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

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

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

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

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1994-01-01

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

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

NASA Technical Reports Server (NTRS)

Armstrong, Jeffrey B.; Simon, Donald L.

2012-01-01

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

Stability analysis of piecewise non-linear systems and its application to chaotic synchronisation with intermittent control

NASA Astrophysics Data System (ADS)

Wang, Qingzhi; Tan, Guanzheng; He, Yong; Wu, Min

2017-10-01

This paper considers a stability analysis issue of piecewise non-linear systems and applies it to intermittent synchronisation of chaotic systems. First, based on piecewise Lyapunov function methods, more general and less conservative stability criteria of piecewise non-linear systems in periodic and aperiodic cases are presented, respectively. Next, intermittent synchronisation conditions of chaotic systems are derived which extend existing results. Finally, Chua's circuit is taken as an example to verify the validity of our methods.

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

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

Canards in a minimal piecewise-linear square-wave burster

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

Desroches, M.; Krupa, M.; Fernández-García, S., E-mail: soledad@us.es

We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that itsmore » fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).« less

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

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

2015-08-23

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

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

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

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

DTIC Science & Technology

2007-05-29

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

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

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

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

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

Time-temperature effect in adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

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

Quadratic spline subroutine package

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

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

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

DTIC Science & Technology

2012-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

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

Robust Neighboring Optimal Guidance for the Advanced Launch System

NASA Technical Reports Server (NTRS)

Hull, David G.

1993-01-01

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

Interaction function of oscillating coupled neurons

PubMed Central

Dodla, Ramana; Wilson, Charles J.

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

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

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

PubMed

Staley, James R; Burgess, Stephen

2017-05-01

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

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

PubMed Central

Staley, James R.

2017-01-01

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

Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

PubMed Central

Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

2013-01-01

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

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

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

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

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

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

Global and local curvature in density functional theory.

PubMed

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

2016-08-07

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

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

PubMed

Langley, Natalie R; Cridlin, Sandra

2016-01-01

Secular changes refer to short-term biological changes ostensibly due to environmental factors. Two well-documented secular trends in many populations are earlier age of menarche and increasing stature. This study synthesizes data on maximum clavicle length and fusion of the medial epiphysis in 1840-1980 American birth cohorts to provide a comprehensive assessment of developmental and morphological change in the clavicle. Clavicles from the Hamann-Todd Human Osteological Collection (n = 354), McKern and Stewart Korean War males (n = 341), Forensic Anthropology Data Bank (n = 1,239), and the McCormick Clavicle Collection (n = 1,137) were used in the analysis. Transition analysis was used to evaluate fusion of the medial epiphysis (scored as unfused, fusing, or fused). Several statistical treatments were used to assess fluctuations in maximum clavicle length. First, Durbin-Watson tests were used to evaluate autocorrelation, and a local regression (LOESS) was used to identify visual shifts in the regression slope. Next, piecewise regression was used to fit linear regression models before and after the estimated breakpoints. Multiple starting parameters were tested in the range determined to contain the breakpoint, and the model with the smallest mean squared error was chosen as the best fit. The parameters from the best-fit models were then used to derive the piecewise models, which were compared with the initial simple linear regression models to determine which model provided the best fit for the secular change data. The epiphyseal union data indicate a decline in the age at onset of fusion since the early twentieth century. Fusion commences approximately four years earlier in mid- to late twentieth-century birth cohorts than in late nineteenth- and early twentieth-century birth cohorts. However, fusion is completed at roughly the same age across cohorts. The most significant decline in age at onset of epiphyseal union appears to have occurred since the mid-twentieth century. LOESS plots show a breakpoint in the clavicle length data around the mid-twentieth century in both sexes, and piecewise regression models indicate a significant decrease in clavicle length in the American population after 1940. The piecewise model provides a slightly better fit than the simple linear model. Since the model standard error is not substantially different from the piecewise model, an argument could be made to select the less complex linear model. However, we chose the piecewise model to detect changes in clavicle length that are overfitted with a linear model. The decrease in maximum clavicle length is in line with a documented narrowing of the American skeletal form, as shown by analyses of cranial and facial breadth and bi-iliac breadth of the pelvis. Environmental influences on skeletal form include increases in body mass index, health improvements, improved socioeconomic status, and elimination of infectious diseases. Secular changes in bony dimensions and skeletal maturation stipulate that medical and forensic standards used to deduce information about growth, health, and biological traits must be derived from modern populations.

Optimal control of parametric oscillations of compressed flexible bars

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

The dynamics of two linearly coupled Goodwin oscillators

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

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

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.

Efficient Digital Implementation of The Sigmoidal Function For Artificial Neural Network

NASA Astrophysics Data System (ADS)

Pratap, Rana; Subadra, M.

2011-10-01

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

Variational models for discontinuity detection

NASA Astrophysics Data System (ADS)

Vitti, Alfonso; Battista Benciolini, G.

2010-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

Farag, Mohammed; Fleckenstein, Matthias; Habibi, Saeid

2017-02-01

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

Semilinear programming: applications and implementation

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

Mohan, S.

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

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Limit cycles in planar piecewise linear differential systems with nonregular separation line

NASA Astrophysics Data System (ADS)

Cardin, Pedro Toniol; Torregrosa, Joan

2016-12-01

In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2 π - α, respectively, for α ∈(0 , π) . We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α = π / 2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.

Control algorithms for dynamic attenuators.

PubMed

Hsieh, Scott S; Pelc, Norbert J

2014-06-01

The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

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

PubMed Central

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

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

DOE PAGES

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

2015-11-12

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

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

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

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

A variable-step-size robust delta modulator.

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Least Squares Approximation By G1 Piecewise Parametric Cubes

DTIC Science & Technology

1993-12-01

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

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

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

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

2012-06-15

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

Geodesic regression for image time-series.

PubMed

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

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

Piecewise polynomial representations of genomic tracks.

PubMed

Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

Hsieh, Scott S.; Pelc, Norbert J.

2014-06-01

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

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

PubMed

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

2013-11-01

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

Control algorithms for dynamic attenuators

PubMed Central

Hsieh, Scott S.; Pelc, Norbert J.

2014-01-01

Purpose: The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. Methods: The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. Results: The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Conclusions: Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods. PMID:24877818

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Balance Contrast Enhancement using piecewise linear stretching

NASA Astrophysics Data System (ADS)

Rahavan, R. V.; Govil, R. C.

1993-04-01

Balance Contrast Enhancement is one of the techniques employed to produce color composites with increased color contrast. It equalizes the three images used for color composition in range and mean. This results in a color composite with large variation in hue. Here, it is shown that piecewise linear stretching can be used for performing the Balance Contrast Enhancement. In comparison with the Balance Contrast Enhancement Technique using parabolic segment as transfer function (BCETP), the method presented here is algorithmically simple, constraint-free and produces comparable results.

An algorithm for the numerical solution of linear differential games

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

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

2001-10-31

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

Tell a Piecewise Story

ERIC Educational Resources Information Center

Sinclair, Nathalie; Armstrong, Alayne

2011-01-01

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

Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

An unsteady lifting surface method for single rotation propellers

NASA Technical Reports Server (NTRS)

Williams, Marc H.

1990-01-01

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor.

PubMed

Du, Yuhuan; Guo, Yingqing

2016-07-15

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor

PubMed Central

Du, Yuhuan; Guo, Yingqing

2016-01-01

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter. PMID:27428976

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

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

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

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

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

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

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

PubMed

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

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

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

PubMed

Xu, Yuesheng; Zhao, Liang

2013-08-01

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

Slow relaxation in weakly open rational polygons.

PubMed

Kokshenev, Valery B; Vicentini, Eduardo

2003-07-01

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

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

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

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

2015-10-15

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

Dynamic Programming for Structured Continuous Markov Decision Problems

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

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

PubMed

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

2007-03-01

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

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

PubMed

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

2017-01-01

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

Bilinear effect in complex systems

NASA Astrophysics Data System (ADS)

Lam, Lui; Bellavia, David C.; Han, Xiao-Pu; Alston Liu, Chih-Hui; Shu, Chang-Qing; Wei, Zhengjin; Zhou, Tao; Zhu, Jichen

2010-09-01

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.

On Discontinuous Piecewise Linear Models for Memristor Oscillators

NASA Astrophysics Data System (ADS)

Amador, Andrés; Freire, Emilio; Ponce, Enrique; Ros, Javier

2017-06-01

In this paper, we provide for the first time rigorous mathematical results regarding the rich dynamics of piecewise linear memristor oscillators. In particular, for each nonlinear oscillator given in [Itoh & Chua, 2008], we show the existence of an infinite family of invariant manifolds and that the dynamics on such manifolds can be modeled without resorting to discontinuous models. Our approach provides topologically equivalent continuous models with one dimension less but with one extra parameter associated to the initial conditions. It is possible to justify the periodic behavior exhibited by three-dimensional memristor oscillators, by taking advantage of known results for planar continuous piecewise linear systems. The analysis developed not only confirms the numerical results contained in previous works [Messias et al., 2010; Scarabello & Messias, 2014] but also goes much further by showing the existence of closed surfaces in the state space which are foliated by periodic orbits. The important role of initial conditions that justify the infinite number of periodic orbits exhibited by these models, is stressed. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Slope Estimation in Noisy Piecewise Linear Functions✩

PubMed Central

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2014-01-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure. PMID:25419020

Slope Estimation in Noisy Piecewise Linear Functions.

PubMed

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2015-03-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

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

PubMed

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

2012-06-01

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

Development of models of the magnetorheological fluid damper

NASA Astrophysics Data System (ADS)

Kazakov, Yu. B.; Morozov, N. A.; Nesterov, S. A.

2017-06-01

The algorithm for analytical calculation of a power characteristic of magnetorheological (MR) dampers taking into account the rheological properties of MR fluid is considered. The nonlinear magnetorheological characteristics are represented by piecewise linear approximation to MR fluid areas with different viscosities. The extended calculated power characteristics of a MR damper are received and they coincide with actual results. The finite element model of a MR damper is developed; it allows carrying out the analysis of a MR damper taking into account the mutual influence of electromagnetic, hydrodynamic and thermal fields. The results of finite element simulation coincide with analytical solutions that allows using them for design development of a MR damper.

Design of multi-body Lambert type orbits with specified departure and arrival positions

NASA Astrophysics Data System (ADS)

Ishii, Nobuaki; Kawaguchi, Jun'ichiro; Matsuo, Hiroki

1991-10-01

A new procedure for designing a multi-body Lambert type orbit comprising a multiple swingby process is developed, aiming at relieving a numerical difficulty inherent to a highly nonlinear swingby mechanism. The proposed algorithm, Recursive Multi-Step Linearization, first divides a whole orbit into several trajectory segments. Then, with a maximum use of piecewised transition matrices, a segmentized orbit is repeatedly upgraded until an approximated orbit initially based on a patched conics method eventually converges. In application to the four body earth-moon system with sun's gravitation, one of the double lunar swingby orbits including 12 lunar swingbys is successfully designed without any velocity mismatch.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Active distribution network planning considering linearized system loss

NASA Astrophysics Data System (ADS)

Li, Xiao; Wang, Mingqiang; Xu, Hao

2018-02-01

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

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

NASA Astrophysics Data System (ADS)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

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

NASA Astrophysics Data System (ADS)

Vjačeslavov, N. S.

1980-02-01

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

Chua's Equation was Proved to BE Chaotic in Two Years, Lorenz Equation in Thirty Six Years

NASA Astrophysics Data System (ADS)

Muthuswamy, Bharathwaj

2013-01-01

Although there are probably more publications on Chua's circuit than any other chaotic circuit, a tutorial with a historical emphasis is still lacking. Hence the goal of this chapter is to provide such a tutorial. This chapter will prove useful for a novice who is looking to understand the basics behind chaotic circuits without too much technical details. The chapter also includes a cookbook approach to a rigorous proof of chaos in piecewise-linear systems. The proof is a summary of the original piecewise-linear proof of chaos in Chua's circuit. The chapter concludes with a discussion of circuits derived from Chua's circuit.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

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

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

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

Linear stability analysis of collective neutrino oscillations without spurious modes

NASA Astrophysics Data System (ADS)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

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

Hypothalamic stimulation and baroceptor reflex interaction on renal nerve activity.

NASA Technical Reports Server (NTRS)

Wilson, M. F.; Ninomiya, I.; Franz, G. N.; Judy, W. V.

1971-01-01

The basal level of mean renal nerve activity (MRNA-0) measured in anesthetized cats was found to be modified by the additive interaction of hypothalamic and baroceptor reflex influences. Data were collected with the four major baroceptor nerves either intact or cut, and with mean aortic pressure (MAP) either clamped with a reservoir or raised with l-epinephrine. With intact baroceptor nerves, MRNA stayed essentially constant at level MRNA-0 for MAP below an initial pressure P1, and fell approximately linearly to zero as MAP was raised to P2. Cutting the baroceptor nerves kept MRNA at MRNA-0 (assumed to represent basal central neural output) independent of MAP. The addition of hypothalamic stimulation produced nearly constant increments in MRNA for all pressure levels up to P2, with complete inhibition at some level above P2. The increments in MRNA depended on frequency and location of the stimulus. A piecewise linear model describes MRNA as a linear combination of hypothalamic, basal central neural, and baroceptor reflex activity.

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

PubMed

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

2015-04-01

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

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Improved Displacement Transfer Functions for Structure Deformed Shape Predictions Using Discretely Distributed Surface Strains

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2012-01-01

In the formulations of earlier Displacement Transfer Functions for structure shape predictions, the surface strain distributions, along a strain-sensing line, were represented with piecewise linear functions. To improve the shape-prediction accuracies, Improved Displacement Transfer Functions were formulated using piecewise nonlinear strain representations. Through discretization of an embedded beam (depth-wise cross section of a structure along a strain-sensing line) into multiple small domains, piecewise nonlinear functions were used to describe the surface strain distributions along the discretized embedded beam. Such piecewise approach enabled the piecewise integrations of the embedded beam curvature equations to yield slope and deflection equations in recursive forms. The resulting Improved Displacement Transfer Functions, written in summation forms, were expressed in terms of beam geometrical parameters and surface strains along the strain-sensing line. By feeding the surface strains into the Improved Displacement Transfer Functions, structural deflections could be calculated at multiple points for mapping out the overall structural deformed shapes for visual display. The shape-prediction accuracies of the Improved Displacement Transfer Functions were then examined in view of finite-element-calculated deflections using different tapered cantilever tubular beams. It was found that by using the piecewise nonlinear strain representations, the shape-prediction accuracies could be greatly improved, especially for highly-tapered cantilever tubular beams.

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

NASA Astrophysics Data System (ADS)

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

2000-04-01

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

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

NASA Technical Reports Server (NTRS)

Kvernadze, George; Hagstrom,Thomas; Shapiro, Henry

1997-01-01

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints.

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

Recent work on material interface reconstruction

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

Mosso, S.J.; Swartz, B.K.

1997-12-31

For the last 15 years, many Eulerian codes have relied on a series of piecewise linear interface reconstruction algorithms developed by David Youngs. In a typical Youngs` method, the material interfaces were reconstructed based upon nearly cell values of volume fractions of each material. The interfaces were locally represented by linear segments in two dimensions and by pieces of planes in three dimensions. The first step in such reconstruction was to locally approximate an interface normal. In Youngs` 3D method, a local gradient of a cell-volume-fraction function was estimated and taken to be the local interface normal. A linear interfacemore » was moved perpendicular to the now known normal until the mass behind it matched the material volume fraction for the cell in question. But for distorted or nonorthogonal meshes, the gradient normal estimate didn`t accurately match that of linear material interfaces. Moreover, curved material interfaces were also poorly represented. The authors will present some recent work in the computation of more accurate interface normals, without necessarily increasing stencil size. Their estimate of the normal is made using an iterative process that, given mass fractions for nearby cells of known but arbitrary variable density, converges in 3 or 4 passes in practice (and quadratically--like Newton`s method--in principle). The method reproduces a linear interface in both orthogonal and nonorthogonal meshes. The local linear approximation is generally 2nd-order accurate, with a 1st-order accurate normal for curved interfaces in both two and three dimensional polyhedral meshes. Recent work demonstrating the interface reconstruction for curved surfaces will /be discussed.« less

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

NASA Astrophysics Data System (ADS)

Modarresi, N.; Rezakhah, S.

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

Payment contracts in a preventive health care system: a perspective from operations management.

PubMed

Yaesoubi, Reza; Roberts, Stephen D

2011-12-01

We consider a health care system consisting of two noncooperative parties: a health purchaser (payer) and a health provider, where the interaction between the two parties is governed by a payment contract. We determine the contracts that coordinate the health purchaser-health provider relationship; i.e. the contracts that maximize the population's welfare while allowing each entity to optimize its own objective function. We show that under certain conditions (1) when the number of customers for a preventive medical intervention is verifiable, there exists a gate-keeping contract and a set of concave piecewise linear contracts that coordinate the system, and (2) when the number of customers is not verifiable, there exists a contract of bounded linear form and a set of incentive-feasible concave piecewise linear contracts that coordinate the system. Copyright © 2011 Elsevier B.V. All rights reserved.

Characterization of intermittency in renewal processes: Application to earthquakes

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

Akimoto, Takuma; Hasumi, Tomohiro; Aizawa, Yoji

2010-03-15

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variablesmore » but that the conditional probability distribution functions in the tail obey the Weibull distribution.« less

A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions.

PubMed

Brighenti, Chiara; Gnudi, Gianni; Avanzolini, Guido

2003-05-01

This paper presents a mathematical model of the oxygen alveolo-capillary exchange to provide the capillary oxygen partial pressure profile in normal and pathological conditions. In fact, a thickening of the blood-gas barrier, heavy exercise or a low oxygen partial pressure (PO2) in the alveolar space can reduce the O2 alveolo-capillary exchange. Since the reversible binding between haemoglobin and oxygen makes it impossible to determine the closed form for the mathematical description of the PO2 profile along the pulmonary capillaries, an approximate analytical solution of the capillary PO2 profile is proposed. Simulation results are compared with the capillary PO2 profile obtained by numerical integration and by a piecewise linear interpolation of the oxyhaemoglobin dissociation curve. Finally, the proposed model is evaluated in a large range of physiopathological diffusive conditions. The good fit to numerical solutions in all experimental conditions seems to represent a substantial improvement with respect to the approach based on a linear approximation of the oxyhaemoglobin dissociation curve, and makes this model a candidate to be incorporated into the integrated descriptions of the entire respiratory system, where the datum of primary interest is the value of end capillary PO2.

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

PubMed Central

Heathcote, Andrew

2016-01-01

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

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

Does transport time help explain the high trauma mortality rates in rural areas? New and traditional predictors assessed by new and traditional statistical methods

PubMed Central

Røislien, Jo; Lossius, Hans Morten; Kristiansen, Thomas

2015-01-01

Background Trauma is a leading global cause of death. Trauma mortality rates are higher in rural areas, constituting a challenge for quality and equality in trauma care. The aim of the study was to explore population density and transport time to hospital care as possible predictors of geographical differences in mortality rates, and to what extent choice of statistical method might affect the analytical results and accompanying clinical conclusions. Methods Using data from the Norwegian Cause of Death registry, deaths from external causes 1998–2007 were analysed. Norway consists of 434 municipalities, and municipality population density and travel time to hospital care were entered as predictors of municipality mortality rates in univariate and multiple regression models of increasing model complexity. We fitted linear regression models with continuous and categorised predictors, as well as piecewise linear and generalised additive models (GAMs). Models were compared using Akaike's information criterion (AIC). Results Population density was an independent predictor of trauma mortality rates, while the contribution of transport time to hospital care was highly dependent on choice of statistical model. A multiple GAM or piecewise linear model was superior, and similar, in terms of AIC. However, while transport time was statistically significant in multiple models with piecewise linear or categorised predictors, it was not in GAM or standard linear regression. Conclusions Population density is an independent predictor of trauma mortality rates. The added explanatory value of transport time to hospital care is marginal and model-dependent, highlighting the importance of exploring several statistical models when studying complex associations in observational data. PMID:25972600

Brittle failure of rock: A review and general linear criterion

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

PubMed

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

2016-12-01

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

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

PubMed

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

2014-03-01

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

Piecewise multivariate modelling of sequential metabolic profiling data.

