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Sample records for piecewise linear approximation

  1. Piecewise linear approximation for hereditary control problems

    NASA Technical Reports Server (NTRS)

    Propst, Georg

    1990-01-01

    This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.

  2. Phase patterns in finite oscillator networks with insights from the piecewise linear approximation

    NASA Astrophysics Data System (ADS)

    Goldstein, Daniel

    2015-03-01

    Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns.

  3. Effective impact ionization threshold and piecewise linear approximation for impact ionization coefficients in a theory of superfast ionizing fronts in semiconductors

    NASA Astrophysics Data System (ADS)

    Minarsky, Andrey; Rodin, Pavel

    2013-04-01

    We focus on theoretical description of superfast ionizing fronts in semiconductor p+-n-n+ structures and argue that in the context of this problem, Townsend's type field dependence of impact ionization coefficients α(E)=α0 exp[(-E0/E)m] can be well approximated by a threshold piecewise linear dependence α(E)=α0'(E -Eb)Θ(E -Eb), where Θ(x) is the unit step function. The possibility of such approximation explains the threshold square dependence υf˜(Em-Eb)2 of the front velocity υf on the maximum electric field Em that the theory of TRAPATT-like ionizing fronts predicts even for threshold-free Townsend's approximation. We suggest a procedure for finding the best-fit parameters of the piecewise linear dependence and determine the values Eb≈0.21 E0, α0'≈0.46α0/E0 for the power m =1 and Eb≈0.5 E0, α0'≈0.7α0/E0 for the power m =2.

  4. Nonlinear Modeling by Assembling Piecewise Linear Models

    NASA Technical Reports Server (NTRS)

    Yao, Weigang; Liou, Meng-Sing

    2013-01-01

    To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

  5. Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity.

    PubMed

    Tamborrino, Massimiliano

    2016-06-01

    The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here, we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal spiking activity. Since analytical expressions of the first passage time density are not available, we propose to approximate the curved boundary by means of a continuous two-piecewise linear threshold. Explicit expressions for the first passage time density towards the new boundary are provided. First, we introduce different approximating linear thresholds. Then, we describe how to choose the optimal one minimizing the distance to the curved boundary, and hence the error in the corresponding passage time density. Theoretical means, variances and coefficients of variation given by our method are compared with empirical quantities from simulated data. Moreover, a further comparison with firing statistics derived under the assumption of a small amplitude of the time-dependent change in the threshold, is also carried out. Finally, maximum likelihood and moment estimators of the parameters of the model are derived and applied on simulated data. PMID:27106189

  6. Mutual inductance between piecewise-linear loops

    NASA Astrophysics Data System (ADS)

    Cristina Barroso, Ana; Silva, J. P.

    2013-11-01

    We consider a current-carrying wire loop made out of linear segments of arbitrary sizes and directions in three-dimensional space. We develop expressions to calculate its vector potential and magnetic field at all points in space. We then calculate the mutual inductance between two such (non-intersecting) piecewise-linear loops. As simple applications, we consider in detail the mutual inductance between two square wires of equal length that either lie in the same plane or lie in parallel horizontal planes with their centers on the same vertical axis. Our expressions can also be used to obtain approximations to the mutual inductance between wires of arbitrary three-dimensional shapes.

  7. Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system

    SciTech Connect

    BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel

    2009-03-05

    In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.

  8. Embedding loop quantum cosmology without piecewise linearity

    NASA Astrophysics Data System (ADS)

