely spaced multiple breaks cannot be discriminated. Based on the known size of the native DNA molecules, breakage cross sections per base pair were calculated. They increased with LET until they reached a transient plateau value of about 6 x 10(-7) microm(2) at about 300-2000 keV/microm; they then rose for the higher LETs, probably reflecting the influence of delta electrons. The relative biological effectiveness for DNA breakage displays a maximum of about 2.5 around 100-200 keV/microm and falls below unity for LET values above 10(3) keV/microm. For these yeast cells, comparison of the derived breakage cross sections with the corresponding cross section for inactivation derived from the terminal slope of the survival curves shows a strong linear relationship between these cross sections, extending over several orders of magnitude.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Update on Bayesian Blocks: Segmented Models for Sequential Data

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2017-01-01

The Bayesian Block algorithm, in wide use in astronomy and other areas, has been improved in several ways. The model for block shape has been generalized to include other than constant signal rate - e.g., linear, exponential, or other parametric models. In addition the computational efficiency has been improved, so that instead of O(N**2) the basic algorithm is O(N) in most cases. Other improvements in the theory and application of segmented representations will be described.

A Fifth-order Symplectic Trigonometrically Fitted Partitioned Runge-Kutta Method

NASA Astrophysics Data System (ADS)

Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.

2007-09-01

Trigonometrically fitted symplectic Partitioned Runge Kutta (EFSPRK) methods for the numerical integration of Hamoltonian systems with oscillatory solutions are derived. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions sin(wx),cos(wx), w∈R. We modify a fifth order symplectic PRK method with six stages so to derive an exponentially fitted SPRK method. The methods are tested on the numerical integration of the two body problem.

Amplification of nonlinear surface waves by wind

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

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.

Multi-hadron spectroscopy in a large physical volume

NASA Astrophysics Data System (ADS)

Bulava, John; Hörz, Ben; Morningstar, Colin

2018-03-01

We demonstrate the effcacy of the stochastic LapH method to treat all-toall quark propagation on a Nf = 2 + 1 CLS ensemble with large linear spatial extent L = 5:5 fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Modeling the dynamics of a phreatic eruption based on a tilt observation: Barrier breakage leading to the 2014 eruption of Mount Ontake, Japan

NASA Astrophysics Data System (ADS)

Maeda, Yuta; Kato, Aitaro; Yamanaka, Yoshiko

2017-02-01

Although phreatic eruptions are common volcanic phenomena that sometimes result in significant disasters, their dynamics are poorly understood. In this study, we address the dynamics of the phreatic eruption of Mount Ontake, Japan, in 2014 based on analyses of a tilt change observed immediately (450 s) before the eruption onset. We conducted two sets of analysis: a waveform inversion and a modified phase-space analysis. Our waveform inversion of the tilt signal points to a vertical tensile crack at a depth of 1100 m. Our modified phase-space analysis suggests that the tilt change was at first a linear function in time that then switched to exponential growth. We constructed simple analytical models to explain these temporal functions. The linear function was explained by the boiling of underground water controlled by a constant heat supply from a greater depth. The exponential function was explained by the decompression-induced boiling of water and the upward Darcy flow of the water vapor through a permeable region of small cracks that were newly created in response to ongoing boiling. We interpret that this region was intact prior to the start of the tilt change, and thus, it has acted as a permeability barrier for the upward migration of fluids; it was a breakage of this barrier that led to the eruption.

[Canopy interception of sub-alpine dark coniferous communities in western Sichuan, China].

PubMed

Lü, Yu-liang; Liu, Shi-rong; Sun, Peng-sen; Liu, Xing-liang; Zhang, Rui-pu

2007-11-01

Based on field measurements of throughfall and stemflow in combination with climatic data collected from the meteorological station adjacent to the studied sub-alpine dark coniferous forest in Wolong, Sichuan Province, canopy interception of sub-alpine dark coniferous forests was analyzed and modeled at both stand scale and catchment scale. The results showed that monthly interception rate of Fargesia nitida, Bashania fangiana--Abies faxoniana old-growth ranged from 33% Grass to 72%, with the average of 48%. In growing season, there was a linear or powerful or exponential relationship between rainfall and interception an. a negative exponential relationship between rainfall and interception rate. The mean maximum canopy interception by the vegetation in the catchment of in.44 km was 1.74 ment and the significant differences among the five communities occurred in the following sequence: Moss-Fargesia nitida, Bashan afanglana-A. faxoniana stand > Grass-F. nitida, B. fangiana-A. faxoniana stand > Moss-Rhododendron spp.-A. faxoniana stand > Grass-Rh. spp.-A. faxoniana stand > Rh. spp. shrub. In addition, a close linear relationship existed between leaf area index (LAI) and maximum canopy interception. The simulated value of canopy interception rate, maximum canopy interception rate and addition interception rate of the vegetation in the catchment were 39%, 25% and 14%, respectively. Simulation of the canopy interception model was better at the overall growing season scale, that the mean relative error was 9%-14%.

Collective behavior of networks with linear (VLSI) integrate-and-fire neurons.

PubMed

Fusi, S; Mattia, M

1999-04-01

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids.

PubMed

Ferrás, L L; Afonso, A M; Alves, M A; Nóbrega, J M; Pinho, F T

2014-04-15

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Experimental and theoretical investigation of temperature effects on an interbedded betavoltaic employing epitaxial Si and bidirectional (63)Ni.