PubMed

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

2008-02-19

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

On the Modeling of the Residual Effects of the Clock Behavior and the Atmosphere Effects in the Analysis of VLBI Data

NASA Astrophysics Data System (ADS)

Bo, Zhang; Li, Jin-Ling; Wang, Guan-Gli

2002-01-01

We checked the dependence of the estimation of parameters on the choice of piecewise interval in the continuous piecewise linear modeling of the residual clock and atmosphere effects by single analysis of 27 VLBI experiments involving Shanghai station (Seshan 25m). The following are tentatively shown: (1) Different choices of the piecewise interval lead to differences in the estimation of station coordinates and in the weighted root mean squares ( wrms ) of the delay residuals, which can be of the order of centimeters or dozens of picoseconds respectively. So the choice of piecewise interval should not be arbitrary . (2) The piecewise interval should not be too long, otherwise the short - term variations in the residual clock and atmospheric effects can not be properly modeled. While in order to maintain enough degrees of freedom in parameter estimation, the interval can not be too short, otherwise the normal equation may become near or solely singular and the noises can not be constrained as well. Therefore the choice of the interval should be within some reasonable range. (3) Since the conditions of clock and atmosphere are different from experiment to experiment and from station to station, the reasonable range of the piecewise interval should be tested and chosen separately for each experiment as well as for each station by real data analysis. This is really arduous work in routine data analysis. (4) Generally speaking, with the default interval for clock as 60min, the reasonable range of piecewise interval for residual atmospheric effect modeling is between 10min to 40min, while with the default interval for atmosphere as 20min, that for residual clock behavior is between 20min to 100min.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

DTIC Science & Technology

1990-11-19

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

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

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

2018-07-01

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

Instabilities in a staircase stratified shear flow

NASA Astrophysics Data System (ADS)

Ponetti, G.; Balmforth, N. J.; Eaves, T. S.

2018-01-01

We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

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

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

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

An Ensemble of Neural Networks for Stock Trading Decision Making

NASA Astrophysics Data System (ADS)

Chang, Pei-Chann; Liu, Chen-Hao; Fan, Chin-Yuan; Lin, Jun-Lin; Lai, Chih-Ming

Stock turning signals detection are very interesting subject arising in numerous financial and economic planning problems. In this paper, Ensemble Neural Network system with Intelligent Piecewise Linear Representation for stock turning points detection is presented. The Intelligent piecewise linear representation method is able to generate numerous stocks turning signals from the historic data base, then Ensemble Neural Network system will be applied to train the pattern and retrieve similar stock price patterns from historic data for training. These turning signals represent short-term and long-term trading signals for selling or buying stocks from the market which are applied to forecast the future turning points from the set of test data. Experimental results demonstrate that the hybrid system can make a significant and constant amount of profit when compared with other approaches using stock data available in the market.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

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.

Identification of cascade water tanks using a PWARX model

NASA Astrophysics Data System (ADS)

Mattsson, Per; Zachariah, Dave; Stoica, Petre

2018-06-01

In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

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

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

Lee, E; Yuan, F; Templeton, A

Purpose: The ultimate goal of radiotherapy treatment planning is to find a treatment that will yield a high tumor-control-probability(TCP) with an acceptable normal-tissue-complication probability(NTCP). Yet most treatment planning today is not based upon optimization of TCPs and NTCPs, but rather upon meeting physical dose and volume constraints defined by the planner. We design treatment plans that optimize TCP directly and contrast them with the clinical dose-based plans. PET image is incorporated to evaluate gain in TCP for dose escalation. Methods: We build a nonlinear mixed integer programming optimization model that maximizes TCP directly while satisfying the dose requirements on themore » targeted organ and healthy tissues. The solution strategy first fits the TCP function with a piecewise-linear approximation, then solves the problem that maximizes the piecewise linear approximation of TCP, and finally performs a local neighborhood search to improve the TCP value. To gauge the feasibility, characteristics, and potential benefit of PET-image guided dose escalation, initial validation consists of fifteen cervical cancer HDR patient cases. These patients have all received prior 45Gy of external radiation dose. For both escalated strategies, we consider 35Gy PTV-dose, and two variations (37Gy-boost to BTV vs 40Gy-boost) to PET-image-pockets. Results: TCP for standard clinical plans range from 59.4% - 63.6%. TCP for dose-based PET-guided escalated-dose-plan ranges from 63.8%–98.6% for all patients; whereas TCP-optimized plans achieves over 91% for all patients. There is marginal difference in TCP among those with 37Gy-boosted vs 40Gy-boosted. There is no increase in rectum and bladder dose among all plans. Conclusion: Optimizing TCP directly results in highly conformed treatment plans. The TCP-optimized plan is individualized based on the biological PET-image of the patients. The TCP-optimization framework is generalizable and has been applied successfully to other external-beam delivery modalities. A clinical trial is on-going to gauge the clinical significance. Partially supported by the National Science Foundation.« less

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

PubMed

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

2017-01-02

Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available, and the more abstract Boolean methods. Copyright © 2016 Elsevier B.V. All rights reserved.

Effect of smoothing on robust chaos.

PubMed

Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

2010-08-01

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

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

Geometric analysis and restitution of digital multispectral scanner data arrays

NASA Technical Reports Server (NTRS)

Baker, J. R.; Mikhail, E. M.

1975-01-01

An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.

On solving three-dimensional open-dimension rectangular packing problems

NASA Astrophysics Data System (ADS)

Junqueira, Leonardo; Morabito, Reinaldo

2017-05-01

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.

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

PubMed

Gardini, L; Sushko, I; Matsuyama, K

2018-05-01

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

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

PubMed

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

2013-10-01

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

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions.

PubMed

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-03-02

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn)featuresfromfixedslidingwindowsonreal-timesteeringwheelanglestimeseries. Afterthat, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: "wake" and "drowsy". The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the "awake" state, and 15.15% false detections of the "drowsy" state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions

PubMed Central

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-01-01

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn) features from fixed sliding windows on real-time steering wheel angles time series. After that, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: “wake” and “drowsy”. The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the “awake” state, and 15.15% false detections of the “drowsy” state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue. PMID:28257094

Accurate upwind methods for the Euler equations

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1993-01-01

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

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

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

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

2016-02-23

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

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Impact of Many-Body Effects on Landau Levels in Graphene

NASA Astrophysics Data System (ADS)

Sonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C.

2018-05-01

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity vF. In contrast to the logarithmic divergence of vF at zero magnetic field, we find a piecewise linear scaling of vF as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

Development of a piecewise linear omnidirectional 3D image registration method

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2013-01-01

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

Variable neighborhood search to solve the vehicle routing problem for hazardous materials transportation.

PubMed

Bula, Gustavo Alfredo; Prodhon, Caroline; Gonzalez, Fabio Augusto; Afsar, H Murat; Velasco, Nubia

2017-02-15

This work focuses on the Heterogeneous Fleet Vehicle Routing problem (HFVRP) in the context of hazardous materials (HazMat) transportation. The objective is to determine a set of routes that minimizes the total expected routing risk. This is a nonlinear function, and it depends on the vehicle load and the population exposed when an incident occurs. Thus, a piecewise linear approximation is used to estimate it. For solving the problem, a variant of the Variable Neighborhood Search (VNS) algorithm is employed. To improve its performance, a post-optimization procedure is implemented via a Set Partitioning (SP) problem. The SP is solved on a pool of routes obtained from executions of the local search procedure embedded on the VNS. The algorithm is tested on two sets of HFVRP instances based on literature with up to 100 nodes, these instances are modified to include vehicle and arc risk parameters. The results are competitive in terms of computational efficiency and quality attested by a comparison with Mixed Integer Linear Programming (MILP) previously proposed. Copyright © 2016 Elsevier B.V. All rights reserved.

A modelling approach to assessing the timescale uncertainties in proxy series with chronological errors

NASA Astrophysics Data System (ADS)

Divine, D. V.; Godtliebsen, F.; Rue, H.

2012-01-01

The paper proposes an approach to assessment of timescale errors in proxy-based series with chronological uncertainties. The method relies on approximation of the physical process(es) forming a proxy archive by a random Gamma process. Parameters of the process are partly data-driven and partly determined from prior assumptions. For a particular case of a linear accumulation model and absolutely dated tie points an analytical solution is found suggesting the Beta-distributed probability density on age estimates along the length of a proxy archive. In a general situation of uncertainties in the ages of the tie points the proposed method employs MCMC simulations of age-depth profiles yielding empirical confidence intervals on the constructed piecewise linear best guess timescale. It is suggested that the approach can be further extended to a more general case of a time-varying expected accumulation between the tie points. The approach is illustrated by using two ice and two lake/marine sediment cores representing the typical examples of paleoproxy archives with age models based on tie points of mixed origin.

Optimal Operation System of the Integrated District Heating System with Multiple Regional Branches

NASA Astrophysics Data System (ADS)

Kim, Ui Sik; Park, Tae Chang; Kim, Lae-Hyun; Yeo, Yeong Koo

This paper presents an optimal production and distribution management for structural and operational optimization of the integrated district heating system (DHS) with multiple regional branches. A DHS consists of energy suppliers and consumers, district heating pipelines network and heat storage facilities in the covered region. In the optimal management system, production of heat and electric power, regional heat demand, electric power bidding and sales, transport and storage of heat at each regional DHS are taken into account. The optimal management system is formulated as a mixed integer linear programming (MILP) where the objectives is to minimize the overall cost of the integrated DHS while satisfying the operation constraints of heat units and networks as well as fulfilling heating demands from consumers. Piecewise linear formulation of the production cost function and stairwise formulation of the start-up cost function are used to compute nonlinear cost function approximately. Evaluation of the total overall cost is based on weekly operations at each district heat branches. Numerical simulations show the increase of energy efficiency due to the introduction of the present optimal management system.

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

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Supervised Learning Based on Temporal Coding in Spiking Neural Networks.

PubMed

Mostafa, Hesham

2017-08-01

Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard nonlinearity and the discrete nature of spike communication. We show that in a feedforward spiking network that uses a temporal coding scheme where information is encoded in spike times instead of spike rates, the network input-output relation is differentiable almost everywhere. Moreover, this relation is piecewise linear after a transformation of variables. Methods for training ANNs thus carry directly to the training of such spiking networks as we show when training on the permutation invariant MNIST task. In contrast to rate-based spiking networks that are often used to approximate the behavior of ANNs, the networks we present spike much more sparsely and their behavior cannot be directly approximated by conventional ANNs. Our results highlight a new approach for controlling the behavior of spiking networks with realistic temporal dynamics, opening up the potential for using these networks to process spike patterns with complex temporal information.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

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

PubMed

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

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Fluid displacement between two parallel plates: a non-empirical model displaying change of type from hyperbolic to elliptic equations

NASA Astrophysics Data System (ADS)

Shariati, M.; Talon, L.; Martin, J.; Rakotomalala, N.; Salin, D.; Yortsos, Y. C.

2004-11-01

We consider miscible displacement between parallel plates in the absence of diffusion, with a concentration-dependent viscosity. By selecting a piecewise viscosity function, this can also be considered as ‘three-fluid’ flow in the same geometry. Assuming symmetry across the gap and based on the lubrication (‘equilibrium’) approximation, a description in terms of two quasi-linear hyperbolic equations is obtained. We find that the system is hyperbolic and can be solved analytically, when the mobility profile is monotonic, or when the mobility of the middle phase is smaller than its neighbours. When the mobility of the middle phase is larger, a change of type is displayed, an elliptic region developing in the composition space. Numerical solutions of Riemann problems of the hyperbolic system spanning the elliptic region, with small diffusion added, show good agreement with the analytical outside, but an unstable behaviour inside the elliptic region. In these problems, the elliptic region arises precisely at the displacement front. Crossing the elliptic region requires the solution of essentially an eigenvalue problem of the full higher-dimensional model, obtained here using lattice BGK simulations. The hyperbolic-to-elliptic change-of-type reflects the failing of the lubrication approximation, underlying the quasi-linear hyperbolic formalism, to describe the problem uniformly. The obtained solution is analogous to non-classical shocks recently suggested in problems with change of type.

Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies.

PubMed

Bardhan, Jaydeep P; Jungwirth, Pavel; Makowski, Lee

2012-09-28

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).

Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies

PubMed Central

Bardhan, Jaydeep P.; Jungwirth, Pavel; Makowski, Lee

2012-01-01

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular “linear response” model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution). PMID:23020318

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

NASA Astrophysics Data System (ADS)

Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

2017-12-01

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

Numerical study of the influence of flow blockage on the aerodynamic coefficients of models in low-speed wind tunnels

NASA Astrophysics Data System (ADS)

Bui, V. T.; Kalugin, V. T.; Lapygin, V. I.; Khlupnov, A. I.

2017-11-01

With the use of ANSYS Fluent software and ANSYS ICEM CFD calculation grid generator, the flows past a wing airfoil, an infinite cylinder, and 3D blunted bodies located in the open and closed test sections of low-speed wind tunnels were calculated. The mathematical model of the flows included the Reynolds equations and the SST model of turbulence. It was found that the ratios between the aerodynamic coefficients in the test section and in the free (unbounded) stream could be fairly well approximated with a piecewise-linear function of the blockage factor, whose value weakly depended on the angle of attack. The calculated data and data gained in the analysis of previously reported experimental studies proved to be in a good agreement. The impact of the extension of the closed test section on the airfoil lift force is analyzed.

A hybridized formulation for the weak Galerkin mixed finite element method

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

Mu, Lin; Wang, Junping; Ye, Xiu

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

A hybridized formulation for the weak Galerkin mixed finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-01-14

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

Optimized Quasi-Interpolators for Image Reconstruction.

PubMed

Sacht, Leonardo; Nehab, Diego

2015-12-01

We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.

Analytic double product integrals for all-frequency relighting.

PubMed

Wang, Rui; Pan, Minghao; Chen, Weifeng; Ren, Zhong; Zhou, Kun; Hua, Wei; Bao, Hujun

2013-07-01

This paper presents a new technique for real-time relighting of static scenes with all-frequency shadows from complex lighting and highly specular reflections from spatially varying BRDFs. The key idea is to depict the boundaries of visible regions using piecewise linear functions, and convert the shading computation into double product integrals—the integral of the product of lighting and BRDF on visible regions. By representing lighting and BRDF with spherical Gaussians and approximating their product using Legendre polynomials locally in visible regions, we show that such double product integrals can be evaluated in an analytic form. Given the precomputed visibility, our technique computes the visibility boundaries on the fly at each shading point, and performs the analytic integral to evaluate the shading color. The result is a real-time all-frequency relighting technique for static scenes with dynamic, spatially varying BRDFs, which can generate more accurate shadows than the state-of-the-art real-time PRT methods.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Microwave moisture sensing through use of a piecewise density-independent function

USDA-ARS?s Scientific Manuscript database

Microwave moisture sensing provides a means to determine nondestructively the amount of water in materials. This is accomplished through the correlation of dielectric properties with moisture in the material. In this study, linear relationships between a density-independent function of the dielectri...

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.

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

PubMed

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

2016-12-01

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

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

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

NASA Astrophysics Data System (ADS)

Li, Yurong; Du, Zhengdong

2017-02-01

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

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.

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

NASA Astrophysics Data System (ADS)

Shui, Xin; Wang, Shimin

2018-02-01

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

Is long-term exposure to traffic pollution associated with mortality? A small-area study in London.

PubMed

Halonen, Jaana I; Blangiardo, Marta; Toledano, Mireille B; Fecht, Daniela; Gulliver, John; Ghosh, Rebecca; Anderson, H Ross; Beevers, Sean D; Dajnak, David; Kelly, Frank J; Wilkinson, Paul; Tonne, Cathryn

2016-01-01

Long-term exposure to primary traffic pollutants may be harmful for health but few studies have investigated effects on mortality. We examined associations for six primary traffic pollutants with all-cause and cause-specific mortality in 2003-2010 at small-area level using linear and piecewise linear Poisson regression models. In linear models most pollutants showed negative or null association with all-cause, cardiovascular or respiratory mortality. In the piecewise models we observed positive associations in the lowest exposure range (e.g. relative risk (RR) for all-cause mortality 1.07 (95% credible interval (CI) = 1.00-1.15) per 0.15 μg/m(3) increase in exhaust related primary particulate matter ≤2.5 μm (PM2.5)) whereas associations in the highest exposure range were negative (corresponding RR 0.93, 95% CI: 0.91-0.96). Overall, there was only weak evidence of positive associations with mortality. That we found the strongest positive associations in the lowest exposure group may reflect residual confounding by unmeasured confounders that varies by exposure group. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

High-Speed Numeric Function Generator Using Piecewise Quadratic Approximations

DTIC Science & Technology

2007-09-01

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

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

NASA Astrophysics Data System (ADS)

Korelin, Ivan A.; Porshnev, Sergey V.

2018-01-01

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

Mathematical Tools for Image Reconstruction

DTIC Science & Technology

1991-07-01

l.Diffuse tomography 2.Concentrating a signal in the physical and spectral domains. 3.New explicit solutions for the Kadomtsev - Petviashvili equation 4...the case of the Schroedinger equation it was possible to "beat Heisenberg" with piecewise linear potentials. Finally let me say that the paper Some

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

PubMed

Durstewitz, Daniel

2017-06-01

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

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

NASA Technical Reports Server (NTRS)

Childs, A. G.

1971-01-01

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

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

PubMed

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

2016-05-01

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

Dynamical properties of maps fitted to data in the noise-free limit

PubMed Central

Lindström, Torsten

2013-01-01

We argue that any attempt to classify dynamical properties from nonlinear finite time-series data requires a mechanistic model fitting the data better than piecewise linear models according to standard model selection criteria. Such a procedure seems necessary but still not sufficient. PMID:23768079

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

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

Theater-Level Stochastic Air-to-Air Engagement Modeling via Event Occurrence Networks Using Piecewise Polynomial Approximation

DTIC Science & Technology

2001-09-01

diagnosis natural language understanding circuit fault diagnosis pattern recognition machine vision nancial auditing map learning sensor... ACCA ACCB A ights degree of command and control FCC value is assumed to be the average of all the ACC values of the aircraft in the

Spatial Holmboe instability

NASA Astrophysics Data System (ADS)

Ortiz, Sabine; Chomaz, Jean-Marc; Loiseleux, Thomas

2002-08-01

In mixing-layers between two parallel streams of different densities, shear and gravity effects interplay; buoyancy acts as a restoring force and the Kelvin-Helmholtz mode is known to be stabilized by the stratification. If the density interface is sharp enough, two new instability modes, known as Holmboe modes, appear, propagating in opposite directions. This mechanism has been studied in the temporal instability framework. The present paper analyzes the associated spatial instability problem. It considers, in the Boussinesq approximation, two immiscible inviscid fluids with a piecewise linear broken-line velocity profile. We show how the classical scenario for transition between absolute and convective instability should be modified due to the presence of propagating waves. In the convective region, the spatial theory is relevant and the slowest propagating wave is shown to be the most spatially amplified, as suggested by intuition. Predictions of spatial linear theory are compared with mixing-layer [C. G. Koop and F. K. Browand, J. Fluid Mech. 93, 135 (1979)] and exchange flow [G. Pawlak and L. Armi, J. Fluid Mech. 376, 1 (1999)] experiments. The physical mechanism for Holmboe mode destabilization is analyzed via an asymptotic expansion that predicts the absolute instability domain at large Richardson number.

A New Model Based on Adaptation of the External Loop to Compensate the Hysteresis of Tactile Sensors

PubMed Central

Sánchez-Durán, José A.; Vidal-Verdú, Fernando; Oballe-Peinado, Óscar; Castellanos-Ramos, Julián; Hidalgo-López, José A.