    Engle, Jonathan

    2013-04-01

    An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh

  9. Multiconlitron: a general piecewise linear classifier.

    PubMed

    Yujian, Li; Bo, Liu; Xinwu, Yang; Yaozong, Fu; Houjun, Li

    2011-02-01

    Based on the "convexly separable" concept, we present a solid geometric theory and a new general framework to design piecewise linear classifiers for two arbitrarily complicated nonintersecting classes by using a "multiconlitron," which is a union of multiple conlitrons that comprise a set of hyperplanes or linear functions surrounding a convex region for separating two convexly separable datasets. We propose a new iterative algorithm called the cross distance minimization algorithm (CDMA) to compute hard margin non-kernel support vector machines (SVMs) via the nearest point pair between two convex polytopes. Using CDMA, we derive two new algorithms, i.e., the support conlitron algorithm (SCA) and the support multiconlitron algorithm (SMA) to construct support conlitrons and support multiconlitrons, respectively, which are unique and can separate two classes by a maximum margin as in an SVM. Comparative experiments show that SMA can outperform linear SVM on many of the selected databases and provide similar results to radial basis function SVM on some of them, while SCA performs better than linear SVM on three out of four applicable databases. Other experiments show that SMA and SCA may be further improved to draw more potential in the new research direction of piecewise linear learning. PMID:21138800

  10. 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

  11. Piecewise linear dimension reduction for nonnegative data

    NASA Astrophysics Data System (ADS)

    Shen, Bin; Wang, Qifan; Allebach, Jan P.

    2015-03-01

    In past decade, the increasing popularity of imaging devices, especially smart phones, has led to a great increase in the amount of visual data. The rapidly increasing large scale data pose challenges to the storage and computational resources, and make many computer vision and pattern recognition tasks prohibitively expensive. Dimension reduction techniques explore hidden structures of the original high dimensional data and learn new low dimensional representation to alleviate the challenges. Popular dimension reduction techniques, such as PCA and NMF, do an efficient linear mapping to low dimensional space, while nonlinear techniques overcomes the limitation of linearity at the cost of expensive computational cost (e.g. computing the pairwise distance to find the geodesic distance). In this paper, a piecewise linear dimension reduction technique with global consistency and smoothness constraint is proposed to overcome the restriction of linearity at relatively low cost. Extensive experimental results show that the proposed methods outperform the linear method in the scenario of clustering both consistently and significantly.

  12. A prototype piecewise-linear dynamic attenuator.

    PubMed

    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. PMID:27284705

  13. 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.

  14. 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.

  15. 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

  16. Progressive Image Coding by Hierarchical Linear Approximation.

    ERIC Educational Resources Information Center

    Wu, Xiaolin; Fang, Yonggang

    1994-01-01

    Proposes a scheme of hierarchical piecewise linear approximation as an adaptive image pyramid. A progressive image coder comes naturally from the proposed image pyramid. The new pyramid is semantically more powerful than regular tessellation but syntactically simpler than free segmentation. This compromise between adaptability and complexity…

  17. Bifurcation Structures in a Bimodal Piecewise Linear Map: Chaotic Dynamics

    NASA Astrophysics Data System (ADS)

    Panchuk, Anastasiia; Sushko, Iryna; Avrutin, Viktor

    In this work, we investigate the bifurcation structure of the parameter space of a generic 1D continuous piecewise linear bimodal map focusing on the regions associated with chaotic attractors (cyclic chaotic intervals). The boundaries of these regions corresponding to chaotic attractors with different number of intervals are identified. The results are obtained analytically using the skew tent map and the map replacement technique.

  18. Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots

    ERIC Educational Resources Information Center

    Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.

    2013-01-01

    Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…

  19. A Piecewise Linear Finite Element Discretization of the Diffusion Equation for Arbitrary Polyhedral Grids

    SciTech Connect

    Bailey, T S; Adams, M L; Yang, B; Zika, M R

    2005-07-15

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  20. The feasibility of a piecewise-linear dynamic bowtie filter

    SciTech Connect

    Hsieh, Scott S.; Pelc, Norbert J.