PubMed

Liu, Yunpeng; Tang, Xiaobin; Xu, Zhiheng; Hong, Liang; Chen, Da

2014-12-01

The performance of an interbedded betavoltaic employing epitaxial Si and bidirectional (63)Ni was measured and calculated at various temperatures. The experimental results indicate that the temperature dependence of the performance of interbedded betavoltaics is similar to that of monolayer betavoltaics: Voc and Pmax decrease approximately linearly with increasing temperature at low temperatures of 213.15-253.15K and decrease exponentially with increasing temperature at high temperatures of 253.15-333.15K. However, the calculation results indicate that the temperature dependences of Voc and Pmax are always linear at both high and low temperatures. Isc increases slightly with increasing temperature in both experiment and calculation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Off-resonance energy absorption in a linear Paul trap due to mass selective resonant quenching

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

Sivarajah, I.; Goodman, D. S.; Wells, J. E.

Linear Paul traps (LPT) are used in many experimental studies such as mass spectrometry, atom-ion collisions, and ion-molecule reactions. Mass selective resonant quenching (MSRQ) is implemented in LPT either to identify a charged particle's mass or to remove unwanted ions from a controlled experimental environment. In the latter case, MSRQ can introduce undesired heating to co-trapped ions of different mass, whose secular motion is off resonance with the quenching ac field, which we call off-resonance energy absorption (OREA). We present simulations and experimental evidence that show that the OREA increases exponentially with the number of ions loaded into the trapmore » and with the amplitude of the off-resonance external ac field.« less

Effects of resonant magnetic perturbation on the triggering and the evolution of double-tearing mode

NASA Astrophysics Data System (ADS)

Wang, L.; Lin, W. B.; Wang, X. Q.

2018-02-01

The effects of resonant magnetic perturbation on the triggering and the evolution of the double-tearing mode are investigated by using nonlinear magnetohydrodynamics simulations in a slab geometry. It is found that the double-tearing mode can be destabilized by boundary magnetic perturbation. Moreover, the mode has three typical development stages before it reaches saturation: the linear stable stage, the linear-growth stage, and the exponential-growth stage. The onset and growth of the double-tearing mode significantly depend on the boundary magnetic perturbations, particularly in the early development stage of the mode. The influences of the magnetic perturbation amplitude on the mode for different separations of the two rational surfaces are also discussed.

A guidance and navigation system for continuous low-thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Jack-Chingtse, C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

The effective supergravity of little string theory

NASA Astrophysics Data System (ADS)

Antoniadis, Ignatios; Delgado, Antonio; Markou, Chrysoula; Pokorski, Stefan

2018-02-01

In this work we present the minimal supersymmetric extension of the five-dimensional dilaton-gravity theory that captures the main properties of the holographic dual of little string theory. It is described by a particular gauging of N=2 supergravity coupled with one vector multiplet associated with the string dilaton, along the U(1) subgroup of SU(2) R-symmetry. The linear dilaton in the fifth coordinate solution of the equations of motion (with flat string frame metric) breaks half of the supersymmetries to N=1 in four dimensions. Interest in the linear dilaton model has lately been revived in the context of the clockwork mechanism, which has recently been proposed as a new source of exponential scale separation in field theory.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Stand Competition Determines How Different Tree Species Will Cope with a Warming Climate

PubMed Central

Fernández-de-Uña, Laura; Cañellas, Isabel; Gea-Izquierdo, Guillermo

2015-01-01

Plant-plant interactions influence how forests cope with climate and contribute to modulate species response to future climate scenarios. We analysed the functional relationships between growth, climate and competition for Pinus sylvestris, Quercus pyrenaica and Quercus faginea to investigate how stand competition modifies forest sensitivity to climate and simulated how annual growth rates of these species with different drought tolerance would change throughout the 21st century. Dendroecological data from stands subjected to thinning were modelled using a novel multiplicative nonlinear approach to overcome biases related to the general assumption of a linear relationship between covariates and to better mimic the biological relationships involved. Growth always decreased exponentially with increasing competition, which explained more growth variability than climate in Q. faginea and P. sylvestris. The effect of precipitation was asymptotic in all cases, while the relationship between growth and temperature reached an optimum after which growth declined with warmer temperatures. Our growth projections indicate that the less drought-tolerant P. sylvestris would be more negatively affected by climate change than the studied sub-Mediterranean oaks. Q. faginea and P. sylvestris mean growth would decrease under all the climate change scenarios assessed. However, P. sylvestris growth would decline regardless of the competition level, whereas this decrease would be offset by reduced competition in Q. faginea. Conversely, Q. pyrenaica growth would remain similar to current rates, except for the warmest scenario. Our models shed light on the nature of the species-specific interaction between climate and competition and yield important implications for management. Assuming that individual growth is directly related to tree performance, trees under low competition would better withstand the warmer conditions predicted under climate change scenarios but in a variable manner depending on the species. Thinning following an exponential rule may be desirable to ensure long-term conservation of high-density Mediterranean woodlands, particularly in drought-limited sites. PMID:25826446

Quantitative Interaction Effects of Carbon Dioxide, Sodium Chloride, and Sodium Nitrite on Neurotoxin Gene Expression in Nonproteolytic Clostridium botulinum Type B

PubMed Central

Lövenklev, Maria; Artin, Ingrid; Hagberg, Oskar; Borch, Elisabeth; Holst, Elisabet; Rådström, Peter