2015-01-01

This paper presents a novel method to compensate for hysteresis nonlinearities observed in the response of a tactile sensor. The External Loop Adaptation Method (ELAM) performs a piecewise linear mapping of the experimentally measured external curves of the hysteresis loop to obtain all possible internal cycles. The optimal division of the input interval where the curve is approximated is provided by the error minimization algorithm. This process is carried out off line and provides parameters to compute the split point in real time. A different linear transformation is then performed at the left and right of this point and a more precise fitting is achieved. The models obtained with the ELAM method are compared with those obtained from three other approaches. The results show that the ELAM method achieves a more accurate fitting. Moreover, the involved mathematical operations are simpler and therefore easier to implement in devices such as Field Programmable Gate Array (FPGAs) for real time applications. Furthermore, the method needs to identify fewer parameters and requires no previous selection process of operators or functions. Finally, the method can be applied to other sensors or actuators with complex hysteresis loop shapes. PMID:26501279

A coarse-grid-projection acceleration method for finite-element incompressible flow computations

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne; FiN Lab Team

2015-11-01

Coarse grid projection (CGP) methodology provides a framework for accelerating computations by performing some part of the computation on a coarsened grid. We apply the CGP to pressure projection methods for finite element-based incompressible flow simulations. Based on it, the predicted velocity field data is restricted to a coarsened grid, the pressure is determined by solving the Poisson equation on the coarse grid, and the resulting data are prolonged to the preset fine grid. The contributions of the CGP method to the pressure correction technique are twofold: first, it substantially lessens the computational cost devoted to the Poisson equation, which is the most time-consuming part of the simulation process. Second, it preserves the accuracy of the velocity field. The velocity and pressure spaces are approximated by Galerkin spectral element using piecewise linear basis functions. A restriction operator is designed so that fine data are directly injected into the coarse grid. The Laplacian and divergence matrices are driven by taking inner products of coarse grid shape functions. Linear interpolation is implemented to construct a prolongation operator. A study of the data accuracy and the CPU time for the CGP-based versus non-CGP computations is presented. Laboratory for Fluid Dynamics in Nature.

Robust stochastic optimization for reservoir operation

NASA Astrophysics Data System (ADS)

Pan, Limeng; Housh, Mashor; Liu, Pan; Cai, Ximing; Chen, Xin

2015-01-01

Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.

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

PubMed

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

2012-01-01

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

Longitudinal Models of Reading Achievement of Students with Learning Disabilities and without Disabilities

ERIC Educational Resources Information Center

Sullivan, Amanda L.; Kohli, Nidhi; Farnsworth, Elyse M.; Sadeh, Shanna; Jones, Leila

2017-01-01

Objective: Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. Method: We drew an analytic sample of 1,990 students from…

Computerized Method for the Generation of Molecular Transmittance Functions in the Infrared.

DTIC Science & Technology

1980-04-01

predict this behavior, we conclude that the first method using linear function of x is accurate enough to be used in the actual application. The...PIECEWISE- ANALITICAL TRANSMISSION FUNCTION.’//20X, * ’STANDARD DEVIATIONS BETWEEN THE ACTUAL TAU AND THE RECOMPUTED’, * ’ TAU VALUES ARE COMPUTED.’////) 77

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

PubMed

Nie, Xiaobing; Zheng, Wei Xing

2015-05-01

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

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

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

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

Resonant activation in piecewise linear asymmetric potentials.

PubMed

Fiasconaro, Alessandro; Spagnolo, Bernardo

2011-04-01

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

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.

A new method for analysis of limit cycle behavior of the NASA/JPL 70-meter antenna axis servos

NASA Technical Reports Server (NTRS)

Hill, R. E.

1989-01-01

A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.

Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

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.

Exponential Approximations Using Fourier Series Partial Sums

NASA Technical Reports Server (NTRS)

Banerjee, Nana S.; Geer, James F.

1997-01-01

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

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

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

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

Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Steinwolf, Alexander

2005-01-01

The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.

Geometry-based ensembles: toward a structural characterization of the classification boundary.

PubMed

Pujol, Oriol; Masip, David

2009-06-01

This paper introduces a novel binary discriminative learning technique based on the approximation of the nonlinear decision boundary by a piecewise linear smooth additive model. The decision border is geometrically defined by means of the characterizing boundary points-points that belong to the optimal boundary under a certain notion of robustness. Based on these points, a set of locally robust linear classifiers is defined and assembled by means of a Tikhonov regularized optimization procedure in an additive model to create a final lambda-smooth decision rule. As a result, a very simple and robust classifier with a strong geometrical meaning and nonlinear behavior is obtained. The simplicity of the method allows its extension to cope with some of today's machine learning challenges, such as online learning, large-scale learning or parallelization, with linear computational complexity. We validate our approach on the UCI database, comparing with several state-of-the-art classification techniques. Finally, we apply our technique in online and large-scale scenarios and in six real-life computer vision and pattern recognition problems: gender recognition based on face images, intravascular ultrasound tissue classification, speed traffic sign detection, Chagas' disease myocardial damage severity detection, old musical scores clef classification, and action recognition using 3D accelerometer data from a wearable device. The results are promising and this paper opens a line of research that deserves further attention.

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

Aleshin, S. S., E-mail: aless2001@mail.ru; Lobanov, A. E., E-mail: lobanov@phys.msu.ru; Kharlanov, O. G., E-mail: okharl@mail.ru

The effect of flavor day-night asymmetry is considered for solar neutrinos of energy about 1 MeV under the assumption that the electron-density distribution within the Earth is approximately piecewise continuous on the scale of the neutrino-oscillation length. In this approximation, the resulting asymmetry factor for beryllium neutrinos does not depend on the structure of the inner Earth's layers or on the properties of the detector used. Its numerical estimate is on the order of -4 Multiplication-Sign 10{sup -4}, which is far beyond the reach of present-day experiments.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

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

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1985-01-01

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

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

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

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

2016-05-13

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

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

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Huang, Zhenkun; Han, Maoan

2007-09-01

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

Tortuosity of lightning return stroke channels

NASA Technical Reports Server (NTRS)

Levine, D. M.; Gilson, B.

1984-01-01

Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data.

Piecewise Linear Approach for Timing Simulation of VLSI (Very-Large-Scale-Integrated) Circuits on Serial and Parallel Computers.

DTIC Science & Technology

1987-12-01

8217ftp.. *,*IS ~. ~bw ~ ft.. p ’ft ’ft ft.. ’ft *I~ P* ’ft ’p 0n-I ci via 1 ca j I .11’ ft~ ’ fttH vialca *- ’ft ft..I ft. ’ft ft.. --ft ..ft ’ft ftp

Bifurcation from an invariant to a non-invariant attractor

NASA Astrophysics Data System (ADS)

Mandal, D.

2016-12-01

Switching dynamical systems are very common in many areas of physics and engineering. We consider a piecewise linear map that periodically switches between more than one different functional forms. We show that in such systems it is possible to have a border collision bifurcation where the system transits from an invariant attractor to a non-invariant attractor.

The influence of ground conductivity on the structure of RF radiation from return strokes

NASA Technical Reports Server (NTRS)

Levine, D. M.; Gesell, L.

1984-01-01

The combination of the finite conductivity of the Earth plus the propagation of the return stroke current up the channel which results in an apparent time delay between the fast field changes and RF radiation for distant observers is shown. The time delay predicted from model return strokes is on the order of 20 micro and the received signal has the characteristics of the data observed in Virginia and Florida. A piecewise linear model for the return stroke channel and a transmission line model for current propagation on each segment was used. Radiation from each segment is calculated over a flat Earth with finite conductivity using asymptotics approximations for the Sommerfeld integrals. The radiation at the observer is processed by a model AM radio receiver. The output voltage was calculated for several frequencies between HF-UHF assuming a system bandwidth (300 kHz) characteristic of the system used to collect data in Florida and Virginia. Comparison with the theoretical fast field changes indicates a time delay of 20 microns.

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

NASA Astrophysics Data System (ADS)

Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Rieben, R.; Tomov, V.

2018-03-01

We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions.

Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators.

PubMed

Campbell, S; Wang, D

1996-01-01

A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, Marco

2009-01-01

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

First-principles photoemission spectroscopy in DNA and RNA nucleobases from Koopmans-compliant functionals

NASA Astrophysics Data System (ADS)

Nguyen, Ngoc Linh; Borghi, Giovanni; Ferretti, Andrea; Marzari, Nicola

The determination of spectral properties of the DNA and RNA nucleobases from first principles can provide theoretical interpretation for experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches such as density-functional theory. In this work, we show that Koopmans-compliant functionals, constructed to enforce piecewise linearity in energy functionals with respect to fractional occupation-i.e., with respect to charged excitations-can predict not only frontier ionization potentials and electron affinities of the nucleobases with accuracy comparable or superior with that of many-body perturbation theory and high-accuracy quantum chemistry methods, but also the molecular photoemission spectra are shown to be in excellent agreement with experimental ultraviolet photoemsision spectroscopy data. The results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential, which transform DFT into a novel dynamical formalism where electronic properties, and not only total energies, can be correctly accounted for.

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

The Use of Orthogonal Polarizations in Microwave Imagery of Isolated Canine Kidney

NASA Astrophysics Data System (ADS)

Larsen, L. E.; Jacobi, J. H.

1980-06-01

A method of imaging biological targets using microwave radiation at a frequency of 4 GHz is presented. Linearly polarized radiation is transmitted through an isolated canine kidney and received with co-polarized and cross-polarized antennas. Images are displayed as the spatial variation of the magnitude of the transmission scattering parameter S21 for each mode of polarization. The relationship between the spatial variation of the magnitude of S21 and canine renal anatomy is discussed. It is shown that within the kidney the cross-polarized image tends to emphasize linear or piecewise linear structures, whereas the co-polarized image balances renal cortical lobulations.

Nonlinear analysis of a family of LC tuned inverters. [dc to square wave circuits for power conditioning

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1974-01-01

A family of four dc-to-square-wave LC tuned inverters are analyzed using singular point. Limit cycles and waveshape characteristics are given for three modes of oscillation: quasi-harmonic, relaxation, and discontinuous. An inverter in which the avalanche breakdown of the transistor emitter-to-base junction occurs is discussed and the starting characteristics of this family of inverters are presented. The LC tuned inverters are shown to belong to a family of inverters with a common equivalent circuit consisting of only three 'series' elements: a five-segment piecewise-linear current-controlled resistor, linear inductor, and linear capacitor.

A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases

NASA Astrophysics Data System (ADS)

Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.

2017-02-01

A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.

Boolean Operations with Prism Algebraic Patches

PubMed Central

Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi

2009-01-01

In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C1-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262

Monitoring with a modified Robel pole on meadows in the central Black Hills of South Dakaota

Treesearch

Daniel W. Uresk; Ted A. Benzon

2007-01-01

This study using a modified Robel pole was conducted in the central Black Hills, South Dakota. The objectives were to test the relationship between visual obstruction readings and standing herbage, develop guidelines for monitoring, and estimate sample size. The relationship between visual obstruction and standing herbage was linear with 2 segments in a piecewise model...

Minimum time acceleration of aircraft turbofan engines by using an algorithm based on nonlinear programming

NASA Technical Reports Server (NTRS)

Teren, F.

1977-01-01

Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Robust Nonlinear Causality Analysis of Nonstationary Multivariate Physiological Time Series.

PubMed

Schack, Tim; Muma, Michael; Feng, Mengling; Guan, Cuntai; Zoubir, Abdelhak M

2018-06-01

An important research area in biomedical signal processing is that of quantifying the relationship between simultaneously observed time series and to reveal interactions between the signals. Since biomedical signals are potentially nonstationary and the measurements may contain outliers and artifacts, we introduce a robust time-varying generalized partial directed coherence (rTV-gPDC) function. The proposed method, which is based on a robust estimator of the time-varying autoregressive (TVAR) parameters, is capable of revealing directed interactions between signals. By definition, the rTV-gPDC only displays the linear relationships between the signals. We therefore suggest to approximate the residuals of the TVAR process, which potentially carry information about the nonlinear causality by a piece-wise linear time-varying moving-average model. The performance of the proposed method is assessed via extensive simulations. To illustrate the method's applicability to real-world problems, it is applied to a neurophysiological study that involves intracranial pressure, arterial blood pressure, and brain tissue oxygenation level (PtiO2) measurements. The rTV-gPDC reveals causal patterns that are in accordance with expected cardiosudoral meachanisms and potentially provides new insights regarding traumatic brain injuries. The rTV-gPDC is not restricted to the above problem but can be useful in revealing interactions in a broad range of applications.

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

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2015-01-01

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

Nonlinear filtering properties of detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Tsujimoto, Yutaka

2016-11-01

Detrended fluctuation analysis (DFA) has been widely used for quantifying long-range correlation and fractal scaling behavior. In DFA, to avoid spurious detection of scaling behavior caused by a nonstationary trend embedded in the analyzed time series, a detrending procedure using piecewise least-squares fitting has been applied. However, it has been pointed out that the nonlinear filtering properties involved with detrending may induce instabilities in the scaling exponent estimation. To understand this issue, we investigate the adverse effects of the DFA detrending procedure on the statistical estimation. We show that the detrending procedure using piecewise least-squares fitting results in the nonuniformly weighted estimation of the root-mean-square deviation and that this property could induce an increase in the estimation error. In addition, for comparison purposes, we investigate the performance of a centered detrending moving average analysis with a linear detrending filter and sliding window DFA and show that these methods have better performance than the standard DFA.

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

NASA Astrophysics Data System (ADS)

Zhang, Zhengfang; Chen, Weifeng

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Thamrin, Sri Astuti; Lawi, Armin

2016-02-01

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

Online Normalization Algorithm for Engine Turbofan Monitoring

DTIC Science & Technology

2014-10-02

Online Normalization Algorithm for Engine Turbofan Monitoring Jérôme Lacaille 1 , Anastasios Bellas 2 1 Snecma, 77550 Moissy-Cramayel, France...understand the behavior of a turbofan engine, one first needs to deal with the variety of data acquisition contexts. Each time a set of measurements is...it auto-adapts itself with piecewise linear models. 1. INTRODUCTION Turbofan engine abnormality diagnosis uses three steps: reduction of

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

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

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

A prototype piecewise-linear dynamic attenuator

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Coulette, David

2016-08-01

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

Regularization by Functions of Bounded Variation and Applications to Image Enhancement

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

Casas, E.; Kunisch, K.; Pola, C.

1999-09-15

Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise.

Growing Readers: A Hierarchical Linear Model of Children's Reading Growth During the First 2 Years of School

ERIC Educational Resources Information Center

McCoach, D. Betsy; O'Connell, Ann A.; Reis, Sally M.; Levitt, Heather A.

2006-01-01

Using the first 4 waves of data from the Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K), this piecewise 3-level (time-student-school) growth-curve model provides a portrait of students' reading growth over the first 2 years of school. On average, students make much greater reading gains in 1st grade than they do in kindergarten.…

COED Transactions, Vol. IX, No. 1, January 1977. Rapid Production of System Phase-Plane Portraits on the EAI 380 Hybrid/Analog Computer.

ERIC Educational Resources Information Center

Marcovitz, Alan B., Ed.

The method of phase-plane presentation as an educational tool in the study of the dynamic behavior of systems is discussed. In the treatment of nonlinear or piecewise-linear systems, the phase-plane portrait is used to exhibit the nature of singular points, regions of stability, and switching lines to aid comprehension. A technique is described by…

On Algorithms for Generating Computationally Simple Piecewise Linear Classifiers

DTIC Science & Technology

1989-05-01

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

A Bayesian model averaging method for the derivation of reservoir operating rules

NASA Astrophysics Data System (ADS)

Zhang, Jingwen; Liu, Pan; Wang, Hao; Lei, Xiaohui; Zhou, Yanlai

2015-09-01

Because the intrinsic dynamics among optimal decision making, inflow processes and reservoir characteristics are complex, functional forms of reservoir operating rules are always determined subjectively. As a result, the uncertainty of selecting form and/or model involved in reservoir operating rules must be analyzed and evaluated. In this study, we analyze the uncertainty of reservoir operating rules using the Bayesian model averaging (BMA) model. Three popular operating rules, namely piecewise linear regression, surface fitting and a least-squares support vector machine, are established based on the optimal deterministic reservoir operation. These individual models provide three-member decisions for the BMA combination, enabling the 90% release interval to be estimated by the Markov Chain Monte Carlo simulation. A case study of China's the Baise reservoir shows that: (1) the optimal deterministic reservoir operation, superior to any reservoir operating rules, is used as the samples to derive the rules; (2) the least-squares support vector machine model is more effective than both piecewise linear regression and surface fitting; (3) BMA outperforms any individual model of operating rules based on the optimal trajectories. It is revealed that the proposed model can reduce the uncertainty of operating rules, which is of great potential benefit in evaluating the confidence interval of decisions.

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

PubMed Central

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

2017-01-01

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

Extraction of object skeletons in multispectral imagery by the orthogonal regression fitting

NASA Astrophysics Data System (ADS)

Palenichka, Roman M.; Zaremba, Marek B.

2003-03-01

Accurate and automatic extraction of skeletal shape of objects of interest from satellite images provides an efficient solution to such image analysis tasks as object detection, object identification, and shape description. The problem of skeletal shape extraction can be effectively solved in three basic steps: intensity clustering (i.e. segmentation) of objects, extraction of a structural graph of the object shape, and refinement of structural graph by the orthogonal regression fitting. The objects of interest are segmented from the background by a clustering transformation of primary features (spectral components) with respect to each pixel. The structural graph is composed of connected skeleton vertices and represents the topology of the skeleton. In the general case, it is a quite rough piecewise-linear representation of object skeletons. The positions of skeleton vertices on the image plane are adjusted by means of the orthogonal regression fitting. It consists of changing positions of existing vertices according to the minimum of the mean orthogonal distances and, eventually, adding new vertices in-between if a given accuracy if not yet satisfied. Vertices of initial piecewise-linear skeletons are extracted by using a multi-scale image relevance function. The relevance function is an image local operator that has local maximums at the centers of the objects of interest.

Advanced Control Considerations for Turbofan Engine Design

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Csank, Jeffrey T.; Chicatelli, Amy

2016-01-01

This paper covers the application of a model-based engine control (MBEC) methodology featuring a self tuning on-board model for an aircraft turbofan engine simulation. The nonlinear engine model is capable of modeling realistic engine performance, allowing for a verification of the advanced control methodology over a wide range of operating points and life cycle conditions. The on-board model is a piece-wise linear model derived from the nonlinear engine model and updated using an optimal tuner Kalman Filter estimation routine, which enables the on-board model to self-tune to account for engine performance variations. MBEC is used here to show how advanced control architectures can improve efficiency during the design phase of a turbofan engine by reducing conservative operability margins. The operability margins that can be reduced, such as stall margin, can expand the engine design space and offer potential for efficiency improvements. Application of MBEC architecture to a nonlinear engine simulation is shown to reduce the thrust specific fuel consumption by approximately 1% over the baseline design, while maintaining safe operation of the engine across the flight envelope.

Pricing of swing options: A Monte Carlo simulation approach

NASA Astrophysics Data System (ADS)

Leow, Kai-Siong

We study the problem of pricing swing options, a class of multiple early exercise options that are traded in energy market, particularly in the electricity and natural gas markets. These contracts permit the option holder to periodically exercise the right to trade a variable amount of energy with a counterparty, subject to local volumetric constraints. In addition, the total amount of energy traded from settlement to expiration with the counterparty is restricted by a global volumetric constraint. Violation of this global volumetric constraint is allowed but would lead to penalty settled at expiration. The pricing problem is formulated as a stochastic optimal control problem in discrete time and state space. We present a stochastic dynamic programming algorithm which is based on piecewise linear concave approximation of value functions. This algorithm yields the value of the swing option under the assumption that the optimal exercise policy is applied by the option holder. We present a proof of an almost sure convergence that the algorithm generates the optimal exercise strategy as the number of iterations approaches to infinity. Finally, we provide a numerical example for pricing a natural gas swing call option.

Stage-discharge relationship in tidal channels

NASA Astrophysics Data System (ADS)

Kearney, W. S.; Mariotti, G.; Deegan, L.; Fagherazzi, S.

2016-12-01

Long-term records of the flow of water through tidal channels are essential to constrain the budgets of sediments and biogeochemical compounds in salt marshes. Statistical models which relate discharge to water level allow the estimation of such records from more easily obtained records of water stage in the channel. While there is clearly structure in the stage-discharge relationship, nonlinearity and nonstationarity of the relationship complicates the construction of statistical stage-discharge models with adequate performance for discharge estimation and uncertainty quantification. Here we compare four different types of stage-discharge models, each of which is designed to capture different characteristics of the stage-discharge relationship. We estimate and validate each of these models on a two-month long time series of stage and discharge obtained with an Acoustic Doppler Current Profiler in a salt marsh channel. We find that the best performance is obtained by models which account for the nonlinear and time-varying nature of the stage-discharge relationship. Good performance can also be obtained from a simplified version of these models which approximates the fully nonlinear and time-varying models with a piecewise linear formulation.