    2013-03-15

    Purpose: The prepatient attenuator (or 'bowtie filter') in CT is used to modulate the flux as a function of fan angle of the x-ray beam incident on the patient. Traditional, static bowtie filters are tailored only for very generic scans and for the average patient. The authors propose a design for a dynamic bowtie that can produce a time-dependent piecewise-linear attenuation profile. This dynamic bowtie may reduce dynamic range, dose or scatter, but in this work they focus on its ability to reduce dynamic range, which may be particularly important for systems employing photon-counting detectors. Methods: The dynamic bowtie is composed of a set of triangular wedges. Each wedge is independently moved in order to produce a time-dependent piecewise-linear attenuation profile. Simulations of the bowtie are conducted to estimate the dynamic range reduction in six clinical datasets. The control of the dynamic bowtie is determined by solving a convex optimization problem, and the dose is estimated using Monte Carlo techniques. Beam hardening artifacts are also simulated. Results: The dynamic range is reduced by factors ranging from 2.4 to 27 depending on the part of the body studied. With a dynamic range minimization objective, the dose to the patient can be reduced from 6% to 33% while maintaining peak image noise. Further reduction in dose may be possible with a specific dose reduction objective. Beam hardening artifacts are suppressed with a two-pass algorithm. Conclusions: A dynamic bowtie producing a time-dependent, piecewise-linear attenuation profile is possible and can be used to modulate the flux of the scanner to the imaging task. Initial simulations show a large reduction in dynamic range. Several other applications are possible.

  1. Piecewise linear manifolds: Einstein metrics and Ricci flows

    NASA Astrophysics Data System (ADS)

    Schrader, Robert

    2016-05-01

    This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. Dedicated to Ludwig Faddeev on the occasion of his 80th birthday.

  2. Understanding cardiac alternans: A piecewise linear modeling framework

    NASA Astrophysics Data System (ADS)

    Thul, R.; Coombes, S.

    2010-12-01

    Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca2+) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of these rhythms and the coupling between cellular Ca2+ and voltage dynamics have been extensively studied leading to the development of a class of physiologically detailed models. These have been shown numerically to reproduce many of the features of myocyte response to pacing, including alternans, and have been analyzed mathematically using various approximation techniques that allow for the formulation of a low dimensional map to describe the evolution of APDs. The seminal work by Shiferaw and Karma is of particular interest in this regard [Shiferaw, Y. and Karma, A., "Turing instability mediated by voltage and calcium diffusion in paced cardiac cells," Proc. Natl. Acad. Sci. U.S.A. 103, 5670-5675 (2006)]. Here, we establish that the key dynamical behaviors of the Shiferaw-Karma model are arranged around a set of switches. These are shown to be the main elements for organizing the nonlinear behavior of the model. Exploiting this observation, we show that a piecewise linear caricature of the Shiferaw-Karma model, with a set of appropriate switching manifolds, can be constructed that preserves the physiological interpretation of the original model while being amenable to a systematic mathematical analysis. In illustration of this point, we formulate the dynamics of Ca2+ cycling (in response to pacing) and compute the properties of periodic orbits in terms of a stroboscopic map that can be constructed without approximation. Using this, we show that alternans emerge via a period-doubling instability and track this bifurcation in terms of physiologically important parameters. We also show that when coupled to a spatially extended model for Ca2+ transport, the model supports spatially varying patterns of alternans. We analyze

  3. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    SciTech Connect

    Bailey, Teresa S. Adams, Marvin L. Yang, Brian Zika, Michael R.

    2008-04-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  4. High-order hidden Markov model for piecewise linear processes and applications to speech recognition.

    PubMed

    Lee, Lee-Min; Jean, Fu-Rong

    2016-08-01

    The hidden Markov models have been widely applied to systems with sequential data. However, the conditional independence of the state outputs will limit the output of a hidden Markov model to be a piecewise constant random sequence, which is not a good approximation for many real processes. In this paper, a high-order hidden Markov model for piecewise linear processes is proposed to better approximate the behavior of a real process. A parameter estimation method based on the expectation-maximization algorithm was derived for the proposed model. Experiments on speech recognition of noisy Mandarin digits were conducted to examine the effectiveness of the proposed method. Experimental results show that the proposed method can reduce the recognition error rate compared to a baseline hidden Markov model. PMID:27586781

  5. Chaotic dynamics and diffusion in a piecewise linear equation

    SciTech Connect

    Shahrear, Pabel; Glass, Leon; Edwards, Rod

    2015-03-15

    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.

  6. 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.

  7. An improved piecewise linear chaotic map based image encryption algorithm.

    PubMed

    Hu, Yuping; Zhu, Congxu; Wang, Zhijian

    2014-01-01

    An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM) model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack. PMID:24592159

  8. Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?