2004-01-01

The effects of carbon dioxide, sodium chloride, and sodium nitrite on type B botulinum neurotoxin (BoNT/B) gene (cntB) expression in nonproteolytic Clostridium botulinum were investigated in a tryptone-peptone-yeast extract (TPY) medium. Various concentrations of these selected food preservatives were studied by using a complete factorial design in order to quantitatively study interaction effects, as well as main effects, on the following responses: lag phase duration (LPD), growth rate, relative cntB expression, and extracellular BoNT/B production. Multiple linear regression was used to set up six statistical models to quantify and predict these responses. All combinations of NaCl and NaNO2 in the growth medium resulted in a prolonged lag phase duration and in a reduction in the specific growth rate. In contrast, the relative BoNT/B gene expression was unchanged, as determined by the cntB-specific quantitative reverse transcription-PCR method. This was confirmed when we measured the extracellular BoNT/B concentration by an enzyme-linked immunosorbent assay. CO2 was found to have a major effect on gene expression when the cntB mRNA levels were monitored in the mid-exponential, late exponential, and late stationary growth phases. The expression of cntB relative to the expression of the 16S rRNA gene was stimulated by an elevated CO2 concentration; the cntB mRNA level was fivefold greater in a 70% CO2 atmosphere than in a 10% CO2 atmosphere. These findings were also confirmed when we analyzed the extracellular BoNT/B concentration; we found that the concentrations were 27 ng · ml−1 · unit of optical density−1 in the 10% CO2 atmosphere and 126 ng · ml−1 · unit of optical density−1 in the 70% CO2 atmosphere. PMID:15128553

MULTIVARIATE LINEAR MIXED MODELS FOR MULTIPLE OUTCOMES. (R824757)

EPA Science Inventory

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of ...

A de Sitter tachyon thick braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

2013-02-01

Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations — derived from the model with a warped 5D geometry — are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalarmore » field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a single zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter H. Finally, the corrections to Newton's law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.« less

Deconstructing the Alcohol Harm Paradox: A Population Based Survey of Adults in England

PubMed Central

Beard, Emma; Brown, Jamie; West, Robert; Angus, Colin; Brennan, Alan; Holmes, John; Kaner, Eileen; Meier, Petra; Michie, Susan

2016-01-01

Background The Alcohol Harm Paradox refers to observations that lower socioeconomic status (SES) groups consume less alcohol but experience more alcohol-related problems. However, SES is a complex concept and its observed relationship to social problems often depends on how it is measured and the demographic groups studied. Thus this study assessed socioeconomic patterning of alcohol consumption and related harm using multiple measures of SES and examined moderation of this patterning by gender and age. Method Data were used from the Alcohol Toolkit Study between March and September 2015 on 31,878 adults (16+) living in England. Participants completed the AUDIT which includes alcohol consumption, harm and dependence modules. SES was measured via qualifications, employment, home and car ownership, income and social-grade, plus a composite of these measures. The composite score was coded such that higher scores reflected greater social-disadvantage. Results We observed the Alcohol Harm Paradox for the composite SES measure, with a linear negative relationship between SES and AUDIT-Consumption scores (β = -0.036, p<0.001) and a positive relationship between lower SES and AUDIT-Harm (β = 0.022, p<0.001) and AUDIT-Dependence (β = 0.024, p<0.001) scores. Individual measures of SES displayed different, and non-linear, relationships with AUDIT modules. For example, social-grade and income had a u-shaped relationship with AUDIT-Consumption scores while education had an inverse u-shaped relationship. Almost all measures displayed an exponential relationship with AUDIT-Dependence and AUDIT-Harm scores. We identified moderating effects from age and gender, with AUDIT-Dependence scores increasing more steeply with lower SES in men and both AUDIT-Harm and AUDIT-Dependence scores increasing more steeply with lower SES in younger age groups. Conclusion Different SES measures appear to influence whether the Alcohol Harm Paradox is observed as a linear trend across SES groups or a phenomenon associated particularly with the most disadvantaged. The paradox also appears more concentrated in men and younger age groups. PMID:27682619

Labeling Actors and Uncovering Causal Accounts of Their States in Social Networks and Social Media

ERIC Educational Resources Information Center

Bui, Ngot P.

2016-01-01

The emergence of social networks and social media has resulted in exponential increase in the amount of data that link diverse types of richly structured digital objects e.g., individuals, articles, images, videos, music, etc. Such data are naturally represented as heterogeneous networks with multiple types of objects e.g., actors, video,…

Continuous-Time Finance and the Waiting Time Distribution: Multiple Characteristic Times

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2012-09-01

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.

PubMed

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution P(Q)(r) of the interoccurrence times r between losses below a negative threshold -Q, for fixed mean interoccurrence times R(Q) in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, P(Q)(r)∝1/{[1+(q-1)βr](1/(q-1))}. We propose that the asset- and time-scale-independent analytic form of P(Q)(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution P(Q)(r) as well as the autocorrelation C(Q)(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of P(Q)(r) and the power-law decay of C(Q)(s).

An Optimization of Inventory Demand Forecasting in University Healthcare Centre

NASA Astrophysics Data System (ADS)

Bon, A. T.; Ng, T. K.

2017-01-01

Healthcare industry becomes an important field for human beings nowadays as it concerns about one’s health. With that, forecasting demand for health services is an important step in managerial decision making for all healthcare organizations. Hence, a case study was conducted in University Health Centre to collect historical demand data of Panadol 650mg for 68 months from January 2009 until August 2014. The aim of the research is to optimize the overall inventory demand through forecasting techniques. Quantitative forecasting or time series forecasting model was used in the case study to forecast future data as a function of past data. Furthermore, the data pattern needs to be identified first before applying the forecasting techniques. Trend is the data pattern and then ten forecasting techniques are applied using Risk Simulator Software. Lastly, the best forecasting techniques will be find out with the least forecasting error. Among the ten forecasting techniques include single moving average, single exponential smoothing, double moving average, double exponential smoothing, regression, Holt-Winter’s additive, Seasonal additive, Holt-Winter’s multiplicative, seasonal multiplicative and Autoregressive Integrated Moving Average (ARIMA). According to the forecasting accuracy measurement, the best forecasting technique is regression analysis.