Adaptive mesh fluid simulations on GPU

NASA Astrophysics Data System (ADS)

Wang, Peng; Abel, Tom; Kaehler, Ralf

2010-10-01

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers.

PubMed

Zhou, Haibo; Ying, Hao

2017-09-01

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

Charge tuning of nonresonant magnetoexciton phonon interactions in graphene.

PubMed

Rémi, Sebastian; Goldberg, Bennett B; Swan, Anna K

2014-02-07

Far from resonance, the coupling of the G-band phonon to magnetoexcitons in single layer graphene displays kinks and splittings versus filling factor that are well described by Pauli blocking and unblocking of inter- and intra-Landau level transitions. We explore the nonresonant electron-phonon coupling by high-magnetic field Raman scattering while electrostatic tuning of the carrier density controls the filling factor. We show qualitative and quantitative agreement between spectra and a linearized model of electron-phonon interactions in magnetic fields. The splitting is caused by dichroism of left- and right-handed circular polarized light due to lifting of the G-band phonon degeneracy, and the piecewise linear slopes are caused by the linear occupancy of sequential Landau levels versus ν.

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

A satellite relative motion model including J_2 and J_3 via Vinti's intermediary

NASA Astrophysics Data System (ADS)

Biria, Ashley D.; Russell, Ryan P.

2018-03-01

Vinti's potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti's spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating J_2, J_3, and generally a partial J_4 in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti's solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti's solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti's solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the J_2 through J_5 terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim-Alfriend state transition matrix, which considers the J_2 perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.

Stability of barotropic vortex strip on a rotating sphere

PubMed Central

Sohn, Sung-Ik; Kim, Sun-Chul

2018-01-01

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined. PMID:29507524

Stability of barotropic vortex strip on a rotating sphere.

PubMed

Sohn, Sung-Ik; Sakajo, Takashi; Kim, Sun-Chul

2018-02-01

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.

Registration of terrestrial mobile laser data on 2D or 3D geographic database by use of a non-rigid ICP approach.

NASA Astrophysics Data System (ADS)

Monnier, F.; Vallet, B.; Paparoditis, N.; Papelard, J.-P.; David, N.

2013-10-01

This article presents a generic and efficient method to register terrestrial mobile data with imperfect location on a geographic database with better overall accuracy but less details. The registration method proposed in this paper is based on a semi-rigid point to plane ICP ("Iterative Closest Point"). The main applications of such registration is to improve existing geographic databases, particularly in terms of accuracy, level of detail and diversity of represented objects. Other applications include fine geometric modelling and fine façade texturing, object extraction such as trees, poles, road signs marks, facilities, vehicles, etc. The geopositionning system of mobile mapping systems is affected by GPS masks that are only partially corrected by an Inertial Navigation System (INS) which can cause an important drift. As this drift varies non-linearly, but slowly in time, it will be modelled by a translation defined as a piecewise linear function of time which variation over time will be minimized (rigidity term). For each iteration of the ICP, the drift is estimated in order to minimise the distance between laser points and planar model primitives (data attachment term). The method has been tested on real data (a scan of the city of Paris of 3.6 million laser points registered on a 3D model of approximately 71,400 triangles).

Effects of soil acidification and liming on the phytoavailability of cadmium in paddy soils of central subtropical China.

PubMed

Zhu, Hanhua; Chen, Cheng; Xu, Chao; Zhu, Qihong; Huang, Daoyou

2016-12-01

Intensive and paired soil and rice grain survey and multiple-field liming experiments were conducted to assess soil acidification in the past 30 years, quantify the relationships of Cd phytoavailability with soil acidity, and determine efficacies of liming on soil acidity and Cd phytoavailability in paddy soils of central subtropical China at a regional scale. Soil pH, total and extractable Cd (Cd tot and Cd ext ), rice grain Cd were determined, and all measured data were analyzed separately in groups of 0.1 pH units intervals. Paddy soil pH averagely declined at 0.031 unit yr -1 between 1980s and 2014 (P < 0.01). Piecewise means of log Cd transfer ratio kept around -0.062 between soil pH 4.0 and 5.5 and around -1.31 between pH 6.9 and 7.3, whereas linearly decreased by a factor of 0.76 with pH 5.5-6.9, and by a factor of 1.38 with pH 7.3-8.2 (P < 0.01), respectively. Similar responses to soil pH were observed for soil Cd ext to Cd tot ratio. However, the former exhibited a lag effect to soil acidification in the acidic soils and a leading effect in alkaline soils. Liming increased soil pH by 0.50 units, and decreased rice grain Cd by 35.3% and log Cd transfer ratio by a factor of 0.76 (P < 0.01). The piecewise relationship based on the survey precisely predicted the changes in Cd transfer ratio across the multiple-field liming experiments. In conclusion, soil acidification occurred and accelerated in the past 30 years, and piecewise-linearly increased Cd phytoavailability of paddy soils in central subtropical China. Mitigating soil acidification, i.e. liming, should be preferentially implemented to minimize Cd phytoavailability. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

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

A new approach to simulating collisionless dark matter fluids

NASA Astrophysics Data System (ADS)

Hahn, Oliver; Abel, Tom; Kaehler, Ralf

2013-09-01

Recently, we have shown how current cosmological N-body codes already follow the fine grained phase-space information of the dark matter fluid. Using a tetrahedral tessellation of the three-dimensional manifold that describes perfectly cold fluids in six-dimensional phase space, the phase-space distribution function can be followed throughout the simulation. This allows one to project the distribution function into configuration space to obtain highly accurate densities, velocities and velocity dispersions. Here, we exploit this technique to show first steps on how to devise an improved particle-mesh technique. At its heart, the new method thus relies on a piecewise linear approximation of the phase-space distribution function rather than the usual particle discretization. We use pseudo-particles that approximate the masses of the tetrahedral cells up to quadrupolar order as the locations for cloud-in-cell (CIC) deposit instead of the particle locations themselves as in standard CIC deposit. We demonstrate that this modification already gives much improved stability and more accurate dynamics of the collisionless dark matter fluid at high force and low mass resolution. We demonstrate the validity and advantages of this method with various test problems as well as hot/warm dark matter simulations which have been known to exhibit artificial fragmentation. This completely unphysical behaviour is much reduced in the new approach. The current limitations of our approach are discussed in detail and future improvements are outlined.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

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

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

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

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

Neighboring Extremal Guidance for Systems with Piecewise Linear Control Using Time As the Reference Variable

DTIC Science & Technology

1993-05-01

obtained to provide a nominal control history . The guidance law is found by minimizing the V second variation of the suboptimal trajectory...deviations from the suboptimal trajectory to required changes in the nominal control history . The deviations from the suboptimal trajectory, used together...with the precomputed gains, determines the change in the nominal control history required to meet the final constraints while minimizing the change in

Resonant power processors. I - State plane analysis

NASA Technical Reports Server (NTRS)

Oruganti, R.; Lee, F. C.

1984-01-01

State-plane techniques in conjunction with piecewise-linear analysis is employed to study the steady-state and transient characteristics of a series resonant converter. With the direct viewing of the resonant tank energy and the device switching instants, the state portrayal provides unique insights into the complex behavior of the converter. Operation of the converter under both continuous and discontinuous current modes and at frequencies both below and above resonant frequency are discussed.

Time-independent Anisotropic Plastic Behavior by Mechanical Subelement Models

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1983-01-01

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the iscoplasticity-theory.

Traveling waves in a spring-block chain sliding down a slope

NASA Astrophysics Data System (ADS)

Morales, J. E.; James, G.; Tonnelier, A.

2017-07-01

Traveling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anticontinuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.

Traveling waves in a spring-block chain sliding down a slope.

PubMed

Morales, J E; James, G; Tonnelier, A

2017-07-01

Traveling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anticontinuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.

Chimeras with multiple coherent regions

NASA Astrophysics Data System (ADS)

Ujjwal, Sangeeta Rani; Ramaswamy, Ramakrishna

2013-09-01

We study chimeric states in a coupled phase oscillator system with piecewise linear nonlocal coupling. By modifying the details of the coupling, it is possible to obtain multiple chimeric states with a specified number of coherent regions and with specified phase relationships. The case of a two-component chimera is illustrated and the generalization to arbitrary chimeric configurations is discussed. The phase relations between the two clusters of phase oscillators is described in some detail.

KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

NASA Astrophysics Data System (ADS)

Wu, Xiaoping; Abbondanza, Claudio; Altamimi, Zuheir; Chin, T. Mike; Collilieux, Xavier; Gross, Richard S.; Heflin, Michael B.; Jiang, Yan; Parker, Jay W.

2015-05-01

The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.

Parameterizations for ensemble Kalman inversion

NASA Astrophysics Data System (ADS)

Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M.

2018-05-01

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

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

Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com; Institut Matematik Kejuruteraan; Saaban, Azizan, E-mail: azizan.s@uum.edu.my

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

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

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

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

2016-10-15

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

Geometric constrained variational calculus I: Piecewise smooth extremals

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Longitudinal models of reading achievement of students with learning disabilities and without disabilities.

PubMed

Sullivan, Amanda L; Kohli, Nidhi; Farnsworth, Elyse M; Sadeh, Shanna; Jones, Leila

2017-09-01

Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. We drew an analytic sample of 1,990 students from the nationally representative Early Childhood Longitudinal Study-Kindergarten Cohort of 1998, using reading achievement scores from kindergarten through eighth grade to estimate three models of students' reading growth. The piecewise mixed-effects models provided the best functional form of the students' reading trajectories as indicated by model fit indices. Results showed slightly different trajectories between students with learning disabilities and without disabilities, with varying but divergent rates of growth throughout elementary grades, as well as an increasing gap over time. These results highlight the need for additional research on appropriate methods for modeling reading trajectories and the implications for students' response to instruction. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Instantaneous frequency based newborn EEG seizure characterisation

NASA Astrophysics Data System (ADS)

Mesbah, Mostefa; O'Toole, John M.; Colditz, Paul B.; Boashash, Boualem

2012-12-01

The electroencephalogram (EEG), used to noninvasively monitor brain activity, remains the most reliable tool in the diagnosis of neonatal seizures. Due to their nonstationary and multi-component nature, newborn EEG seizures are better represented in the joint time-frequency domain than in either the time domain or the frequency domain. Characterising newborn EEG seizure nonstationarities helps to better understand their time-varying nature and, therefore, allow developing efficient signal processing methods for both modelling and seizure detection and classification. In this article, we used the instantaneous frequency (IF) extracted from a time-frequency distribution to characterise newborn EEG seizures. We fitted four frequency modulated (FM) models to the extracted IFs, namely a linear FM, a piecewise-linear FM, a sinusoidal FM, and a hyperbolic FM. Using a database of 30-s EEG seizure epochs acquired from 35 newborns, we were able to show that, depending on EEG channel, the sinusoidal and piecewise-linear FM models best fitted 80-98% of seizure epochs. To further characterise the EEG seizures, we calculated the mean frequency and frequency span of the extracted IFs. We showed that in the majority of the cases (>95%), the mean frequency resides in the 0.6-3 Hz band with a frequency span of 0.2-1 Hz. In terms of the frequency of occurrence of the four seizure models, the statistical analysis showed that there is no significant difference( p = 0.332) between the two hemispheres. The results also indicate that there is no significant differences between the two hemispheres in terms of the mean frequency ( p = 0.186) and the frequency span ( p = 0.302).

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.

Isogeometric Analysis of Boundary Integral Equations

DTIC Science & Technology

2015-04-21

methods, IgA relies on Non-Uniform Rational B- splines (NURBS) [43, 46], T- splines [55, 53] or subdivision surfaces [21, 48, 51] rather than piece- wise...structural dynamics [25, 26], plates and shells [15, 16, 27, 28, 37, 22, 23], phase-field models [17, 32, 33], and shape optimization [40, 41, 45, 59...polynomials for approximating the geometry and field variables. Thus, by replacing piecewise polynomials with NURBS or T- splines , one can develop

A method for digital image registration using a mathematical programming technique

NASA Technical Reports Server (NTRS)

Yao, S. S.

1973-01-01

A new algorithm based on a nonlinear programming technique to correct the geometrical distortions of one digital image with respect to another is discussed. This algorithm promises to be superior to existing ones in that it is capable of treating localized differential scaling, translational and rotational errors over the whole image plane. A series of piece-wise 'rubber-sheet' approximations are used, constrained in such a manner that a smooth approximation over the entire image can be obtained. The theoretical derivation is included. The result of using the algorithm to register four channel S065 Apollo IX digitized photography over Imperial Valley, California, is discussed in detail.

Multiuser receiver for DS-CDMA signals in multipath channels: an enhanced multisurface method.

PubMed

Mahendra, Chetan; Puthusserypady, Sadasivan

2006-11-01

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters

NASA Astrophysics Data System (ADS)

Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik

2017-04-01

Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Liang, Feng; Wang, Dechang

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

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

Higher direct bilirubin levels during mid-pregnancy are associated with lower risk of gestational diabetes mellitus.

PubMed

Liu, Chaoqun; Zhong, Chunrong; Zhou, Xuezhen; Chen, Renjuan; Wu, Jiangyue; Wang, Weiye; Li, Xiating; Ding, Huisi; Guo, Yanfang; Gao, Qin; Hu, Xingwen; Xiong, Guoping; Yang, Xuefeng; Hao, Liping; Xiao, Mei; Yang, Nianhong

2017-01-01

Bilirubin concentrations have been recently reported to be negatively associated with type 2 diabetes mellitus. We examined the association between bilirubin concentrations and gestational diabetes mellitus. In a prospective cohort study, 2969 pregnant women were recruited prior to 16 weeks of gestation and were followed up until delivery. The value of bilirubin was tested and oral glucose tolerance test was conducted to screen gestational diabetes mellitus. The relationship between serum bilirubin concentration and gestational weeks was studied by two-piecewise linear regression. A subsample of 1135 participants with serum bilirubin test during 16-18 weeks gestation was conducted to research the association between serum bilirubin levels and risk of gestational diabetes mellitus by logistic regression. Gestational diabetes mellitus developed in 8.5 % of the participants (223 of 2969). Two-piecewise linear regression analyses demonstrated that the levels of bilirubin decreased with gestational week up to the turning point 23 and after that point, levels of bilirubin were increased slightly. In multiple logistic regression analysis, the relative risk of developing gestational diabetes mellitus was lower in the highest tertile of direct bilirubin than that in the lowest tertile (RR 0.60; 95 % CI, 0.35-0.89). The results suggested that women with higher serum direct bilirubin levels during the second trimester of pregnancy have lower risk for development of gestational diabetes mellitus.

Optimized multiple linear mappings for single image super-resolution

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Algorithms for the explicit computation of Penrose diagrams

NASA Astrophysics Data System (ADS)

Schindler, J. C.; Aguirre, A.

2018-05-01

An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form . The resulting diagram coordinates are shown to extend the metric continuously and nondegenerately across an arbitrary number of horizons. The method is extended to include piecewise approximations to dynamically evolving spacetimes using a standard hypersurface junction procedure. Examples generated by an implementation of the algorithm are shown for standard and new cases. In the appendix, this algorithm is compared to existing methods.

Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems.

PubMed

Amaral, Gleison F V; Letellier, Christophe; Aguirre, Luis Antonio

2006-03-01

This paper proposes a procedure by which it is possible to synthesize Rossler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.

Supervised variational model with statistical inference and its application in medical image segmentation.

PubMed

Li, Changyang; Wang, Xiuying; Eberl, Stefan; Fulham, Michael; Yin, Yong; Dagan Feng, David

2015-01-01

Automated and general medical image segmentation can be challenging because the foreground and the background may have complicated and overlapping density distributions in medical imaging. Conventional region-based level set algorithms often assume piecewise constant or piecewise smooth for segments, which are implausible for general medical image segmentation. Furthermore, low contrast and noise make identification of the boundaries between foreground and background difficult for edge-based level set algorithms. Thus, to address these problems, we suggest a supervised variational level set segmentation model to harness the statistical region energy functional with a weighted probability approximation. Our approach models the region density distributions by using the mixture-of-mixtures Gaussian model to better approximate real intensity distributions and distinguish statistical intensity differences between foreground and background. The region-based statistical model in our algorithm can intuitively provide better performance on noisy images. We constructed a weighted probability map on graphs to incorporate spatial indications from user input with a contextual constraint based on the minimization of contextual graphs energy functional. We measured the performance of our approach on ten noisy synthetic images and 58 medical datasets with heterogeneous intensities and ill-defined boundaries and compared our technique to the Chan-Vese region-based level set model, the geodesic active contour model with distance regularization, and the random walker model. Our method consistently achieved the highest Dice similarity coefficient when compared to the other methods.

Response of an oscillatory differential delay equation to a single stimulus.

PubMed

Mackey, Michael C; Tyran-Kamińska, Marta; Walther, Hans-Otto

2017-04-01

Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; di Bernardo, Mario; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-12-01

We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population.

Synthesis of stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Thornton, W. A.

1974-01-01

Computer programs for the synthesis of shells of various configurations were developed. The conditions considered are: (1) uniform shells (mainly cones) using a membrane buckling analysis, (2) completely uniform shells (cones, spheres, toroidal segments) using linear bending prebuckling analysis, and (3) revision of second design process to reduce the number of design variables to about 30 by considering piecewise uniform designs. A perturbation formula was derived and this allows exact derivatives of the general buckling load to be computed with little additional computer time.

Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part 1. Boundary Value Problems for Linear Ellilptic Equation of Second Order.

DTIC Science & Technology

1986-05-01

neighborhood of the Program PROBE of Noetic Technologies, St. Louis. corners of the domain, place where the type of the boundary condition changes, etc...is studied . , r ° -. o. - *- . ,. .- -*. ... - - . . . ’ , ..- , .- *- , . --s,." . ",-:, "j’ . ], k i-, j!3 ,, :,’ - .A L...Manual. Noetic Technologies Corp., St. Louis, Missouri (1985). 318] Szab’, B. A.: Implementation of a Finite Element Software System with h and p

Elimination of numerical diffusion in 1 - phase and 2 - phase flows

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

Rajamaeki, M.

1997-07-01

The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.

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.

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

PubMed Central

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-01-01

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research. PMID:28353664

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata.

PubMed

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-03-29

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.

A modelling approach to assessing the timescale uncertainties in proxy series with chronological errors

NASA Astrophysics Data System (ADS)

Divine, D.; Godtliebsen, F.; Rue, H.

2012-04-01

Detailed knowledge of past climate variations is of high importance for gaining a better insight into the possible future climate scenarios. The relative shortness of available high quality instrumental climate data conditions the use of various climate proxy archives in making inference about past climate evolution. It, however, requires an accurate assessment of timescale errors in proxy-based paleoclimatic reconstructions. We here propose an approach to assessment of timescale errors in proxy-based series with chronological uncertainties. The method relies on approximation of the physical process(es) forming a proxy archive by a random Gamma process. Parameters of the process are partly data-driven and partly determined from prior assumptions. For a particular case of a linear accumulation model and absolutely dated tie points an analytical solution is found suggesting the Beta-distributed probability density on age estimates along the length of a proxy archive. In a general situation of uncertainties in the ages of the tie points the proposed method employs MCMC simulations of age-depth profiles yielding empirical confidence intervals on the constructed piecewise linear best guess timescale. It is suggested that the approach can be further extended to a more general case of a time-varying expected accumulation between the tie points. The approach is illustrated by using two ice and two lake/marine sediment cores representing the typical examples of paleoproxy archives with age models constructed using tie points of mixed origin.

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

DOEpatents

Terwilliger, Steve [Albuquerque, NM

2012-06-05

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

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

NASA Astrophysics Data System (ADS)

Zheng, Youqi; Choi, Sooyoung; Lee, Deokjung

2017-12-01

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

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

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

Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu; Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex; Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr

2016-08-15

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to themore » VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.« less

The Inverse of Banded Matrices

DTIC Science & Technology

2013-01-01

indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower

Automatic variance reduction for Monte Carlo simulations via the local importance function transform

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

Turner, S.A.

1996-02-01

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditionalmore » Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.« less

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

DOE PAGES

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

2014-10-22

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

Affine connection form of Regge calculus

NASA Astrophysics Data System (ADS)

Khatsymovsky, V. M.