    NASA Astrophysics Data System (ADS)

    Dubey, Awadhesh K.; Procaccia, Itamar; Shor, Carmel A. B. Z.; Singh, Murari

    2016-02-01

    Quasistatic strain-controlled measurements of stress versus strain curves in macroscopic amorphous solids result in a nonlinear-looking curve that ends up either in mechanical collapse or in a steady state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress versus strain curves and propose that a useful description of the mechanical response is given by a stress (or strain) -dependent shear modulus for which a theoretical evaluation exists. The elastic response is piecewise linear rather than nonlinear.

  9. An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm

    PubMed Central

    Hu, Yuping; Wang, Zhijian

    2014-01-01

    An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM) model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack. PMID:24592159

  10. Study of a piecewise linear dynamic system with negative and positive stiffness

    NASA Astrophysics Data System (ADS)

    Zou, Keguan; Nagarajaiah, Satish

    2015-05-01

    The present paper mainly focuses on numerical and analytical study of a piecewise linear dynamic oscillator with negative stiffness followed by positive stiffness which has not been studied to date. The dynamic system of interest stems from a previous analytical and experimental research on adaptive negative stiffness for the purpose of seismic protection. Numerical algorithms meant specifically for simulating piecewise smooth (PWS) systems like this nonlinear system are studied. An appropriate combination of negative stiffness and adequate damping can reduce the peak restoring or transmitted force with a slightly larger peak displacement. Essentially, the negative stiffness system in a dynamic system is very beneficial in reducing the amount of force transmitted. The exact solution is derived for free vibration. A modified Lindstedt-Poincaré method (modified L-P method) is adopted to derive approximate periodic solutions for the forced and damped system and its frequency-response curves are obtained through numerical simulation. The modified L-P solution obtained for the forced and damped case is found to agree well with the numerical results. In the piecewise linear dynamic system with initial negative stiffness followed by positive stiffness, it is found that the response remains bounded in a limit cycle. This system behaves similar to a van der Pol oscillator wherein negative damping is followed by positive damping. Presented herein is a special case as defined by the specified parameter ranges; thus, to make it more general future work is needed.

  11. A Neurodynamic Approach for Real-Time Scheduling via Maximizing Piecewise Linear Utility.

    PubMed

    Guo, Zhishan; Baruah, Sanjoy K

    2016-02-01

    In this paper, we study a set of real-time scheduling problems whose objectives can be expressed as piecewise linear utility functions. This model has very wide applications in scheduling-related problems, such as mixed criticality, response time minimization, and tardiness analysis. Approximation schemes and matrix vectorization techniques are applied to transform scheduling problems into linear constraint optimization with a piecewise linear and concave objective; thus, a neural network-based optimization method can be adopted to solve such scheduling problems efficiently. This neural network model has a parallel structure, and can also be implemented on circuits, on which the converging time can be significantly limited to meet real-time requirements. Examples are provided to illustrate how to solve the optimization problem and to form a schedule. An approximation ratio bound of 0.5 is further provided. Experimental studies on a large number of randomly generated sets suggest that our algorithm is optimal when the set is nonoverloaded, and outperforms existing typical scheduling strategies when there is overload. Moreover, the number of steps for finding an approximate solution remains at the same level when the size of the problem (number of jobs within a set) increases. PMID:26336153

  12. Optimal Piecewise Linear Basis Functions in Two Dimensions

    SciTech Connect

    Brooks III, E D; Szoke, A

    2009-01-26

    We use a variational approach to optimize the center point coefficients associated with the piecewise linear basis functions introduced by Stone and Adams [1], for polygonal zones in two Cartesian dimensions. Our strategy provides optimal center point coefficients, as a function of the location of the center point, by minimizing the error induced when the basis function interpolation is used for the solution of the time independent diffusion equation within the polygonal zone. By using optimal center point coefficients, one expects to minimize the errors that occur when these basis functions are used to discretize diffusion equations, or transport equations in optically thick zones (where they approach the solution of the diffusion equation). Our optimal center point coefficients satisfy the requirements placed upon the basis functions for any location of the center point. We also find that the location of the center point can be optimized, but this requires numerical calculations. Curiously, the optimum center point location is independent of the values of the dependent variable on the corners only for quadrilaterals.