Universal behavior of the interoccurrence times between losses in financial markets: Independence of the time resolution

NASA Astrophysics Data System (ADS)

Ludescher, Josef; Bunde, Armin

2014-12-01

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution PQ(r ) of the interoccurrence times r between losses below a negative threshold -Q , for fixed mean interoccurrence times RQ in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, PQ(r ) ∝1 /{[1+(q -1 ) β r ] 1 /(q -1 )} . We propose that the asset- and time-scale-independent analytic form of PQ(r ) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution PQ(r ) as well as the autocorrelation CQ(s ) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q -exponential form of PQ(r ) and the power-law decay of CQ(s ) .

From webs to polylogarithms

NASA Astrophysics Data System (ADS)

Gardi, Einan

2014-04-01

We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1 /α ij , at the level of the symbol the result also admits a crossing symmetry α ij → - α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis.

PubMed

Marchand, A J; Hitti, E; Monge, F; Saint-Jalmes, H; Guillin, R; Duvauferrier, R; Gambarota, G

2014-11-01

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg-Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10(-3) mm(2)/s), D*=28±9 (10(-3) mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10(-3) mm2/s), D*=63±145 (10(-3) mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior. Copyright © 2014 Elsevier Inc. All rights reserved.

Rimonabant reduces the essential value of food in the genetically obese Zucker rat: an exponential demand analysis.

PubMed

Rasmussen, Erin B; Reilly, William; Buckley, Jessica; Boomhower, Steven R

2012-02-01

Research on free-food intake suggests that cannabinoids are implicated in the regulation of feeding. Few studies, however, have characterized how environmental factors that affect food procurement interact with cannabinoid drugs that reduce food intake. Demand analysis provides a framework to understand how cannabinoid blockers, such as rimonabant, interact with effort in reducing demand for food. The present study examined the effects rimonabant had on demand for sucrose in obese Zucker rats when effort to obtain food varied and characterized the data using the exponential ("essential value") model of demand. Twenty-nine male (15 lean, 14 obese) Zucker rats lever-pressed under eight fixed ratio (FR) schedules of sucrose reinforcement, in which the number of lever-presses to gain access to a single sucrose pellet varied between 1 and 300. After behavior stabilized under each FR schedule, acute doses of rimonabant (1-10mg/kg) were administered prior to some sessions. The number of food reinforcers and responses in each condition was averaged and the exponential and linear demand equations were fit to the data. These demand equations quantify the value of a reinforcer by its sensitivity to price (FR) increases. Under vehicle conditions, obese Zucker rats consumed more sucrose pellets than leans at smaller fixed ratios; however, they were equally sensitive to price increases with both models of demand. Rimonabant dose-dependently reduced reinforcers and responses for lean and obese rats across all FR schedules. Data from the exponential analysis suggest that rimonabant dose-dependently increased elasticity, i.e., reduced the essential value of sucrose, a finding that is consistent with graphical depictions of normalized demand curves. Copyright © 2011 Elsevier Inc. All rights reserved.

Attractors of three-dimensional fast-rotating Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Trahe, Markus

The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.

A UNIVERSAL NEUTRAL GAS PROFILE FOR NEARBY DISK GALAXIES

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

Bigiel, F.; Blitz, L., E-mail: bigiel@uni-heidelberg.de

2012-09-10

Based on sensitive CO measurements from HERACLES and H I data from THINGS, we show that the azimuthally averaged radial distribution of the neutral gas surface density ({Sigma}{sub HI}+ {Sigma}{sub H2}) in 33 nearby spiral galaxies exhibits a well-constrained universal exponential distribution beyond 0.2 Multiplication-Sign r{sub 25} (inside of which the scatter is large) with less than a factor of two scatter out to two optical radii r{sub 25}. Scaling the radius to r{sub 25} and the total gas surface density to the surface density at the transition radius, i.e., where {Sigma}{sub HI} and {Sigma}{sub H2} are equal, as wellmore » as removing galaxies that are interacting with their environment, yields a tightly constrained exponential fit with average scale length 0.61 {+-} 0.06 r{sub 25}. In this case, the scatter reduces to less than 40% across the optical disks (and remains below a factor of two at larger radii). We show that the tight exponential distribution of neutral gas implies that the total neutral gas mass of nearby disk galaxies depends primarily on the size of the stellar disk (influenced to some degree by the great variability of {Sigma}{sub H2} inside 0.2 Multiplication-Sign r{sub 25}). The derived prescription predicts the total gas mass in our sub-sample of 17 non-interacting disk galaxies to within a factor of two. Given the short timescale over which star formation depletes the H{sub 2} content of these galaxies and the large range of r{sub 25} in our sample, there appears to be some mechanism leading to these largely self-similar radial gas distributions in nearby disk galaxies.« less

Effects of correlations and fees in random multiplicative environments: Implications for portfolio management.