2016-12-01

Regge action is represented analogously to how the Palatini action for general relativity (GR) as some functional of the metric and a general connection as independent variables represents the Einstein-Hilbert action. The piecewise flat (or simplicial) spacetime of Regge calculus is equipped with some world coordinates and some piecewise affine metric which is completely defined by the set of edge lengths and the world coordinates of the vertices. The conjugate variables are the general nondegenerate matrices on the three-simplices which play the role of a general discrete connection. Our previous result on some representation of the Regge calculus action in terms of the local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as independent variables is somewhat modified for the considered case of the general linear group GL(4, R) of the connection matrices. As a result, we have some action invariant w.r.t. arbitrary change of coordinates of the vertices (and related GL(4, R) transformations in the four-simplices). Excluding GL(4, R) connection from this action via the equations of motion we have exactly the Regge action for the considered spacetime.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Spatial distribution of loggerhead turtle (Caretta caretta) emergences along a highly dynamic beach in the northern Gulf of Mexico

USGS Publications Warehouse

Lamont, Margaret M.; Houser, Chris

2014-01-01

As coastlines change due to sea level rise and an increasing human presence, understanding how species, such as marine turtles, respond to alterations in habitat is necessary for proper management and conservation. Survey data from a major nesting beach in the northern Gulf of Mexico, where a revetment was installed, was used to assess spatial distribution of loggerhead emergences. Through use of Quadrat analysis and piecewise linear regression with breakpoint, we present evidence to suggest that nest site selection in loggerheads is determined in the nearshore environment, and by characteristics such as wave height, alongshore currents, depth and patterns of erosion and accretion. Areas of relatively dense nesting were found in areas with relatively strong alongshore currents, relatively small waves, a steep offshore slope and the largest historical rates of erosion. Areas of relatively dense nesting also corresponded to areas of low nesting success. Both nesting and non-nesting emergences were clustered immediately adjacent to the revetment and at other eroding sites along the beach. These results suggest that alterations to the nearshore environment from activities such as construction of a jetty, dredging or installation of pilings, may impact sea turtle nest distribution alongshore. We also show that piecewise linear regression with breakpoint is a technique that can be used with geomorphological and oceanographic data to predict locations of nest clumping and may be useful for managers at other nesting beaches.

Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

NASA Astrophysics Data System (ADS)

Everett, R. A.; Packer, A. M.; Kuang, Y.

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

NASA Astrophysics Data System (ADS)

Everett, R. A.; Packer, A. M.; Kuang, Y.

2014-04-01

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

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

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

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

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

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

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

2015-02-01

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

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

Roessler, O. E.; Kahiert, C.; Ughleke, B.

A piecewise-linear autonomous 3-variable ordinary differential equation is presented which permits analytical modeling of chaotic attractors. A once-differentiable system of equations is defined which consists of two linear half-systems which meet along a threshold plane. The trajectories described by each equation is thereby continuous along the divide, forming a one-parameter family of invariant tori. The addition of a damping term produces a system of equations for various chaotic attractors. Extension of the system by means of a 4-variable generalization yields hypertori and hyperchaos. It is noted that the hierarchy established is amenable to analysis by the use of Poincare half-maps. Applications of the systems of ordinary differential equations to modeling turbulent flows are discussed.

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

PubMed

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

2017-09-09

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

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

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

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

A green vehicle routing problem with customer satisfaction criteria

NASA Astrophysics Data System (ADS)

Afshar-Bakeshloo, M.; Mehrabi, A.; Safari, H.; Maleki, M.; Jolai, F.

2016-12-01

This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers' satisfaction have been taken into account. Meanwhile, the introduced model prepares an effective dashboard for decision-makers that determines appropriate routes, the best mixed fleet, speed and idle time of vehicles. Additionally, some new factors evaluate the greening of each decision based on three criteria. This model applies piecewise linear functions (PLFs) to linearize a nonlinear fuzzy interval for incorporating customers' satisfaction into other linear objectives. We have presented a mixed integer linear programming formulation for the S-GVRP. This model enriches managerial insights by providing trade-offs between customers' satisfaction, total costs and emission levels. Finally, we have provided a numerical study for showing the applicability of the model.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

2018-04-01

In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

Rotation relaxation splitting for optimizing parallel RF excitation pulses with T1 - and T2 -relaxations in MRI

NASA Astrophysics Data System (ADS)

Majewski, Kurt

2018-03-01

Exact solutions of the Bloch equations with T1 - and T2 -relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T1 - and T2 -relaxations in several examples.

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

Treesearch

Sandra E. Ryan; Laurie S. Porth

2007-01-01

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

Application of NASTRAN in nonlinear analysis of a cartridge case neck separation malfunction

NASA Technical Reports Server (NTRS)

Yang, J. C. S.; Frederick, D. L.

1975-01-01

The problem of case neck separation malfunction in the field of ammunition structural analysis is investigated. The axi-symmetric solid of revolution RING element was utilized in the manual piecewise linear analysis to obtain the expansion of the wall of the cartridge case and barrel chamber by the pressure of propellant gases and the stresses in the structure. The analysis included the varying material properties along the wall of the case and the chamber. Additional instructions were provided to change the element material ID's without recomputing the entire stiffness matrix.

Local Bifurcations and Optimal Theory in a Delayed Predator-Prey Model with Threshold Prey Harvesting

NASA Astrophysics Data System (ADS)

Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel

2015-06-01

We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.

FAST TRACK COMMUNICATION: Weyl law for fat fractals

NASA Astrophysics Data System (ADS)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Threshold detection in an on-off binary communications channel with atmospheric scintillation

NASA Technical Reports Server (NTRS)

Webb, W. E.; Marino, J. T., Jr.

1974-01-01

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-emperical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. Bit error probabilities for non-optimum threshold detection system were also investigated.

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

Threshold detection in an on-off binary communications channel with atmospheric scintillation

NASA Technical Reports Server (NTRS)

Webb, W. E.

1975-01-01

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-empirical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. The bit error probabilities for nonoptimum threshold detection systems were also investigated.

Endogenous Business Cycle Dynamics within Metzlers Inventory Model: Adding an Inventory Floor.

PubMed

Sushko, Irina; Wegener, Michael; Westerhoff, Frank; Zaklan, Georg

2009-04-01

Metzlers inventory model may produce dampened fluctuations in economic activity, thus contributing to our understanding of business cycle dynamics. For some parameter combinations, however, the model generates oscillations with increasing amplitude, implying that the inventory stock of firms eventually turns negative. Taking this observation into account, we reformulate Metzlers model by simply putting a floor to the inventory level. Within the new piecewise linear model, endogenous business cycle dynamics may now be triggered via a center bifurcation, i.e. for certain parameter combinations production changes are (quasi-)periodic.

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

PubMed

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

2006-02-15

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

Generation of dark hollow beam by use of phase-only filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Dai, Jingmin; Zhao, Xiaoyi; Sun, Xiaogang; Liu, Shutian; Ashfaq Ahmad, Muhammad

2009-11-01

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.

A simple finite element method for the Stokes equations

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-21

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

A simple finite element method for the Stokes equations

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

Mu, Lin; Ye, Xiu

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

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.

Near-road air pollutant concentrations of CO and PM 2.5: A comparison of MOBILE6.2/CALINE4 and generalized additive models

NASA Astrophysics Data System (ADS)

Zhang, Kai; Batterman, Stuart

2010-05-01

The contribution of vehicular traffic to air pollutant concentrations is often difficult to establish. This paper utilizes both time-series and simulation models to estimate vehicle contributions to pollutant levels near roadways. The time-series model used generalized additive models (GAMs) and fitted pollutant observations to traffic counts and meteorological variables. A one year period (2004) was analyzed on a seasonal basis using hourly measurements of carbon monoxide (CO) and particulate matter less than 2.5 μm in diameter (PM 2.5) monitored near a major highway in Detroit, Michigan, along with hourly traffic counts and local meteorological data. Traffic counts showed statistically significant and approximately linear relationships with CO concentrations in fall, and piecewise linear relationships in spring, summer and winter. The same period was simulated using emission and dispersion models (Motor Vehicle Emissions Factor Model/MOBILE6.2; California Line Source Dispersion Model/CALINE4). CO emissions derived from the GAM were similar, on average, to those estimated by MOBILE6.2. The same analyses for PM 2.5 showed that GAM emission estimates were much higher (by 4-5 times) than the dispersion model results, and that the traffic-PM 2.5 relationship varied seasonally. This analysis suggests that the simulation model performed reasonably well for CO, but it significantly underestimated PM 2.5 concentrations, a likely result of underestimating PM 2.5 emission factors. Comparisons between statistical and simulation models can help identify model deficiencies and improve estimates of vehicle emissions and near-road air quality.

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

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

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

High-Order Space-Time Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2013-01-01

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

A novel method for identifying a graph-based representation of 3-D microvascular networks from fluorescence microscopy image stacks.

PubMed

Almasi, Sepideh; Xu, Xiaoyin; Ben-Zvi, Ayal; Lacoste, Baptiste; Gu, Chenghua; Miller, Eric L

2015-02-01

A novel approach to determine the global topological structure of a microvasculature network from noisy and low-resolution fluorescence microscopy data that does not require the detailed segmentation of the vessel structure is proposed here. The method is most appropriate for problems where the tortuosity of the network is relatively low and proceeds by directly computing a piecewise linear approximation to the vasculature skeleton through the construction of a graph in three dimensions whose edges represent the skeletal approximation and vertices are located at Critical Points (CPs) on the microvasculature. The CPs are defined as vessel junctions or locations of relatively large curvature along the centerline of a vessel. Our method consists of two phases. First, we provide a CP detection technique that, for junctions in particular, does not require any a priori geometric information such as direction or degree. Second, connectivity between detected nodes is determined via the solution of a Binary Integer Program (BIP) whose variables determine whether a potential edge between nodes is or is not included in the final graph. The utility function in this problem reflects both intensity-based and structural information along the path connecting the two nodes. Qualitative and quantitative results confirm the usefulness and accuracy of this method. This approach provides a mean of correctly capturing the connectivity patterns in vessels that are missed by more traditional segmentation and binarization schemes because of imperfections in the images which manifest as dim or broken vessels. Copyright © 2014 Elsevier B.V. All rights reserved.

Some Properties of Generalized Connections in Quantum Gravity

NASA Astrophysics Data System (ADS)

Velhinho, J. M.

2002-12-01

Theories of connections play an important role in fundamental interactions, including Yang-Mills theories and gravity in the Ashtekar formulation. Typically in such cases, the classical configuration space {A}/ {G} of connections modulo gauge transformations is an infinite dimensional non-linear space of great complexity. Having in mind a rigorous quantization procedure, methods of functional calculus in an extension of {A}/ {G} have been developed. For a compact gauge group G, the compact space /line { {A}{ {/}} {G}} ( ⊃ {A}/ {G}) introduced by Ashtekar and Isham using C*-algebraic methods is a natural candidate to replace {A}/ {G} in the quantum context, 1 allowing the construction of diffeomorphism invariant measures. 2,3,4 Equally important is the space of generalized connections bar {A} introduced in a similar way by Baez. 5 bar {A} is particularly useful for the definition of vector fields in /line { {A}{ {/}} {G}} , fundamental in the construction of quantum observables. 6 These works crucially depend on the use of (generalized) Wilson variables associated to certain types of curves. We will consider the case of piecewise analytic curves, 1,2,5 althought most of the arguments apply equally to the piecewise smooth case. 7,8...

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

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

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

Mitigation of epidemics in contact networks through optimal contact adaptation *

PubMed Central

Youssef, Mina; Scoglio, Caterina

2013-01-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights. PMID:23906209

Mitigation of epidemics in contact networks through optimal contact adaptation.

PubMed

Youssef, Mina; Scoglio, Caterina

2013-08-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.

Retinal oxygen distribution and the role of neuroglobin.

PubMed

Roberts, Paul A; Gaffney, Eamonn A; Luthert, Philip J; Foss, Alexander J E; Byrne, Helen M

2016-07-01

The retina is the tissue layer at the back of the eye that is responsible for light detection. Whilst equipped with a rich supply of oxygen, it has one of the highest oxygen demands of any tissue in the body and, as such, supply and demand are finely balanced. It has been suggested that the protein neuroglobin (Ngb), which is found in high concentrations within the retina, may help to maintain an adequate supply of oxygen via the processes of transport and storage. We construct mathematical models, formulated as systems of reaction-diffusion equations in one-dimension, to test this hypothesis. Numerical simulations show that Ngb may play an important role in oxygen transport, but not in storage. Our models predict that the retina is most susceptible to hypoxia in the regions of the photoreceptor inner segment and inner plexiform layers, where Ngb has the potential to prevent hypoxia and increase oxygen uptake by 30-40 %. Analysis of a simplified model confirms the utility of Ngb in transport and shows that its oxygen affinity ([Formula: see text] value) is near optimal for this process. Lastly, asymptotic analysis enables us to identify conditions under which the piecewise linear and quadratic approximations to the retinal oxygen profile, used in the literature, are valid.

An exploratory analysis of Indiana and Illinois biotic ...

EPA Pesticide Factsheets

EPA recognizes the importance of nutrient criteria in protecting designated uses from eutrophication effects associated with elevated phosphorus and nitrogen in streams and has worked with states over the past 12 years to assist them in developing nutrient criteria. Towards that end, EPA has provided states and tribes with technical guidance to assess nutrient impacts and to develop criteria. EPA published recommendations in 2000 on scientifically defensible empirical approaches for setting numeric criteria. EPA also published eco-regional criteria recommendations in 2000-2001 based on a frequency distribution approach meant to approximate reference condition concentrations. In 2010, EPA elaborated on one of these empirical approaches (i.e., stressor-response relationships) for developing nutrient criteria. The purpose of this report was to conduct exploratory analyses of state datasets from Illinois and Indiana to determine threshold values for nutrients and chlorophyll a that could guide Indiana and Illinois criteria development. Box and whisker plots were used to compare nutrient and chlorophyll a concentrations between Illinois and Indiana. Stressor response analyses, using piece-wise linear regression and change-point analysis (Illinois only) were conducted to determine thresholds of change in relationships between nutrients and biotic assemblages. Impact stmt: The purpose of this report was to conduct exploratory analyses of state datasets from Illinois

Analysis of cardiovascular regulation.

PubMed

Wilhelm, F H; Grossman, P; Roth, W T

1999-01-01

Adequate characterization of hemodynamic and autonomic responses to physical and mental stress can elucidate underlying mechanisms of cardiovascular disease or anxiety disorders. We developed a physiological signal processing system for analysis of continuously recorded ECG, arterial blood pressure (BP), and respiratory signals using the programming language Matlab. Data collection devices are a 16-channel digital, physiological recorder (Vitaport), a finger arterial pressure transducer (Finapres), and a respiratory inductance plethysmograph (Respitrace). Besides the conventional analysis of the physiological channels, power spectral density and transfer functions of respiration, heart rate, and blood pressure variability are used to characterize respiratory sinus arrhythmia (RSA), 0.10-Hz BP oscillatory activity (Mayer-waves), and baroreflex sensitivity. The arterial pressure transducer waveforms permit noninvasive estimation of stroke volume, cardiac output, and systemic vascular resistance. Time trends in spectral composition of indices are assessed using complex demodulation. Transient dynamic changes of cardiovascular parameters at the onset of stress and recovery periods are quantified using a regression breakpoint model that optimizes piecewise linear curve fitting. Approximate entropy (ApEn) is computed to quantify the degree of chaos in heartbeat dynamics. Using our signal processing system we found distinct response patterns in subgroups of patients with coronary artery disease or anxiety disorders, which were related to specific pharmacological and behavioral factors.

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.

1986-01-01

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

A Unified Theory for the Great Plains Nocturnal Low-Level Jet

NASA Astrophysics Data System (ADS)

Shapiro, A.; Fedorovich, E.; Rahimi, S.

2014-12-01

The nocturnal low-level jet (LLJ) is a warm-season atmospheric boundary layer phenomenon common to the Great Plains of the United States and other places worldwide, typically in regions east of mountain ranges. Low-level jets develop around sunset in fair weather conditions conducive to strong radiational cooling, reach peak intensity in the pre-dawn hours, and then dissipate with the onset of daytime convective mixing. In this study we consider the LLJ as a diurnal oscillation of a stably stratified atmosphere overlying a planar slope on the rotating Earth. The oscillations arise from diurnal cycles in both the heating of the slope (mechanism proposed by Holton in 1967) and the turbulent mixing (mechanism proposed by Blackadar in 1957). The governing equations are the equations of motion, incompressibility condition, and thermal energy in the Boussinesq approximation, with turbulent heat and momentum exchange parameterized through spatially constant but diurnally varying turbulent diffusion coefficients (diffusivities). Analytical solutions are obtained for diffusivities with piecewise constant waveforms (step-changes at sunrise and sunset) and slope temperatures/buoyancies with piecewise linear waveforms (saw-tooth function with minimum at sunrise and maximum before sunset). The jet characteristics are governed by eleven parameters: slope angle, Coriolis parameter, environmental buoyancy frequency, geostrophic wind strength, daytime and nighttime diffusivities, maximum (daytime) and minimum (nighttime) slope buoyancies, duration of daylight, lag time between peak slope buoyancy and sunset, and a Newtonian cooling time scale. An exploration of the parameter space yields results that are broadly consistent with findings particular to the Holton and Blackadar theories, and agree with climatological observations, for example, that stronger jets tend to occur over slopes of 0.15-0.25 degrees characteristic of the Great Plains. The solutions also yield intriguing predictions that peak jet strength increases with attenuation of the minimum surface buoyancy, and that the single most important parameter determining jet height is the nighttime diffusivity, with weaker nightime diffusion associated with smaller jet heights. These and other highlights will be discussed in the presentation.

Remote sensing measurements of sea surface temperature as an indicator of Vibrio parahaemolyticus in oyster meat and human illnesses.

PubMed

Konrad, Stephanie; Paduraru, Peggy; Romero-Barrios, Pablo; Henderson, Sarah B; Galanis, Eleni

2017-08-31

Vibrio parahaemolyticus (Vp) is a naturally occurring bacterium found in marine environments worldwide. It can cause gastrointestinal illness in humans, primarily through raw oyster consumption. Water temperatures, and potentially other environmental factors, play an important role in the growth and proliferation of Vp in the environment. Quantifying the relationships between environmental variables and indicators or incidence of Vp illness is valuable for public health surveillance to inform and enable suitable preventative measures. This study aimed to assess the relationship between environmental parameters and Vp in British Columbia (BC), Canada. The study used Vp counts in oyster meat from 2002-2015 and laboratory confirmed Vp illnesses from 2011-2015 for the province of BC. The data were matched to environmental parameters from publicly available sources, including remote sensing measurements of nighttime sea surface temperature (SST) obtained from satellite readings at a spatial resolution of 1 km. Using three separate models, this paper assessed the relationship between (1) daily SST and Vp counts in oyster meat, (2) weekly mean Vp counts in oysters and weekly Vp illnesses, and (3) weekly mean SST and weekly Vp illnesses. The effects of salinity and chlorophyll a were also evaluated. Linear regression was used to quantify the relationship between SST and Vp, and piecewise regression was used to identify SST thresholds of concern. A total of 2327 oyster samples and 293 laboratory confirmed illnesses were included. In model 1, both SST and salinity were significant predictors of log(Vp) counts in oyster meat. In model 2, the mean log(Vp) count in oyster meat was a significant predictor of Vp illnesses. In model 3, weekly mean SST was a significant predictor of weekly Vp illnesses. The piecewise regression models identified a SST threshold of approximately 14 o C for both model 1 and 3, indicating increased risk of Vp in oyster meat and Vp illnesses at higher temperatures. Monitoring of SST, particularly through readily accessible remote sensing data, could serve as a warning signal for Vp and help inform the introduction and cessation of preventative or control measures.

A model of the wall boundary layer for ducted propellers

NASA Technical Reports Server (NTRS)

Eversman, Walter; Moehring, Willi

1987-01-01

The objective of the present study is to include a representation of a wall boundary layer in an existing finite element model of the propeller in the wind tunnel environment. The major consideration is that the new formulation should introduce only modest alterations in the numerical model and should still be capable of producing economical predictions of the radiated acoustic field. This is accomplished by using a stepped approximation in which the velocity profile is piecewise constant in layers. In the limit of infinitesimally thin layers, the velocity profile of the stepped approximation coincides with that of the continuous profile. The approach described here could also be useful in modeling the boundary layer in other duct applications, particularly in the computation of the radiated acoustic field for sources contained in a duct.