PubMed

Alper, Ofer; Somekh-Baruch, Anelia; Pirvandy, Oz; Schaps, Malka; Yaari, Gur

2017-08-01

Geometric Brownian motion (GBM) is frequently used to model price dynamics of financial assets, and a weighted average of multiple GBMs is commonly used to model a financial portfolio. Diversified portfolios can lead to an increased exponential growth compared to a single asset by effectively reducing the effective noise. The sum of GBM processes is no longer a log-normal process and has a complex statistical properties. The nonergodicity of the weighted average process results in constant degradation of the exponential growth from the ensemble average toward the time average. One way to stay closer to the ensemble average is to maintain a balanced portfolio: keep the relative weights of the different assets constant over time. To keep these proportions constant, whenever assets values change, it is necessary to rebalance their relative weights, exposing this strategy to fees (transaction costs). Two strategies that were suggested in the past for cases that involve fees are rebalance the portfolio periodically and rebalance it in a partial way. In this paper, we study these two strategies in the presence of correlations and fees. We show that using periodic and partial rebalance strategies, it is possible to maintain a steady exponential growth while minimizing the losses due to fees. We also demonstrate how these redistribution strategies perform in a phenomenal way on real-world market data, despite the fact that not all assumptions of the model hold in these real-world systems. Our results have important implications for stochastic dynamics in general and to portfolio management in particular, as we show that there is a superior alternative to the common buy-and-hold strategy, even in the presence of correlations and fees.

Effects of correlations and fees in random multiplicative environments: Implications for portfolio management

NASA Astrophysics Data System (ADS)

Alper, Ofer; Somekh-Baruch, Anelia; Pirvandy, Oz; Schaps, Malka; Yaari, Gur

2017-08-01

Geometric Brownian motion (GBM) is frequently used to model price dynamics of financial assets, and a weighted average of multiple GBMs is commonly used to model a financial portfolio. Diversified portfolios can lead to an increased exponential growth compared to a single asset by effectively reducing the effective noise. The sum of GBM processes is no longer a log-normal process and has a complex statistical properties. The nonergodicity of the weighted average process results in constant degradation of the exponential growth from the ensemble average toward the time average. One way to stay closer to the ensemble average is to maintain a balanced portfolio: keep the relative weights of the different assets constant over time. To keep these proportions constant, whenever assets values change, it is necessary to rebalance their relative weights, exposing this strategy to fees (transaction costs). Two strategies that were suggested in the past for cases that involve fees are rebalance the portfolio periodically and rebalance it in a partial way. In this paper, we study these two strategies in the presence of correlations and fees. We show that using periodic and partial rebalance strategies, it is possible to maintain a steady exponential growth while minimizing the losses due to fees. We also demonstrate how these redistribution strategies perform in a phenomenal way on real-world market data, despite the fact that not all assumptions of the model hold in these real-world systems. Our results have important implications for stochastic dynamics in general and to portfolio management in particular, as we show that there is a superior alternative to the common buy-and-hold strategy, even in the presence of correlations and fees.

Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News

NASA Astrophysics Data System (ADS)

Handmer, Casey; Szilagyi, Bela; Winicour, Jeff

2015-04-01

We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries.

PREdator: a python based GUI for data analysis, evaluation and fitting

PubMed Central

2014-01-01

The analysis of a series of experimental data is an essential procedure in virtually every field of research. The information contained in the data is extracted by fitting the experimental data to a mathematical model. The type of the mathematical model (linear, exponential, logarithmic, etc.) reflects the physical laws that underlie the experimental data. Here, we aim to provide a readily accessible, user-friendly python script for data analysis, evaluation and fitting. PREdator is presented at the example of NMR paramagnetic relaxation enhancement analysis.

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Exceptional point in a simple textbook example

NASA Astrophysics Data System (ADS)

Fernández, Francisco M.

2018-07-01

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

The growth rate of vertex-transitive planar graphs

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

Babai, L.

1997-06-01

A graph is vertex-transitive if all of its vertices axe equivalent under automorphisms. Confirming a conjecture of Jon Kleinberg and Eva Tardos, we prove the following trichotomy theorem concerning locally finite vertex-transitive planar graphs: the rate of growth of a graph with these properties is either linear or quadratic or exponential. The same result holds more generally for locally finite, almost vertex-transitive planar graphs (the automorphism group has a finite number of orbits). The proof uses the elements of hyperbolic plane geometry.

STOCK Mechanics:. a General Theory and Method of Energy Conservation with Applications on Djia

NASA Astrophysics Data System (ADS)

Tuncay, Çağlar

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on the Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e., positive definite quadratic, negative definite quadratic and linear potential energy for exponential rises (and falls), sinusoidal oscillations and parabolic trajectories, respectively. Corresponding expressions for force (impact) are also given.

Asymptotic stability estimates near an equilibrium point

NASA Astrophysics Data System (ADS)

Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2017-07-01

We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.

Confining potential in momentum space

NASA Technical Reports Server (NTRS)

Norbury, John W.; Kahana, David E.; Maung, Khin Maung

1992-01-01

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

Transition records of stationary Markov chains.

PubMed

Naudts, Jan; Van der Straeten, Erik

2006-10-01

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Lin, C. A.

1985-01-01

The tracking and disturbance rejection of a class of MIMO nonlinear systems with a linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Lin, C.-A.

1985-01-01

The tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Koopman Mode Decomposition Methods in Dynamic Stall: Reduced Order Modeling and Control

DTIC Science & Technology

2015-11-10

the flow phenomena by separating them into individual modes. The technique of Proper Orthogonal Decomposition (POD), see [ Holmes : 1998] is a popular...sampled values h(k), k = 0,…,2M-1, of the exponential sum 1. Solve the following linear system where 2. Compute all zeros zj  D, j = 1,…,M...of the Prony polynomial i.e., calculate all eigenvalues of the associated companion matrix and form fj = log zj for j = 1,…,M, where log is the

Nonlinear dust-lattice waves: a modified Toda lattice

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

Cramer, N. F.

Charged dust grains in a plasma interact with a Coulomb potential, but also with an exponential component to the potential, due to Debye shielding in the background plasma. Here we investigate large-amplitude oscillations and waves in dust-lattices, employing techniques used in Toda lattice analysis. The lattice consists of a linear chain of particles, or a periodic ring as occurs in experimentally observed dust particle clusters. The particle motion has a triangular waveform, and chaotic motion for large amplitude motion of a grain.

General job stress: a unidimensional measure and its non-linear relations with outcome variables.

PubMed

Yankelevich, Maya; Broadfoot, Alison; Gillespie, Jennifer Z; Gillespie, Michael A; Guidroz, Ashley

2012-04-01

This article aims to examine the non-linear relations between a general measure of job stress [Stress in General (SIG)] and two outcome variables: intentions to quit and job satisfaction. In so doing, we also re-examine the factor structure of the SIG and determine that, as a two-factor scale, it obscures non-linear relations with outcomes. Thus, in this research, we not only test for non-linear relations between stress and outcome variables but also present an updated version of the SIG scale. Using two distinct samples of working adults (sample 1, N = 589; sample 2, N = 4322), results indicate that a more parsimonious eight-item SIG has better model-data fit than the 15-item two-factor SIG and that the eight-item SIG has non-linear relations with job satisfaction and intentions to quit. Specifically, the revised SIG has an inverted curvilinear J-shaped relation with job satisfaction such that job satisfaction drops precipitously after a certain level of stress; the SIG has a J-shaped curvilinear relation with intentions to quit such that turnover intentions increase exponentially after a certain level of stress. Copyright © 2011 John Wiley & Sons, Ltd.

Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

DOE PAGES

Michalak, Sarah E.; Morris, Carl N.

2015-07-17

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonlymore » used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).« less

Vortex creep and the internal temperature of neutron stars - Linear and nonlinear response to a glitch

NASA Technical Reports Server (NTRS)

Alpar, M. A.; Cheng, K. S.; Pines, D.

1989-01-01

The dynamics of pinned superfluid in neutron stars is determined by the thermal 'creep' of vortices. Vortex creep can respond to changes in the rotation rate of the neutron star crust and provide the observed types of dynamical relaxation following pulsar glitches. It also gives rise to energy dissipation, which determines the thermal evolution of pulsars once the initial heat content has been radiated away. The different possible regimes of vortex creep are explored, and it is shown that the nature of the dynamical response of the pinned superfluid evolves with a pulsar's age. Younger pulsars display a linear regime, where the response is linear in the initial perturbation and is a simple exponential relaxation as a function of time. A nonliner response, with a characteristic nonlinear dependence on the initial perturbation, is responsible for energy dissipation and becomes the predominant mode of response as the pulsar ages. The transition from the linear to the nonlinear regime depends sensitively on the temperature of the neutron star interior. A preliminary review of existing postglitch observations is given within this general evolutionary framework.

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

Quantum Linear System Algorithm for Dense Matrices

NASA Astrophysics Data System (ADS)

Wossnig, Leonard; Zhao, Zhikuan; Prakash, Anupam

2018-02-01

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix A and a vector b the task is to find the vector x such that A x =b . We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of O (κ2√{n }polylog(n )/ɛ ) for an n ×n dimensional A with bounded spectral norm, where κ denotes the condition number of A , and ɛ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of A is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of A and the vector of Euclidean norms of the rows of A .

Inhomogeneous growth of fluctuations of concentration of inertial particles in channel turbulence

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Schmidt, Lukas; Ditlevsen, Peter; van Reeuwijk, Maarten; Holzner, Markus

2018-06-01

We study the growth of concentration fluctuations of weakly inertial particles in the turbulent channel flow starting with a smooth initial distribution. The steady-state concentration is singular and multifractal so the growth describes the increasingly rugged structure of the distribution. We demonstrate that inhomogeneity influences the growth of concentration fluctuations profoundly. For homogeneous turbulence the growth is exponential and is fully determined by Kolmogorov scale eddies.We derive lognormality of the statistics in this case. The growth exponents of the moments are proportional to the sum of Lyapunov exponents, which is quadratic in the small inertia of the particles. In contrast, for inhomogeneous turbulence the growth is linear in inertia. It involves correlations of inertial range and viscous scale eddies that turn the growth into a stretched exponential law with exponent three halves. We demonstrate using direct numerical simulations that the resulting growth rate can differ by orders of magnitude over channel height. This strong variation might have relevance in the planetary boundary layer.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

Rogue Waves for a (2+1)-Dimensional Coupled Nonlinear Schrödinger System with Variable Coefficients in a Graded-Index Waveguide

NASA Astrophysics Data System (ADS)

Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Yuan, Yu-Qiang

2018-05-01

Studied in this paper is a (2+1)-dimensional coupled nonlinear Schrödinger system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-I and type-II rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves. When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach.

PubMed

Huang, Chuangxia; Cao, Jie; Cao, Jinde

2016-10-01

This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Studies on color-center formation in glass utilizing measurements made during 1 to 3 MeV electron irradiation

NASA Technical Reports Server (NTRS)

Swyler, K. J.; Levy, P. W.

1976-01-01

The coloring of NBS 710 glass was studied using a facility for making optical absorption measurements during and after electron irradiation. The induced absorption contains three Gaussian shaped bands. The color center growth curves contain two saturating exponential and one linear components. After irradiation the coloring decays can be described by three decreasing exponentials. At room temperature both the coloring curve plateau and coloring rate increases with increasing dose rate. Coloring measurements made at fixed dose rate but at increasing temperature indicate: (1) The coloring curve plateau decreases with increasing temperature and coloring is barely measurable near 400 C. (2) The plateau is reached more rapidly as the temperature increases. (3) The decay occurring after irradiation cannot be described by Arrhenius kinetics. At each temperature the coloring can be explained by simple kinetics. The temperature dependence of the decay can be explained if it is assumed that the thermal untrapping is controlled by a distribution of activation energies.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

Determination of relationship between sensory viscosity rating and instrumental flow behaviour of soluble dietary fibers.