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

PubMed

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

2017-03-01

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

Model-Based Learning of Local Image Features for Unsupervised Texture Segmentation

NASA Astrophysics Data System (ADS)

Kiechle, Martin; Storath, Martin; Weinmann, Andreas; Kleinsteuber, Martin

2018-04-01

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images.

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

PubMed

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

2017-06-06

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

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

PubMed

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

2015-12-01

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

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Advanced control concepts. [for shuttle ascent vehicles

NASA Technical Reports Server (NTRS)

Sharp, J. B.; Coppey, J. M.

1973-01-01

The problems of excess control devices and insufficient trim control capability on shuttle ascent vehicles were investigated. The trim problem is solved at all time points of interest using Lagrangian multipliers and a Simplex based iterative algorithm developed as a result of the study. This algorithm has the capability to solve any bounded linear problem with physically realizable constraints, and to minimize any piecewise differentiable cost function. Both solution methods also automatically distribute the command torques to the control devices. It is shown that trim requirements are unrealizable if only the orbiter engines and the aerodynamic surfaces are used.

Effects of static tensile load on the thermal expansion of Gr/PI composite material

NASA Technical Reports Server (NTRS)

Farley, G. L.

1981-01-01

The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.

On estimating the effects of clock instability with flicker noise characteristics

NASA Technical Reports Server (NTRS)

Wu, S. C.

1981-01-01

A scheme for flicker noise generation is given. The second approach is that of successive segmentation: A clock fluctuation is represented by 2N piecewise linear segments and then converted into a summation of N+1 triangular pulse train functions. The statistics of the clock instability are then formulated in terms of two sample variances at N+1 specified averaging times. The summation converges very rapidly that a value of N 6 is seldom necessary. An application to radio interferometric geodesy shows excellent agreement between the two approaches. Limitations to and the relative merits of the two approaches are discussed.

Monte Carlo Simulation of Nonlinear Radiation Induced Plasmas. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wang, B. S.

1972-01-01

A Monte Carlo simulation model for radiation induced plasmas with nonlinear properties due to recombination was, employing a piecewise linearized predict-correct iterative technique. Several important variance reduction techniques were developed and incorporated into the model, including an antithetic variates technique. This approach is especially efficient for plasma systems with inhomogeneous media, multidimensions, and irregular boundaries. The Monte Carlo code developed has been applied to the determination of the electron energy distribution function and related parameters for a noble gas plasma created by alpha-particle irradiation. The characteristics of the radiation induced plasma involved are given.

Memristor emulator causes dissimilarity on a coupled memristive systems

NASA Astrophysics Data System (ADS)

Sabarathinam, S.; Prasad, Awadhesh

2018-04-01

The memristor is known as abasic fourth passive solid state circuit element. Itgaining increasing attention to create the next generation electronic devices commonly used as fundamental chaotic circuit although often arbitrary (typically piecewise linear or cubic) fluxcharge characteristics. In thispresent work, the causes of the memristor emulator studied in a coupled memristive chaoticoscillator for the first time. We confirm that the emulator that allows synchronization between theoscillators and cause the dissimilarity between the systems when increasing the couplingstrength, and co-efficient of the memristor emulator. The detailed statistical analysis was performed to confirm such phenomenon.

Applying SDDP to very large hydro-economic models with a simplified formulation for irrigation: the case of the Tigris-Euphrates river basin.

NASA Astrophysics Data System (ADS)

Rougé, Charles; Tilmant, Amaury

2015-04-01

Stochastic dual dynamic programming (SDDP) is an optimization algorithm well-suited for the study of large-scale water resources systems comprising reservoirs - and hydropower plants - as well as irrigation nodes. It generates intertemporal allocation policies that balance the present and future marginal value of water while taking into account hydrological uncertainty. It is scalable, in the sense that the time and memory required for computation do not grow exponentially with the number of state variables. Still, this scalability relies on the sampling of a few relevant trajectories for the system, and the approximation of the future value of water through cuts -i.e., hyperplanes - at points along these trajectories. Therefore, the accuracy of this approximation arguably decreases as the number of state variables increases, and it is important not to have more than necessary. In previous formulations, SDDP had three types of state variables, namely storage in each reservoir, inflow at each node and water accumulated during the irrigation season for each crop at each node. We present a simplified formulation for irrigation that does not require using the latter type of state variable. It also requires only two decision variables for each irrigation site, where the previous formulation had four per crop - and there may be several crops at the same site. This reduction in decision variables effectively reduces computation time, since SDDP decomposes the stochastic, multiperiodic, non-linear maximization problem into a series of linear ones. The proposed formulation, while computationally simpler, is mathematically equivalent to the previous one, and therefore the model gives the same results. A corollary of this formulation is that marginal utility of water at an irrigation site is effectively related to consumption at that site, through a piecewise linear function representing the net benefits from irrigation. Last but not least, the proposed formulation can be extended to any type of consumptive use of water beyond irrigation, e.g., municipal, industrial, etc This slightly different version of SDDP is applied to a large portion of the Tigris-Euphrates river basin. It comprises 24 state variables representing storage in reservoirs, 28 hydrologic state variables, and 51 demand nodes. It is the largest yet to simultaneously consider hydropower and irrigation within the same river system, and the proposed formulation almost halves the number of state variables to be considered.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

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

PubMed Central

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

2013-01-01

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

Stability analysis of confined V-shaped flames in high-velocity streams.

PubMed

El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

2010-06-01

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

Analysis Balance Parameter of Optimal Ramp metering

NASA Astrophysics Data System (ADS)

Li, Y.; Duan, N.; Yang, X.

2018-05-01

Ramp metering is a motorway control method to avoid onset congestion through limiting the access of ramp inflows into the main road of the motorway. The optimization model of ramp metering is developed based upon cell transmission model (CTM). With the piecewise linear structure of CTM, the corresponding motorway traffic optimization problem can be formulated as a linear programming (LP) problem. It is known that LP problem can be solved by established solution algorithms such as SIMPLEX or interior-point methods for the global optimal solution. The commercial software (CPLEX) is adopted in this study to solve the LP problem within reasonable computational time. The concept is illustrated through a case study of the United Kingdom M25 Motorway. The optimal solution provides useful insights and guidances on how to manage motorway traffic in order to maximize the corresponding efficiency.

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

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

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

Unsupervised parameter optimization for automated retention time alignment of severely shifted gas chromatographic data using the piecework alignment algorithm.

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

Pierce, Karisa M.; Wright, Bob W.; Synovec, Robert E.

2007-02-02

First, simulated chromatographic separations with declining retention time precision were used to study the performance of the piecewise retention time alignment algorithm and to demonstrate an unsupervised parameter optimization method. The average correlation coefficient between the first chromatogram and every other chromatogram in the data set was used to optimize the alignment parameters. This correlation method does not require a training set, so it is unsupervised and automated. This frees the user from needing to provide class information and makes the alignment algorithm more generally applicable to classifying completely unknown data sets. For a data set of simulated chromatograms wheremore » the average chromatographic peak was shifted past two neighboring peaks between runs, the average correlation coefficient of the raw data was 0.46 ± 0.25. After automated, optimized piecewise alignment, the average correlation coefficient was 0.93 ± 0.02. Additionally, a relative shift metric and principal component analysis (PCA) were used to independently quantify and categorize the alignment performance, respectively. The relative shift metric was defined as four times the standard deviation of a given peak’s retention time in all of the chromatograms, divided by the peak-width-at-base. The raw simulated data sets that were studied contained peaks with average relative shifts ranging between 0.3 and 3.0. Second, a “real” data set of gasoline separations was gathered using three different GC methods to induce severe retention time shifting. In these gasoline separations, retention time precision improved ~8 fold following alignment. Finally, piecewise alignment and the unsupervised correlation optimization method were applied to severely shifted GC separations of reformate distillation fractions. The effect of piecewise alignment on peak heights and peak areas is also reported. Piecewise alignment either did not change the peak height, or caused it to slightly decrease. The average relative difference in peak height after piecewise alignment was –0.20%. Piecewise alignment caused the peak areas to either stay the same, slightly increase, or slightly decrease. The average absolute relative difference in area after piecewise alignment was 0.15%.« less

The question of nonlinearity in the dose-response relation between particulate matter air pollution and mortality: can Akaike's Information Criterion be trusted to take the right turn?

PubMed

Roberts, Steven; Martin, Michael A

2006-12-15

The shape of the dose-response relation between particulate matter air pollution and mortality is crucial for public health assessment, and departures of this relation from linearity could have important regulatory consequences. A number of investigators have studied the shape of the particulate matter-mortality dose-response relation and concluded that the relation could be adequately described by a linear model. Some of these researchers examined the hypothesis of linearity by comparing Akaike's Information Criterion (AIC) values obtained under linear, piecewise linear, and spline alternative models. However, at the current time, the efficacy of the AIC in this context has not been assessed. The authors investigated AIC as a means of comparing competing dose-response models, using data from Cook County, Illinois, for the period 1987-2000. They found that if nonlinearities exist, the AIC is not always successful in detecting them. In a number of the scenarios considered, AIC was equivocal, picking the correct simulated dose-response model about half of the time. These findings suggest that further research into the shape of the dose-response relation using alternative model selection criteria may be warranted.

Comparative Analysis of Various Single-tone Frequency Estimation Techniques in High-order Instantaneous Moments Based Phase Estimation Method

NASA Astrophysics Data System (ADS)

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2010-04-01

For phase estimation in digital holographic interferometry, a high-order instantaneous moments (HIM) based method was recently developed which relies on piecewise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients using the HIM operator. A crucial step in the method is mapping the polynomial coefficient estimation to single-tone frequency determination for which various techniques exist. The paper presents a comparative analysis of the performance of the HIM operator based method in using different single-tone frequency estimation techniques for phase estimation. The analysis is supplemented by simulation results.

A discontinuous Galerkin method for two-dimensional PDE models of Asian options

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.; Cvejnová, D.

2016-06-01

In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

Estimation of Phase in Fringe Projection Technique Using High-order Instantaneous Moments Based Method

NASA Astrophysics Data System (ADS)

Gorthi, Sai Siva; Rajshekhar, G.; Rastogi, Pramod

2010-04-01

For three-dimensional (3D) shape measurement using fringe projection techniques, the information about the 3D shape of an object is encoded in the phase of a recorded fringe pattern. The paper proposes a high-order instantaneous moments based method to estimate phase from a single fringe pattern in fringe projection. The proposed method works by approximating the phase as a piece-wise polynomial and subsequently determining the polynomial coefficients using high-order instantaneous moments to construct the polynomial phase. Simulation results are presented to show the method's potential.

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

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

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

Glomerular structural-functional relationship models of diabetic nephropathy are robust in type 1 diabetic patients.

PubMed

Mauer, Michael; Caramori, Maria Luiza; Fioretto, Paola; Najafian, Behzad

2015-06-01

Studies of structural-functional relationships have improved understanding of the natural history of diabetic nephropathy (DN). However, in order to consider structural end points for clinical trials, the robustness of the resultant models needs to be verified. This study examined whether structural-functional relationship models derived from a large cohort of type 1 diabetic (T1D) patients with a wide range of renal function are robust. The predictability of models derived from multiple regression analysis and piecewise linear regression analysis was also compared. T1D patients (n = 161) with research renal biopsies were divided into two equal groups matched for albumin excretion rate (AER). Models to explain AER and glomerular filtration rate (GFR) by classical DN lesions in one group (T1D-model, or T1D-M) were applied to the other group (T1D-test, or T1D-T) and regression analyses were performed. T1D-M-derived models explained 70 and 63% of AER variance and 32 and 21% of GFR variance in T1D-M and T1D-T, respectively, supporting the substantial robustness of the models. Piecewise linear regression analyses substantially improved predictability of the models with 83% of AER variance and 66% of GFR variance explained by classical DN glomerular lesions alone. These studies demonstrate that DN structural-functional relationship models are robust, and if appropriate models are used, glomerular lesions alone explain a major proportion of AER and GFR variance in T1D patients. © The Author 2014. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Effects of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, C.; Altamimi, Z.; Chin, T. M.; Collilieux, X.; Dach, R.; Heflin, M. B.; Gross, R. S.; König, R.; Lemoine, F. G.; MacMillan, D. S.; Parker, J. W.; van Dam, T. M.; Wu, X.

2013-12-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS global networks used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, the effect of non-tidal atmospheric loading (NTAL) corrections on the TRF is assessed adopting a Remove/Restore approach: (i) Focusing on the a-posteriori approach, the NTAL model derived from the National Center for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations. (ii) Adopting a Kalman-filter based approach, a linear TRF is estimated combining the 4 SG solutions free from NTAL displacements. (iii) Linear fits to the NTAL displacements removed at step (i) are restored to the linear reference frame estimated at (ii). The velocity fields of the (standard) linear reference frame in which the NTAL model has not been removed and the one in which the model has been removed/restored are compared and discussed.

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

PubMed

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

2011-10-10

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

Proposing an adaptive mutation to improve XCSF performance to classify ADHD and BMD patients

NASA Astrophysics Data System (ADS)

Sadatnezhad, Khadijeh; Boostani, Reza; Ghanizadeh, Ahmad

2010-12-01

There is extensive overlap of clinical symptoms observed among children with bipolar mood disorder (BMD) and those with attention deficit hyperactivity disorder (ADHD). Thus, diagnosis according to clinical symptoms cannot be very accurate. It is therefore desirable to develop quantitative criteria for automatic discrimination between these disorders. This study is aimed at designing an efficient decision maker to accurately classify ADHD and BMD patients by analyzing their electroencephalogram (EEG) signals. In this study, 22 channels of EEGs have been recorded from 21 subjects with ADHD and 22 individuals with BMD. Several informative features, such as fractal dimension, band power and autoregressive coefficients, were extracted from the recorded signals. Considering the multimodal overlapping distribution of the obtained features, linear discriminant analysis (LDA) was used to reduce the input dimension in a more separable space to make it more appropriate for the proposed classifier. A piecewise linear classifier based on the extended classifier system for function approximation (XCSF) was modified by developing an adaptive mutation rate, which was proportional to the genotypic content of best individuals and their fitness in each generation. The proposed operator controlled the trade-off between exploration and exploitation while maintaining the diversity in the classifier's population to avoid premature convergence. To assess the effectiveness of the proposed scheme, the extracted features were applied to support vector machine, LDA, nearest neighbor and XCSF classifiers. To evaluate the method, a noisy environment was simulated with different noise amplitudes. It is shown that the results of the proposed technique are more robust as compared to conventional classifiers. Statistical tests demonstrate that the proposed classifier is a promising method for discriminating between ADHD and BMD patients.

Proposing an adaptive mutation to improve XCSF performance to classify ADHD and BMD patients.

PubMed

Sadatnezhad, Khadijeh; Boostani, Reza; Ghanizadeh, Ahmad

2010-12-01

There is extensive overlap of clinical symptoms observed among children with bipolar mood disorder (BMD) and those with attention deficit hyperactivity disorder (ADHD). Thus, diagnosis according to clinical symptoms cannot be very accurate. It is therefore desirable to develop quantitative criteria for automatic discrimination between these disorders. This study is aimed at designing an efficient decision maker to accurately classify ADHD and BMD patients by analyzing their electroencephalogram (EEG) signals. In this study, 22 channels of EEGs have been recorded from 21 subjects with ADHD and 22 individuals with BMD. Several informative features, such as fractal dimension, band power and autoregressive coefficients, were extracted from the recorded signals. Considering the multimodal overlapping distribution of the obtained features, linear discriminant analysis (LDA) was used to reduce the input dimension in a more separable space to make it more appropriate for the proposed classifier. A piecewise linear classifier based on the extended classifier system for function approximation (XCSF) was modified by developing an adaptive mutation rate, which was proportional to the genotypic content of best individuals and their fitness in each generation. The proposed operator controlled the trade-off between exploration and exploitation while maintaining the diversity in the classifier's population to avoid premature convergence. To assess the effectiveness of the proposed scheme, the extracted features were applied to support vector machine, LDA, nearest neighbor and XCSF classifiers. To evaluate the method, a noisy environment was simulated with different noise amplitudes. It is shown that the results of the proposed technique are more robust as compared to conventional classifiers. Statistical tests demonstrate that the proposed classifier is a promising method for discriminating between ADHD and BMD patients.

Wide Area Security Region Final Report

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

Makarov, Yuri V.; Lu, Shuai; Guo, Xinxin

2010-03-31

This report develops innovative and efficient methodologies and practical procedures to determine the wide-area security region of a power system, which take into consideration all types of system constraints including thermal, voltage, voltage stability, transient and potentially oscillatory stability limits in the system. The approach expands the idea of transmission system nomograms to a multidimensional case, involving multiple system limits and parameters such as transmission path constraints, zonal generation or load, etc., considered concurrently. The security region boundary is represented using its piecewise approximation with the help of linear inequalities (so called hyperplanes) in a multi-dimensional space, consisting of systemmore » parameters that are critical for security analyses. The goal of this approximation is to find a minimum set of hyperplanes that describe the boundary with a given accuracy. Methodologies are also developed to use the security hyperplanes, pre-calculated offline, to determine system security margins in real-time system operations, to identify weak elements in the system, and to calculate key contributing factors and sensitivities to determine the best system controls in real time and to assist in developing remedial actions and transmission system enhancements offline . A prototype program that automates the simulation procedures used to build the set of security hyperplanes has also been developed. The program makes it convenient to update the set of security hyperplanes necessitated by changes in system configurations. A prototype operational tool that uses the security hyperplanes to assess security margins and to calculate optimal control directions in real time has been built to demonstrate the project success. Numerical simulations have been conducted using the full-size Western Electricity Coordinating Council (WECC) system model, and they clearly demonstrated the feasibility and the effectiveness of the developed technology. Recommendations for the future work have also been formulated.« less

Toward Complete Statistics of Massive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey

NASA Astrophysics Data System (ADS)

Kobulnicky, Henry A.; Kiminki, Daniel C.; Lundquist, Michael J.; Burke, Jamison; Chapman, James; Keller, Erica; Lester, Kathryn; Rolen, Emily K.; Topel, Eric; Bhattacharjee, Anirban; Smullen, Rachel A.; Vargas Álvarez, Carlos A.; Runnoe, Jessie C.; Dale, Daniel A.; Brotherton, Michael M.

2014-08-01

We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P < 45 days, but it is not scale-free. Inflections in the cumulative distribution near 6 days, 14 days, and 45 days suggest key physical scales of sime0.2, sime0.4, and sime1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent β ~= -0.22 provides a crude approximation over P = 1.4-2000 days, as does a piece-wise linear function with a break near 45 days. The cumulative period distribution flattens at P > 45 days, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P <~ 25 days are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 days. Completeness corrections imply a binary fraction near 55% for P < 5000 days. The observed distribution of mass ratios 0.2 < q < 1 is consistent with uniform, while the observed distribution of eccentricities 0.1 < e < 0.6 is consistent with uniform plus an excess of e ~= 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ~30 km s-1 attributed to atmospheric fluctuations.

Optimal Load Shedding and Generation Rescheduling for Overload Suppression in Large Power Systems.

NASA Astrophysics Data System (ADS)

Moon, Young-Hyun

Ever-increasing size, complexity and operation costs in modern power systems have stimulated the intensive study of an optimal Load Shedding and Generator Rescheduling (LSGR) strategy in the sense of a secure and economic system operation. The conventional approach to LSGR has been based on the application of LP (Linear Programming) with the use of an approximately linearized model, and the LP algorithm is currently considered to be the most powerful tool for solving the LSGR problem. However, all of the LP algorithms presented in the literature essentially lead to the following disadvantages: (i) piecewise linearization involved in the LP algorithms requires the introduction of a number of new inequalities and slack variables, which creates significant burden to the computing facilities, and (ii) objective functions are not formulated in terms of the state variables of the adopted models, resulting in considerable numerical inefficiency in the process of computing the optimal solution. A new approach is presented, based on the development of a new linearized model and on the application of QP (Quadratic Programming). The changes in line flows as a result of changes to bus injection power are taken into account in the proposed model by the introduction of sensitivity coefficients, which avoids the mentioned second disadvantages. A precise method to calculate these sensitivity coefficients is given. A comprehensive review of the theory of optimization is included, in which results of the development of QP algorithms for LSGR as based on Wolfe's method and Kuhn -Tucker theory are evaluated in detail. The validity of the proposed model and QP algorithms has been verified and tested on practical power systems, showing the significant reduction of both computation time and memory requirements as well as the expected lower generation costs of the optimal solution as compared with those obtained from computing the optimal solution with LP. Finally, it is noted that an efficient reactive power compensation algorithm is developed to suppress voltage disturbances due to load sheddings, and that a new method for multiple contingency simulation is presented.