PubMed

Arora, Simran Kaur; Patel, A A; Kumar, Naveen; Chauhan, O P

2016-04-01

The shear-thinning low, medium and high-viscosity fiber preparations (0.15-1.05 % psyllium husk, 0.07-0.6 % guar gum, 0.15-1.20 % gum tragacanth, 0.1-0.8 % gum karaya, 0.15-1.05 % high-viscosity Carboxy Methyl Cellulose and 0.1-0.7 % xanthan gum) showed that the consistency coefficient (k) was a function of concentration, the relationship being exponential (R(2), 0.87-0.96; P < 0.01). The flow behaviour index (n) (except for gum karaya and CMC) was exponentially related to concentration (R(2), 0.61-0.98). The relationship between k and sensory viscosity rating (SVR) was essentially linear in nearly all cases. The SVR could be predicted from the consistency coefficient using the regression equations developed. Also, the relationship of k with fiber concentration would make it possible to identify the concentration of a particular gum required to have desired consistency in terms of SVR.

Rainbow net analysis of VAXcluster system availability

NASA Technical Reports Server (NTRS)

Johnson, Allen M., Jr.; Schoenfelder, Michael A.

1991-01-01

A system modeling technique, Rainbow Nets, is used to evaluate the availability and mean-time-to-interrupt of the VAXcluster. These results are compared to the exact analytic results showing that reasonable accuracy is achieved through simulation. The complexity of the Rainbow Net does not increase as the number of processors increases, but remains constant, unlike a Markov model which expands exponentially. The constancy is achieved by using tokens with identity attributes (items) that can have additional attributes associated with them (features) which can exist in multiple states. The time to perform the simulation increases, but this is a polynomial increase rather than exponential. There is no restriction on distributions used for transition firing times, allowing real situations to be modeled more accurately by choosing the distribution which best fits the system performance and eliminating the need for simplifying assumptions.

Double closed-loop control of integrated optical resonance gyroscope with mean-square exponential stability.

PubMed

Li, Hui; Liu, Liying; Lin, Zhili; Wang, Qiwei; Wang, Xiao; Feng, Lishuang

2018-01-22

A new double closed-loop control system with mean-square exponential stability is firstly proposed to optimize the detection accuracy and dynamic response characteristic of the integrated optical resonance gyroscope (IORG). The influence mechanism of optical nonlinear effects on system detection sensitivity is investigated to optimize the demodulation gain, the maximum sensitivity and the linear work region of a gyro system. Especially, we analyze the effect of optical parameter fluctuation on the parameter uncertainty of system, and investigate the influence principle of laser locking-frequency noise on the closed-loop detection accuracy of angular velocity. The stochastic disturbance model of double closed-loop IORG is established that takes the unfavorable factors such as optical effect nonlinearity, disturbed disturbance, optical parameter fluctuation and unavoidable system noise into consideration. A robust control algorithm is also designed to guarantee the mean-square exponential stability of system with a prescribed H ∞ performance in order to improve the detection accuracy and dynamic performance of IORG. The conducted experiment results demonstrate that the IORG has a dynamic response time less than 76us, a long-term bias stability 7.04°/h with an integration time of 10s over one-hour test, and the corresponding bias stability 1.841°/h based on Allan deviation, which validate the effectiveness and usefulness of the proposed detection scheme.

On the hardness of high carbon ferrous martensite

NASA Astrophysics Data System (ADS)

Mola, J.; Ren, M.

2018-06-01

Due to the presence of retained austenite in martensitic steels, especially steels with high carbon concentrations, it is difficult to estimate the hardness of martensite independent of the hardness of the coexisting austenite. In the present work, the hardness of ferrous martensite with carbon concentrations in the range 0.23-1.46 mass-% was estimated by the regression analysis of hardnesses for hardened martensitic-austenitic steels containing various martensite fractions. For a given carbon concentration, the hardness of martensitic-austenitic steels was found to increase exponentially with an increase in the fraction of the martensitic constituent. The hardness of the martensitic constituent was subsequently estimated by the exponential extrapolation of the hardness of phase mixtures to 100 vol.% martensite. For martensite containing 1.46 mass-% carbon, the hardness was estimated to be 1791 HV. This estimate of martensite hardness is significantly higher than the experimental hardness of 822 HV for a phase mixture of 68 vol.% martensite and 32 vol.% austenite. The hardness obtained by exponential extrapolation is also much higher than the hardness of 1104 HV based on the rule of mixtures. The underestimated hardness of high carbon martensite in the presence of austenite is due to the non-linear dependence of hardness on the martensite fraction. The latter is also a common observation in composite materials with a soft matrix and hard reinforcing particles.

Polypeptide multilayer films on colloidal particles: an in situ electro-optical study.

PubMed

Radeva, Tsetska; Kamburova, Kamelia

2007-04-15

The buildup of poly(L-glutamic acid) (PGA) and poly(L-lysine) (PLL) multilayers on beta-FeOOH colloidal particles was investigated by means of electro-optics and electrophoresis. The films were built at different (acidic) pH in the absence of salt. We found that the thickness of the film grows linearly when the fully charged PLL (at pH 5.5) is combined with almost fully charged PGA (at pH 6.5), with a thickness of about 2 nm per single layer. When the fully charged PLL is combined with weakly charged PGA (at pH 4.5), the film thickness increases exponentially with the number of deposited layers. The thickness of the exponentially growing film increases to 300 nm after deposition of 16 layers. The exponential film growth is attributed to the ability of the PLL to diffuse "in" and "out" of the film bulk at each deposition step. The variation in the electrical polarizability of the film-coated particles was also monitored as a function of the number of adsorbed layers. The result reveals that the PLL chains, which can diffuse into the film bulk, have no measurable contribution to the electro-optical effect of the films terminated with PLL. It is only due to the polarization of counterions of the PLL adsorbed on the film surface.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

A FORTRAN program for multivariate survival analysis on the personal computer.

PubMed

Mulder, P G

1988-01-01

In this paper a FORTRAN program is presented for multivariate survival or life table regression analysis in a competing risks' situation. The relevant failure rate (for example, a particular disease or mortality rate) is modelled as a log-linear function of a vector of (possibly time-dependent) explanatory variables. The explanatory variables may also include the variable time itself, which is useful for parameterizing piecewise exponential time-to-failure distributions in a Gompertz-like or Weibull-like way as a more efficient alternative to Cox's proportional hazards model. Maximum likelihood estimates of the coefficients of the log-linear relationship are obtained from the iterative Newton-Raphson method. The program runs on a personal computer under DOS; running time is quite acceptable, even for large samples.

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

VizieR Online Data Catalog: HARPS timeseries data for HD41248 (Jenkins+, 2014)

NASA Astrophysics Data System (ADS)

Jenkins, J. S.; Tuomi, M.

2017-05-01

We modeled the HARPS radial velocities of HD 42148 by adopting the analysis techniques and the statistical model applied in Tuomi et al. (2014, arXiv:1405.2016). This model contains Keplerian signals, a linear trend, a moving average component with exponential smoothing, and linear correlations with activity indices, namely, BIS, FWHM, and chromospheric activity S index. We applied our statistical model outlined above to the full data set of radial velocities for HD 41248, combining the previously published data in Jenkins et al. (2013ApJ...771...41J) with the newly published data in Santos et al. (2014, J/A+A/566/A35), giving rise to a total time series of 223 HARPS (Mayor et al. 2003Msngr.114...20M) velocities. (1 data file).

Determining the optimal isoleucine:lysine ratio for ten- to twenty-two-kilogram and twenty-four- to thirty-nine-kilogram pigs fed diets containing nonexcess levels of leucine.

PubMed

Htoo, J K; Zhu, C L; Huber, L; de Lange, C F M; Quant, A D; Kerr, B J; Cromwell, G L; Lindemann, M D

2014-08-01

Three 21-d experiments were conducted to determine the optimum standardized ileal digestible (SID) Ile:Lys ratio in 10- to 22-kg and 24- to 39-kg pigs. In Exp. 1, 144 Yorkshire pigs (initial BW = 10.2 kg) were assigned to 6 diets with 6 pens per treatment. Diets 1 to 5 were formulated to contain 5 graded SID Ile:Lys (44, 51, 57, 63, and 70%), 1.18% SID Leu, and 0.90% SID Lys (second limiting). Diet 6 (diet 5 with added Lys) was formulated (1.06% SID Lys) as a positive control. Pigs fed diet 6 had higher (P < 0.05) ADG and G:F and lower (P < 0.05) plasma urea N (PUN) than pigs fed diet 5 (P < 0.02), indicating that Lys was limiting in diets 1 to 5. Final BW, ADG, and ADFI increased (linear and quadratic, P < 0.05) while G:F and PUN at d 21 were not affected (P > 0.10) by dietary Ile:Lys. Overall, ADG and ADFI were highest for pigs fed diet 2 (51% SID Ile:Lys). In Exp. 2, 216 Yorkshire pigs (initial BW = 9.6 kg) were assigned to 9 diets with 6 pens per treatment. Diets 1 to 4 contained 0.40, 0.47, 0.54, and 0.61% SID Ile, respectively, and 1.21% SID Lys; diets 5 to 8 contained 0.72, 0.84, 0.96, and 1.08% SID Lys, respectively, and 0.68% SID Ile. Diet 9 was high in both Ile and Lys (0.68% SID Ile and 1.21% SID Lys). All diets contained 1.21% SID Leu. The ADG and G:F increased (linear and quadratic, P < 0.05) as SID Ile:Lys increased (diets 1 to 4 and 9). The ADG and G:F increased (linear, P < 0.05) as SID Lys increased (diets 5 to 9). The PUN at d 21 decreased (linear, P < 0.05) by increasing dietary Ile:Lys. The SID Ile:Lys to optimize ADG was 46% by curvilinear plateau or exponential regression. For G:F, the optimal SID Ile:Lys was 47 and 51% by curvilinear plateau and exponential regressions, respectively. In Exp. 3, 80 pigs (PIC 327 × C23; initial BW = 24.0 kg) were allotted to 5 treatments with 4 pigs per pen. Diets 1 to 5 were formulated to contain 5 graded SID Ile:Lys (39, 46, 53, 61, and 68%), 1.17% SID Leu, and 0.91% SID Lys (second limiting). Final BW and ADG increased (linear and quadratic, P < 0.05) and ADFI increased (linear, P = 0.047) as SID Ile:Lys increased. Using ADG and G:F, the optimum SID Ile:Lys was 54 and 53%, respectively, by curvilinear plateau and exponential regression. The PUN was minimized at 53 and 59% SID Ile:Lys by curvilinear plateau and broken line regression. Overall, the average optimum SID Ile:Lys was approximately 51% for 10- to 22-kg pigs and 54% for 24- to 39-kg pigs fed diets containing nonexcess levels of Leu.