A Distribution-class Locational Marginal Price (DLMP) Index for Enhanced Distribution Systems

NASA Astrophysics Data System (ADS)

Akinbode, Oluwaseyi Wemimo

The smart grid initiative is the impetus behind changes that are expected to culminate into an enhanced distribution system with the communication and control infrastructure to support advanced distribution system applications and resources such as distributed generation, energy storage systems, and price responsive loads. This research proposes a distribution-class analog of the transmission LMP (DLMP) as an enabler of the advanced applications of the enhanced distribution system. The DLMP is envisioned as a control signal that can incentivize distribution system resources to behave optimally in a manner that benefits economic efficiency and system reliability and that can optimally couple the transmission and the distribution systems. The DLMP is calculated from a two-stage optimization problem; a transmission system OPF and a distribution system OPF. An iterative framework that ensures accurate representation of the distribution system's price sensitive resources for the transmission system problem and vice versa is developed and its convergence problem is discussed. As part of the DLMP calculation framework, a DCOPF formulation that endogenously captures the effect of real power losses is discussed. The formulation uses piecewise linear functions to approximate losses. This thesis explores, with theoretical proofs, the breakdown of the loss approximation technique when non-positive DLMPs/LMPs occur and discusses a mixed integer linear programming formulation that corrects the breakdown. The DLMP is numerically illustrated in traditional and enhanced distribution systems and its superiority to contemporary pricing mechanisms is demonstrated using price responsive loads. Results show that the impact of the inaccuracy of contemporary pricing schemes becomes significant as flexible resources increase. At high elasticity, aggregate load consumption deviated from the optimal consumption by up to about 45 percent when using a flat or time-of-use rate. Individual load consumption deviated by up to 25 percent when using a real-time price. The superiority of the DLMP is more pronounced when important distribution network conditions are not reflected by contemporary prices. The individual load consumption incentivized by the real-time price deviated by up to 90 percent from the optimal consumption in a congested distribution network. While the DLMP internalizes congestion management, the consumption incentivized by the real-time price caused overloads.

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

PubMed

Catsigeras, Eleonora; Guiraud, Pierre

2013-09-01

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

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

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Analysis and modeling of a family of two-transistor parallel inverters

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1973-01-01

A family of five static dc-to-square-wave inverters, each employing a square-loop magnetic core in conjunction with two switching transistors, is analyzed using piecewise-linear models for the nonlinear characteristics of the transistors, diodes, and saturable-core devices. Four of the inverters are analyzed in detail for the first time. These analyses show that, by proper choice of a frame of reference, each of the five quite differently appearing inverter circuits can be described by a common equivalent circuit. This equivalent circuit consists of a five-segment nonlinear resistor, a nonlinear saturable reactor, and a linear capacitor. Thus, by proper interpretation and identification of the parameters in the different circuits, the results of a detailed solution for one of the inverter circuits provide similar information and insight into the local and global behavior of each inverter in the family.

Aircraft MSS data registration and vegetation classification of wetland change detection

USGS Publications Warehouse

Christensen, E.J.; Jensen, J.R.; Ramsey, Elijah W.; Mackey, H.E.

1988-01-01

Portions of the Savannah River floodplain swamp were evaluated for vegetation change using high resolution (5a??6 m) aircraft multispectral scanner (MSS) data. Image distortion from aircraft movement prevented precise image-to-image registration in some areas. However, when small scenes were used (200-250 ha), a first-order linear transformation provided registration accuracies of less than or equal to one pixel. A larger area was registered using a piecewise linear method. Five major wetland classes were identified and evaluated for change. Phenological differences and the variable distribution of vegetation limited wetland type discrimination. Using unsupervised methods and ground-collected vegetation data, overall classification accuracies ranged from 84 per cent to 87 per cent for each scene. Results suggest that high-resolution aircraft MSS data can be precisely registered, if small areas are used, and that wetland vegetation change can be accurately detected and monitored.

Inferring the demographic history from DNA sequences: An importance sampling approach based on non-homogeneous processes.

PubMed

Ait Kaci Azzou, S; Larribe, F; Froda, S

2016-10-01

In Ait Kaci Azzou et al. (2015) we introduced an Importance Sampling (IS) approach for estimating the demographic history of a sample of DNA sequences, the skywis plot. More precisely, we proposed a new nonparametric estimate of a population size that changes over time. We showed on simulated data that the skywis plot can work well in typical situations where the effective population size does not undergo very steep changes. In this paper, we introduce an iterative procedure which extends the previous method and gives good estimates under such rapid variations. In the iterative calibrated skywis plot we approximate the effective population size by a piecewise constant function, whose values are re-estimated at each step. These piecewise constant functions are used to generate the waiting times of non homogeneous Poisson processes related to a coalescent process with mutation under a variable population size model. Moreover, the present IS procedure is based on a modified version of the Stephens and Donnelly (2000) proposal distribution. Finally, we apply the iterative calibrated skywis plot method to a simulated data set from a rapidly expanding exponential model, and we show that the method based on this new IS strategy correctly reconstructs the demographic history. Copyright © 2016. Published by Elsevier Inc.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

Generation and tooth contact analysis of spiral bevel gears with predesigned parabolic functions of transmission errors

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Lee, Hong-Tao

1989-01-01

A new approach for determination of machine-tool settings for spiral bevel gears is proposed. The proposed settings provide a predesigned parabolic function of transmission errors and the desired location and orientation of the bearing contact. The predesigned parabolic function of transmission errors is able to absorb piece-wise linear functions of transmission errors that are caused by the gear misalignment and reduce gear noise. The gears are face-milled by head cutters with conical surfaces or surfaces of revolution. A computer program for simulation of meshing, bearing contact and determination of transmission errors for misaligned gear has been developed.

Hiding message into DNA sequence through DNA coding and chaotic maps.

PubMed

Liu, Guoyan; Liu, Hongjun; Kadir, Abdurahman

2014-09-01

The paper proposes an improved reversible substitution method to hide data into deoxyribonucleic acid (DNA) sequence, and four measures have been taken to enhance the robustness and enlarge the hiding capacity, such as encode the secret message by DNA coding, encrypt it by pseudo-random sequence, generate the relative hiding locations by piecewise linear chaotic map, and embed the encoded and encrypted message into a randomly selected DNA sequence using the complementary rule. The key space and the hiding capacity are analyzed. Experimental results indicate that the proposed method has a better performance compared with the competing methods with respect to robustness and capacity.

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

Experimental verification of rank 1 chaos in switch-controlled Chua circuit.

PubMed

Oksasoglu, Ali; Ozoguz, Serdar; Demirkol, Ahmet S; Akgul, Tayfun; Wang, Qiudong

2009-03-01

In this paper, we provide the first experimental proof for the existence of rank 1 chaos in the switch-controlled Chua circuit by following a step-by-step procedure given by the theory of rank 1 maps. At the center of this procedure is a periodically kicked limit cycle obtained from the unforced system. Then, this limit cycle is subjected to periodic kicks by adding externally controlled switches to the original circuit. Both the smooth nonlinearity and the piecewise linear cases are considered in this experimental investigation. Experimental results are found to be in concordance with the conclusions of the theory.

Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.

PubMed

Tsyganov, M A; Ivanitsky, G R; Zemskov, E P

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Wave reflection in a reaction-diffusion system: Breathing patterns and attenuation of the echo

NASA Astrophysics Data System (ADS)

Tsyganov, M. A.; Ivanitsky, G. R.; Zemskov, E. P.

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Vision-based guidance for an automated roving vehicle

NASA Technical Reports Server (NTRS)

Griffin, M. D.; Cunningham, R. T.; Eskenazi, R.

1978-01-01

A controller designed to guide an automated vehicle to a specified target without external intervention is described. The intended application is to the requirements of planetary exploration, where substantial autonomy is required because of the prohibitive time lags associated with closed-loop ground control. The guidance algorithm consists of a set of piecewise-linear control laws for velocity and steering commands, and is executable in real time with fixed-point arithmetic. The use of a previously-reported object tracking algorithm for the vision system to provide position feedback data is described. Test results of the control system on a breadboard rover at the Jet Propulsion Laboratory are included.

Piecewise adiabatic following in non-Hermitian cycling

NASA Astrophysics Data System (ADS)

Gong, Jiangbin; Wang, Qing-hai

2018-05-01

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

Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

PubMed Central

Gálvez, Akemi; Iglesias, Andrés; Cabellos, Luis

2014-01-01

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way. PMID:24977175

Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting.

PubMed

Gálvez, Akemi; Iglesias, Andrés; Cabellos, Luis

2014-01-01

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Gherlone, Marco; Versino, Daniele; DiSciuva, Marco

2012-01-01

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C(sup 0)-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite element approximations thus provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Orbit-determination performance of Doppler data for interplanetary cruise trajectories. Part 1: Error analysis methodology

NASA Technical Reports Server (NTRS)

Ulvestad, J. S.; Thurman, S. W.

1992-01-01

An error covariance analysis methodology is used to investigate different weighting schemes for two-way (coherent) Doppler data in the presence of transmission-media and observing-platform calibration errors. The analysis focuses on orbit-determination performance in the interplanetary cruise phase of deep-space missions. Analytical models for the Doppler observable and for transmission-media and observing-platform calibration errors are presented, drawn primarily from previous work. Previously published analytical models were improved upon by the following: (1) considering the effects of errors in the calibration of radio signal propagation through the troposphere and ionosphere as well as station-location errors; (2) modelling the spacecraft state transition matrix using a more accurate piecewise-linear approximation to represent the evolution of the spacecraft trajectory; and (3) incorporating Doppler data weighting functions that are functions of elevation angle, which reduce the sensitivity of the estimated spacecraft trajectory to troposphere and ionosphere calibration errors. The analysis is motivated by the need to develop suitable weighting functions for two-way Doppler data acquired at 8.4 GHz (X-band) and 32 GHz (Ka-band). This weighting is likely to be different from that in the weighting functions currently in use; the current functions were constructed originally for use with 2.3 GHz (S-band) Doppler data, which are affected much more strongly by the ionosphere than are the higher frequency data.

Combining Mixture Components for Clustering*

PubMed Central

Baudry, Jean-Patrick; Raftery, Adrian E.; Celeux, Gilles; Lo, Kenneth; Gottardo, Raphaël

2010-01-01

Model-based clustering consists of fitting a mixture model to data and identifying each cluster with one of its components. Multivariate normal distributions are typically used. The number of clusters is usually determined from the data, often using BIC. In practice, however, individual clusters can be poorly fitted by Gaussian distributions, and in that case model-based clustering tends to represent one non-Gaussian cluster by a mixture of two or more Gaussian distributions. If the number of mixture components is interpreted as the number of clusters, this can lead to overestimation of the number of clusters. This is because BIC selects the number of mixture components needed to provide a good approximation to the density, rather than the number of clusters as such. We propose first selecting the total number of Gaussian mixture components, K, using BIC and then combining them hierarchically according to an entropy criterion. This yields a unique soft clustering for each number of clusters less than or equal to K. These clusterings can be compared on substantive grounds, and we also describe an automatic way of selecting the number of clusters via a piecewise linear regression fit to the rescaled entropy plot. We illustrate the method with simulated data and a flow cytometry dataset. Supplemental Materials are available on the journal Web site and described at the end of the paper. PMID:20953302

Pituitary iron and volume imaging in healthy controls.

PubMed

Noetzli, L J; Panigrahy, A; Hyderi, A; Dongelyan, A; Coates, T D; Wood, J C

2012-02-01

Patients with transfusional iron overload develop iron deposits in the pituitary gland, which are associated with volume loss and HH. The purpose of this study was to characterize R2 and volumetric data in a healthy population for diagnostic use in patients with transfusional iron overload. One hundred healthy controls without iron overload between the ages of 2 and 48 were recruited to have MR imaging of the brain to assess their pituitary R2 and volume. Pituitary R2 was assessed with a 8-echo spin-echo sequence, and pituitary volumes, by a 3D spoiled gradient-echo sequence with 1-mm(3) resolution. A 2-component continuous piecewise linear approximation was used for creating volumetric and R2 nomograms. Equations were generated from regression relationships for convenient z-score calculation. Pituitary R2 rose weakly with age (r(2) = 0.19, P < .0001). Anterior and total pituitary volumes increased steadily up to 18 years of age, after which volume slightly decreased. Females had larger pituitary glands, most likely representing their larger lactotroph population. From these data, a clinician can calculate the z scores for R2 and pituitary volume in patients with iron overload. Normal ranges are well-differentiated from values previously associated with endocrine disease in transfusional siderosis; this finding suggests that preclinical iron overload can be recognized and appropriately treated.

Modeling of the Through-the-Thickness Electric Potentials of a Piezoelectric Bimorph Using the Spectral Element Method

PubMed Central

Dong, Xingjian; Peng, Zhike; Hua, Hongxing; Meng, Guang

2014-01-01

An efficient spectral element (SE) with electric potential degrees of freedom (DOF) is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL) model based on first-order shear deformation theory (FSDT) is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE) analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator. PMID:24561399

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Nonlinear solar cycle forecasting: theory and perspectives

NASA Astrophysics Data System (ADS)

Baranovski, A. L.; Clette, F.; Nollau, V.

2008-02-01

In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Higher-Dimensional Signal Processing via Multiscale Geometric Analysis

DTIC Science & Technology

2010-02-10

dimensions. Surflets allowed a multiscale, piecewise polynomial approximation of discontinuities. We also created a compression algorithm using ...h (p) g (p) g (p) 0 1 g (p) g (p) 1,p 2,p 2,p dg h d h d 1,p 3,p 3,p 3,p 3,p Figure 1: The 1-D dual-tree CWT is implemented using a pair of...ψh(x)ψh(y) + j1ψg(x)ψh(y) + j2ψh(x)ψg(y) + j3ψg(x)ψg(y). (19) To compute the QWT coefficients, we can use a separable 2-D implementation [4] of the

Modeling the effects of AADT on predicting multiple-vehicle crashes at urban and suburban signalized intersections.

PubMed

Chen, Chen; Xie, Yuanchang

2016-06-01

Annual Average Daily Traffic (AADT) is often considered as a main covariate for predicting crash frequencies at urban and suburban intersections. A linear functional form is typically assumed for the Safety Performance Function (SPF) to describe the relationship between the natural logarithm of expected crash frequency and covariates derived from AADTs. Such a linearity assumption has been questioned by many researchers. This study applies Generalized Additive Models (GAMs) and Piecewise Linear Negative Binomial (PLNB) regression models to fit intersection crash data. Various covariates derived from minor-and major-approach AADTs are considered. Three different dependent variables are modeled, which are total multiple-vehicle crashes, rear-end crashes, and angle crashes. The modeling results suggest that a nonlinear functional form may be more appropriate. Also, the results show that it is important to take into consideration the joint safety effects of multiple covariates. Additionally, it is found that the ratio of minor to major-approach AADT has a varying impact on intersection safety and deserves further investigations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stereo matching and view interpolation based on image domain triangulation.

PubMed

Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce

2013-09-01

This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.

Linearized motion estimation for articulated planes.

PubMed

Datta, Ankur; Sheikh, Yaser; Kanade, Takeo

2011-04-01

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

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

The performance of a reduced-order adaptive controller when used in multi-antenna hyperthermia treatments with nonlinear temperature-dependent perfusion.

PubMed

Cheng, Kung-Shan; Yuan, Yu; Li, Zhen; Stauffer, Paul R; Maccarini, Paolo; Joines, William T; Dewhirst, Mark W; Das, Shiva K

2009-04-07

In large multi-antenna systems, adaptive controllers can aid in steering the heat focus toward the tumor. However, the large number of sources can greatly increase the steering time. Additionally, controller performance can be degraded due to changes in tissue perfusion which vary non-linearly with temperature, as well as with time and spatial position. The current work investigates whether a reduced-order controller with the assumption of piecewise constant perfusion is robust to temperature-dependent perfusion and achieves steering in a shorter time than required by a full-order controller. The reduced-order controller assumes that the optimal heating setting lies in a subspace spanned by the best heating vectors (virtual sources) of an initial, approximate, patient model. An initial, approximate, reduced-order model is iteratively updated by the controller, using feedback thermal images, until convergence of the heat focus to the tumor. Numerical tests were conducted in a patient model with a right lower leg sarcoma, heated in a 10-antenna cylindrical mini-annual phased array applicator operating at 150 MHz. A half-Gaussian model was used to simulate temperature-dependent perfusion. Simulated magnetic resonance temperature images were used as feedback at each iteration step. Robustness was validated for the controller, starting from four approximate initial models: (1) a 'standard' constant perfusion lower leg model ('standard' implies a model that exactly models the patient with the exception that perfusion is considered constant, i.e., not temperature dependent), (2) a model with electrical and thermal tissue properties varied from 50% higher to 50% lower than the standard model, (3) a simplified constant perfusion pure-muscle lower leg model with +/-50% deviated properties and (4) a standard model with the tumor position in the leg shifted by 1.5 cm. Convergence to the desired focus of heating in the tumor was achieved for all four simulated models. The controller accomplished satisfactory therapeutic outcomes: approximately 80% of the tumor was heated to temperatures 43 degrees C and approximately 93% was maintained at temperatures <41 degrees C. Compared to the controller without model reduction, a approximately 9-25 fold reduction in convergence time was accomplished using approximately 2-3 orthonormal virtual sources. In the situations tested, the controller was robust to the presence of temperature-dependent perfusion. The results of this work can help to lay the foundation for real-time thermal control of multi-antenna hyperthermia systems in clinical situations where perfusion can change rapidly with temperature.

Class Identification Efficacy in Piecewise GMM with Unknown Turning Points

ERIC Educational Resources Information Center

Ning, Ling; Luo, Wen

2018-01-01

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

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

A refined analysis of composite laminates. [theory of statics and dynamics

NASA Technical Reports Server (NTRS)

Srinivas, S.

1973-01-01

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

Evolution of complex dynamics

NASA Astrophysics Data System (ADS)

Wilds, Roy; Kauffman, Stuart A.; Glass, Leon

2008-09-01

We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

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

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

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

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

PubMed

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

2005-03-01

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

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

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

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

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Hodges, Dewey H.; Leung, Martin S.; Bless, Robert R.

1991-01-01

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

NASA Astrophysics Data System (ADS)

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-01

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics

NASA Technical Reports Server (NTRS)

Kobayashi, Takahisa; Simon, Donald L.

2006-01-01

In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.

[Shock shape representation of sinus heart rate based on cloud model].

PubMed

Yin, Wenfeng; Zhao, Jie; Chen, Tiantian; Zhang, Junjian; Zhang, Chunyou; Li, Dapeng; An, Baijing

2014-04-01

The present paper is to analyze the trend of sinus heart rate RR interphase sequence after a single ventricular premature beat and to compare it with the two parameters, turbulence onset (TO) and turbulence slope (TS). Based on the acquisition of sinus rhythm concussion sample, we in this paper use a piecewise linearization method to extract its linear characteristics, following which we describe shock form with natural language through cloud model. In the process of acquisition, we use the exponential smoothing method to forecast the position where QRS wave may appear to assist QRS wave detection, and use template to judge whether current cardiac is sinus rhythm. And we choose some signals from MIT-BIH Arrhythmia Database to detect whether the algorithm is effective in Matlab. The results show that our method can correctly detect the changing trend of sinus heart rate. The proposed method can achieve real-time detection of sinus rhythm shocks, which is simple and easily implemented, so that it is effective as a supplementary method.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

The role of density discontinuity in the inviscid instability of two-phase parallel flows

NASA Astrophysics Data System (ADS)

Behzad, M.; Ashgriz, N.

2014-02-01

We re-examine the inviscid instability of two-phase parallel flows with piecewise linear velocity profiles. Although such configuration has been theoretically investigated, we employ the concept of waves resonance to physically interpret the instability mechanism as well as the essential role of density discontinuity in the flow. Upon performing linear stability analysis, we demonstrate the existence of neutrally stable "density" and "density-vorticity" waves which are emerged due to the density jump in the flow, in addition to the well-known vorticity waves. Such waves are capable of resonating with each other to form unstable modes in the flow. Although unstable modes in this study are classified as the "shear instability" type, we demonstrate that they are not necessarily of the Rayleigh type. The results also show that the density can have both stabilizing and destabilizing effects on the flow stability. We verify that the difference in the resonating pair of neutral waves leads to such distinct behavior of the density variation.

Stress estimation in reservoirs using an integrated inverse method

NASA Astrophysics Data System (ADS)

Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre

2018-05-01

Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

PubMed

Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

2018-01-01

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

NASA Technical Reports Server (NTRS)

Kuhlman, J. M.; Shu, J. Y.

1981-01-01

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).

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

PubMed

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

2018-03-15

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

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

ERIC Educational Resources Information Center

Thipbharos, Titirut

2014-01-01

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

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

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

Xiong, Yanqin

2016-06-01

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

Quasi-conformal mapping with genetic algorithms applied to coordinate transformations

NASA Astrophysics Data System (ADS)

González-Matesanz, F. J.; Malpica, J. A.

2006-11-01

In this paper, piecewise conformal mapping for the transformation of geodetic coordinates is studied. An algorithm, which is an improved version of a previous algorithm published by Lippus [2004a. On some properties of piecewise conformal mappings. Eesti NSV Teaduste Akademmia Toimetised Füüsika-Matemaakika 53, 92-98; 2004b. Transformation of coordinates using piecewise conformal mapping. Journal of Geodesy 78 (1-2), 40] is presented; the improvement comes from using a genetic algorithm to partition the complex plane into convex polygons, whereas the original one did so manually. As a case study, the method is applied to the transformation of the Spanish datum ED50 and ETRS89, and both its advantages and disadvantages are discussed herein.

Modeling and optimization of lipid accumulation by Yarrowia lipolytica from glucose under nitrogen depletion conditions.

PubMed

Robles-Rodríguez, Carlos E; Muñoz-Tamayo, Rafael; Bideaux, Carine; Gorret, Nathalie; Guillouet, Stéphane E; Molina-Jouve, Carole; Roux, Gilles; Aceves-Lara, César A

2018-05-01

Oleaginous yeasts have been seen as a feasible alternative to produce the precursors of biodiesel due to their capacity to accumulate lipids as triacylglycerol having profiles with high content of unsaturated fatty acids. The yeast Yarrowia lipolytica is a promising microorganism that can produce lipids under nitrogen depletion conditions and excess of the carbon source. However, under these conditions, this yeast also produces citric acid (overflow metabolism) decreasing lipid productivity. This work presents two mathematical models for lipid production by Y. lipolytica from glucose. The first model is based on Monod and inhibition kinetics, and the second one is based on the Droop quota model approach, which is extended to yeast. The two models showed good agreements with the experimental data used for calibration and validation. The quota based model presented a better description of the dynamics of nitrogen and glucose dynamics leading to a good management of N/C ratio which makes this model interesting for control purposes. Then, quota model was used to evaluate, by means of simulation, a scenario for optimizing lipid productivity and lipid content. For that, a control strategy was designed by approximating the flow rates of glucose and nitrogen with piecewise linear functions. Simulation results achieved productivity of 0.95 g L -1  hr -1 and lipid content fraction of 0.23 g g -1 , which indicates that this strategy is a promising alternative for the optimization of lipid production. © 2017 Wiley Periodicals, Inc.

Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; den Hertog, Dick; Siem, Alex Y. D.; Kaanders, Johannes H. A. M.; Huizenga, Henk

2008-11-01

Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

NASA Astrophysics Data System (ADS)

Aioanei, Daniel; Samorì, Bruno; Brucale, Marco

2009-12-01

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

A Study of the Unstable Modes in High Mach Number Gaseous Jets and Shear Layers

NASA Astrophysics Data System (ADS)

Bassett, Gene Marcel

1993-01-01

Instabilities affecting the propagation of supersonic gaseous jets have been studied using high resolution computer simulations with the Piecewise-Parabolic-Method (PPM). These results are discussed in relation to jets from galactic nuclei. These studies involve a detailed treatment of a single section of a very long jet, approximating the dynamics by using periodic boundary conditions. Shear layer simulations have explored the effects of shear layers on the growth of nonlinear instabilities. Convergence of the numerical approximations has been tested by comparing jet simulations with different grid resolutions. The effects of initial conditions and geometry on the dominant disruptive instabilities have also been explored. Simulations of shear layers with a variety of thicknesses, Mach numbers and densities perturbed by incident sound waves imply that the time for the excited kink modes to grow large in amplitude and disrupt the shear layer is taug = (546 +/- 24) (M/4)^{1.7 } (Apert/0.02) ^{-0.4} delta/c, where M is the jet Mach number, delta is the half-width of the shear layer, and A_ {pert} is the perturbation amplitude. For simulations of periodic jets, the initial velocity perturbations set up zig-zag shock patterns inside the jet. In each case a single zig-zag shock pattern (an odd mode) or a double zig-zag shock pattern (an even mode) grows to dominate the flow. The dominant kink instability responsible for these shock patterns moves approximately at the linear resonance velocity, nu_ {mode} = cextnu_ {relative}/(cjet + c_ {ext}). For high resolution simulations (those with 150 or more computational zones across the jet width), the even mode dominates if the even penetration is higher in amplitude initially than the odd perturbation. For low resolution simulations, the odd mode dominates even for a stronger even mode perturbation. In high resolution simulations the jet boundary rolls up and large amounts of external gas are entrained into the jet. In low resolution simulations this entrainment process is impeded by numerical viscosity. The three-dimensional jet simulations behave similarly to two-dimensional jet runs with the same grid resolutions.

Relativistic effects in the intermolecular interaction-induced nuclear magnetic resonance parameters of xenon dimer.

PubMed

Hanni, Matti; Lantto, Perttu; Ilias, Miroslav; Jensen, Hans Jorgen Aagaard; Vaara, Juha

2007-10-28

Relativistic effects on the (129)Xe nuclear magnetic resonance shielding and (131)Xe nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe(2) system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular interaction-induced binary chemical shift delta, the anisotropy of the shielding tensor Deltasigma, and the NQC constant along the internuclear axis chi( parallel) are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full leading-order one-electron Breit-Pauli perturbation theory (BPPT) is applied using a common gauge origin. Electron correlation effects are studied at the nonrelativistic (NR) coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level of theory. The fully relativistic second-order Moller-Plesset many-body perturbation (DMP2) theory is used to examine the cross coupling between correlation and relativity on NQC. The same is investigated for delta and Deltasigma by BPPT with a density functional theory model. A semiquantitative agreement between the BPPT and DHF binary property curves is obtained for delta and Deltasigma in Xe(2). For these properties, the currently most complete theoretical description is obtained by a piecewise approximation where the uncorrelated relativistic DHF results obtained close to the basis-set limit are corrected, on the one hand, for NR correlation effects and, on the other hand, for the BPPT-based cross coupling of relativity and correlation. For chi( parallel), the fully relativistic DMP2 results obtain a correction for NR correlation effects beyond MP2. The computed temperature dependence of the second virial coefficient of the (129)Xe nuclear shielding is compared to experiment in Xe gas. Our best results, obtained with the piecewise approximation for the binary chemical shift combined with the previously published state of the art theoretical potential energy curve for Xe(2), are in excellent agreement with the experiment for the first time.

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

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

Ganapol, B.; Picca, P.; Previti, A.

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making usemore » of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)« less

Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

PubMed

Zana, F; Klein, J C

2001-01-01

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

Unified halo-independent formalism from convex hulls for direct dark matter searches

NASA Astrophysics Data System (ADS)

Gelmini, Graciela B.; Huh, Ji-Haeng; Witte, Samuel J.

2017-12-01

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution F(v) in Earth's frame or 2- Galactic velocity distribution fgal(vec u), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (Script N‑1), where Script N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is Script N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function tilde eta0BF(vmin) (which is an integral of the speed distribution) with at most (Script N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of fgal(vec u), which is a sum of Galactic streams, yields a periodic time-dependent halo function tilde etaBF(vmin, t) which at any fixed time is a piecewise constant function of vmin with at most Script N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u) that is once again a sum of delta functions, and produces a time-dependent tilde etaBF(vmin, t) function (and a time-averaged tilde eta0BF(vmin)) that is piecewise linear, differing significantly from best-fit halo functions obtained without the assumption of isotropy.

PROGRAM VSAERO: A computer program for calculating the non-linear aerodynamic characteristics of arbitrary configurations: User's manual

NASA Technical Reports Server (NTRS)

Maskew, B.

1982-01-01

VSAERO is a computer program used to predict the nonlinear aerodynamic characteristics of arbitrary three-dimensional configurations in subsonic flow. Nonlinear effects of vortex separation and vortex surface interaction are treated in an iterative wake-shape calculation procedure, while the effects of viscosity are treated in an iterative loop coupling potential-flow and integral boundary-layer calculations. The program employs a surface singularity panel method using quadrilateral panels on which doublet and source singularities are distributed in a piecewise constant form. This user's manual provides a brief overview of the mathematical model, instructions for configuration modeling and a description of the input and output data. A listing of a sample case is included.

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

Enhancements of Bayesian Blocks; Application to Large Light Curve Databases

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2015-01-01

Bayesian Blocks are optimal piecewise linear representations (step function fits) of light-curves. The simple algorithm implementing this idea, using dynamic programming, has been extended to include more data modes and fitness metrics, multivariate analysis, and data on the circle (Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations, Scargle, Norris, Jackson and Chiang 2013, ApJ, 764, 167), as well as new results on background subtraction and refinement of the procedure for precise timing of transient events in sparse data. Example demonstrations will include exploratory analysis of the Kepler light curve archive in a search for "star-tickling" signals from extraterrestrial civilizations. (The Cepheid Galactic Internet, Learned, Kudritzki, Pakvasa1, and Zee, 2008, arXiv: 0809.0339; Walkowicz et al., in progress).

A financial market model with two discontinuities: Bifurcation structures in the chaotic domain

NASA Astrophysics Data System (ADS)

Panchuk, Anastasiia; Sushko, Iryna; Westerhoff, Frank

2018-05-01

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

NASA Astrophysics Data System (ADS)

de Niem, D.; Kührt, E.; Motschmann, U.

2007-02-01

A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.

Fatigue life prediction of rotor blade composites: Validation of constant amplitude formulations with variable amplitude experiments

NASA Astrophysics Data System (ADS)

Westphal, T.; Nijssen, R. P. L.

2014-12-01

The effect of Constant Life Diagram (CLD) formulation on the fatigue life prediction under variable amplitude (VA) loading was investigated based on variable amplitude tests using three different load spectra representative for wind turbine loading. Next to the Wisper and WisperX spectra, the recently developed NewWisper2 spectrum was used. Based on these variable amplitude fatigue results the prediction accuracy of 4 CLD formulations is investigated. In the study a piecewise linear CLD based on the S-N curves for 9 load ratios compares favourably in terms of prediction accuracy and conservativeness. For the specific laminate used in this study Boerstra's Multislope model provides a good alternative at reduced test effort.

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1982-01-01

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Strain rate orientations near the Coso Geothermal Field

NASA Astrophysics Data System (ADS)

Ogasa, N. T.; Kaven, J. O.; Barbour, A. J.; von Huene, R.

2016-12-01

Many geothermal reservoirs derive their sustained capacity for heat exchange in large part due to continuous deformation of preexisting faults and fractures that permit permeability to be maintained. Similarly, enhanced geothermal systems rely on the creation of suitable permeability from fracture and faults networks to be viable. Stress measurements from boreholes or earthquake source mechanisms are commonly used to infer the tectonic conditions that drive deformation, but here we show that geodetic data can also be used. Specifically, we quantify variations in the horizontal strain rate tensor in the area surrounding the Coso Geothermal Field (CGF) by analyzing more than two decades of high accuracy differential GPS data from a network of 14 stations from the University of Nevada Reno Geodetic Laboratory. To handle offsets in the data, from equipment changes and coseismic deformation, we segment the data, perform a piecewise linear fit and take the average of each segment's strain rate to determine secular velocities at each station. With respect to North America, all stations tend to travel northwest at velocities ranging from 1 to 10 mm/yr. The nearest station to CGF shows anomalous motion compared to regional stations, which otherwise show a coherent increase in network velocity from the northeast to the southwest. We determine strain rates via linear approximation using GPS velocities in Cartesian reference frame due to the small area of our network. Principal strain rate components derived from this inversion show maximum extensional strain rates of 30 nanostrain/a occur at N87W with compressional strain rates of 37nanostrain/a at N3E. These results generally align with previous stress measurements from borehole breakouts, which indicate the least compressive horizontal principal stress is east-west oriented, and indicative of the basin and range tectonic setting. Our results suggest that the CGF represents an anomaly in the crustal deformation field, which may be influenced by the hydrothermal anomaly and possibly by the geothermal reservoir operations as well.

A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

DOE PAGES

Zhang, Tengfei; Lewis, E. E.; Smith, M. A.; ...

2017-04-18

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method ofmore » characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P N) on the axial interfaces. The x-y surfaces are treated with high-order P N combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.« less

A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

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

Zhang, Tengfei; Lewis, E. E.; Smith, M. A.

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method ofmore » characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P N) on the axial interfaces. The x-y surfaces are treated with high-order P N combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.« less

A new relativistic viscous hydrodynamics code and its application to the Kelvin–Helmholtz instability in high-energy heavy-ion collisions

DOE PAGES

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-09

Here, we construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We also split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. Furthemore, we check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken’s flow and the Israel–Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin–Helmholtz instability inmore » high-energy heavy-ion collisions.« less

Investigation to realize a computationally efficient implementation of the high-order instantaneous-moments-based fringe analysis method

NASA Astrophysics Data System (ADS)

Gorthi, Sai Siva; Rajshekhar, Gannavarpu; Rastogi, Pramod

2010-06-01

Recently, a high-order instantaneous moments (HIM)-operator-based method was proposed for accurate phase estimation in digital holographic interferometry. The method relies on piece-wise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients from the HIM operator using single-tone frequency estimation. The work presents a comparative analysis of the performance of different single-tone frequency estimation techniques, like Fourier transform followed by optimization, estimation of signal parameters by rotational invariance technique (ESPRIT), multiple signal classification (MUSIC), and iterative frequency estimation by interpolation on Fourier coefficients (IFEIF) in HIM-operator-based methods for phase estimation. Simulation and experimental results demonstrate the potential of the IFEIF technique with respect to computational efficiency and estimation accuracy.

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

ERIC Educational Resources Information Center

Zvoch, Keith

2016-01-01

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

DESCARTES' RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA.

PubMed

Bhaskar, Anand; Song, Yun S

2014-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.

DESCARTES’ RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA1

PubMed Central

Bhaskar, Anand; Song, Yun S.

2016-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the “folded” SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes’ rule of signs for polynomials to the Laplace transform of piecewise continuous functions. PMID:28018011

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

PubMed

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

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

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

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

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

2014-12-04

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

Cubic Zig-Zag Enrichment of the Classical Kirchhoff Kinematics for Laminated and Sandwich Plates

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2012-01-01

A detailed anaylsis and examples are presented that show how to enrich the kinematics of classical Kirchhoff plate theory by appending them with a set of continuous piecewise-cubic functions. This analysis is used to obtain functions that contain the effects of laminate heterogeneity and asymmetry on the variations of the inplane displacements and transverse shearing stresses, for use with a {3, 0} plate theory in which these distributions are specified apriori. The functions used for the enrichment are based on the improved zig-zag plate theory presented recently by Tessler, Di Scuva, and Gherlone. With the approach presented herein, the inplane displacements are represented by a set of continuous piecewise-cubic functions, and the transverse shearing stresses and strains are represented by a set of piecewise-quadratic functions that are discontinuous at the ply interfaces.

Limit cycles via higher order perturbations for some piecewise differential systems

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals

PubMed Central

Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G.

2016-01-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors’ previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp–p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat. PMID:27382478

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

PubMed

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.

Evolutionary technology adoption in an oligopoly market with forward-looking firms

NASA Astrophysics Data System (ADS)

Lamantia, F.; Radi, D.

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

Neighboring Optimal Aircraft Guidance in a General Wind Environment

NASA Technical Reports Server (NTRS)

Jardin, Matthew R. (Inventor)

2003-01-01

Method and system for determining an optimal route for an aircraft moving between first and second waypoints in a general wind environment. A selected first wind environment is analyzed for which a nominal solution can be determined. A second wind environment is then incorporated; and a neighboring optimal control (NOC) analysis is performed to estimate an optimal route for the second wind environment. In particular examples with flight distances of 2500 and 6000 nautical miles in the presence of constant or piecewise linearly varying winds, the difference in flight time between a nominal solution and an optimal solution is 3.4 to 5 percent. Constant or variable winds and aircraft speeds can be used. Updated second wind environment information can be provided and used to obtain an updated optimal route.

Acousto-optic replication of ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Yushkov, Konstantin B.; Molchanov, Vladimir Ya.; Ovchinnikov, Andrey V.; Chefonov, Oleg V.

2017-10-01

Precisely controlled sequences of ultrashort laser pulses are required in various scientific and engineering applications. We developed a phase-only acousto-optic pulse shaping method for replication of ultrashort laser pulses in a TW laser system. A sequence of several Fourier-transform-limited pulses is generated from a single femtosecond laser pulse by means of applying a piecewise linear phase modulation over the whole emission spectrum. Analysis demonstrates that the main factor which limits maximum delay between the pulse replicas is spectral resolution of the acousto-optic dispersive delay line used for pulse shaping. In experiments with a Cr:forsterite laser system, we obtained delays from 0.3 to 3.5 ps between two replicas of 190 fs transform-limited pulses at the central wavelength of laser emission, 1230 nm.

Plate and butt-weld stresses beyond elastic limit, material and structural modeling

NASA Technical Reports Server (NTRS)

Verderaime, V.

1991-01-01

Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.

Evolutionary technology adoption in an oligopoly market with forward-looking firms.

PubMed

Lamantia, F; Radi, D

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

On the stability, storage capacity, and design of nonlinear continuous neural networks

NASA Technical Reports Server (NTRS)

Guez, Allon; Protopopsecu, Vladimir; Barhen, Jacob

1988-01-01

The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the post synaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3N equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. Moreover, it is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.

Image encryption algorithm based on multiple mixed hash functions and cyclic shift

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Zhu, Xiaoqiang; Wu, Xiangjun; Zhang, Yingqian

2018-08-01

This paper proposes a new one-time pad scheme for chaotic image encryption that is based on the multiple mixed hash functions and the cyclic-shift function. The initial value is generated using both information of the plaintext image and the chaotic sequences, which are calculated from the SHA1 and MD5 hash algorithms. The scrambling sequences are generated by the nonlinear equations and logistic map. This paper aims to improve the deficiencies of traditional Baptista algorithms and its improved algorithms. We employ the cyclic-shift function and piece-wise linear chaotic maps (PWLCM), which give each shift number the characteristics of chaos, to diffuse the image. Experimental results and security analysis show that the new scheme has better security and can resist common attacks.

Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation

PubMed Central

Gao, Zhanheng; Yu, Zeyun; Holst, Michael

2012-01-01

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522

Colorimetric characterization models based on colorimetric characteristics evaluation for active matrix organic light emitting diode panels.

PubMed

Gong, Rui; Xu, Haisong; Tong, Qingfen

2012-10-20

The colorimetric characterization of active matrix organic light emitting diode (AMOLED) panels suffers from their poor channel independence. Based on the colorimetric characteristics evaluation of channel independence and chromaticity constancy, an accurate colorimetric characterization method, namely, the polynomial compensation model (PC model) considering channel interactions was proposed for AMOLED panels. In this model, polynomial expressions are employed to calculate the relationship between the prediction errors of XYZ tristimulus values and the digital inputs to compensate the XYZ prediction errors of the conventional piecewise linear interpolation assuming the variable chromaticity coordinates (PLVC) model. The experimental results indicated that the proposed PC model outperformed other typical characterization models for the two tested AMOLED smart-phone displays and for the professional liquid crystal display monitor as well.