  13. A Low Processing Cost Adaptive Algorithm Identifying Nonlinear Unknown System with Piecewise Linear Curve

    NASA Astrophysics Data System (ADS)

    Fujii, Kensaku; Aoki, Ryo; Muneyasu, Mitsuji

    This paper proposes an adaptive algorithm for identifying unknown systems containing nonlinear amplitude characteristics. Usually, the nonlinearity is so small as to be negligible. However, in low cost systems, such as acoustic echo canceller using a small loudspeaker, the nonlinearity deteriorates the performance of the identification. Several methods preventing the deterioration, polynomial or Volterra series approximations, have been hence proposed and studied. However, the conventional methods require high processing cost. In this paper, we propose a method approximating the nonlinear characteristics with a piecewise linear curve and show using computer simulations that the performance can be extremely improved. The proposed method can also reduce the processing cost to only about twice that of the linear adaptive filter system.

  14. Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

    NASA Technical Reports Server (NTRS)

    Jenkins, Jerald M.

    1987-01-01

    An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

  15. Dose reduction using a dynamic, piecewise-linear attenuator

    SciTech Connect

    Hsieh, Scott S.; Fleischmann, Dominik; Pelc, Norbert J.

    2014-02-15

    Purpose: The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations. Methods: The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuminga priori knowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or “bowtie filter”) was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals. Results: Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used withouta priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the dynamic

  16. Dose reduction using a dynamic, piecewise-linear attenuator

    PubMed Central

    Hsieh, Scott S.; Fleischmann, Dominik; Pelc, Norbert J.

    2014-01-01

    Purpose: The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations. Methods: The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuming a priori knowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or “bowtie filter”) was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals. Results: Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used without a priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the

  17. On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones

    NASA Astrophysics Data System (ADS)

    Lima, Maurício Firmino Silva; Pessoa, Claudio; Pereira, Weber F.

    Lima and Llibre [2012] have studied a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map, they proved that this class admits always a unique limit cycle, which is hyperbolic. The class studied in [Lima & Llibre, 2012] belongs to a larger set of planar continuous piecewise linear vector fields with three zones that can be separated into four other classes. Here, we consider some of these classes and we prove that some of them always admit a unique limit cycle, which is hyperbolic. However we find a class that does not have limit cycles.

  18. Canards in a minimal piecewise-linear square-wave burster

    NASA Astrophysics Data System (ADS)

    Desroches, M.; Fernández-García, S.; Krupa, M.

    2016-07-01

    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 its 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).

  19. Canards in a minimal piecewise-linear square-wave burster.

    PubMed

    Desroches, M; Fernández-García, S; Krupa, M

    2016-07-01

    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 its 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). PMID:27475071

  20. Gadgets, approximation, and linear programming

    SciTech Connect

    Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P.

    1996-12-31

    We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.

  1. Mixed-mode oscillations in a stochastic, piecewise-linear system

    NASA Astrophysics Data System (ADS)

    Simpson, D. J. W.; Kuske, R.

    2011-07-01

    We analyse a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity of the canard point. We determine the effect of each model parameter on the stochastically driven MMOs. In particular we show that any parameter variation (such as a modification of the piecewise-linear function in the model) that leaves the ratio of noise amplitude to time-scale separation unchanged typically has little effect on the width of the interval of the primary bifurcation parameter over which MMOs occur. In that sense, the MMOs are robust. Furthermore, we show that the piecewise-linear model exhibits MMOs more readily than the classical FitzHugh-Nagumo model for which a cubic polynomial is the only nonlinearity. By studying a piecewise-linear model, we are able to explain results using analytical expressions and compare these with numerical investigations.

  2. Piecewise-homogeneous model for electron side injection into linear plasma waves

    NASA Astrophysics Data System (ADS)

    Golovanov, A. A.; Kostyukov, I. Yu.

    2016-09-01

    An analytical piecewise-homogeneous model for electron side injection into linear plasma waves is developed. The dynamics of transverse betatron oscillations are studied. Based on the characteristics of the transversal motion the longitudinal motion of electrons is described. The electron parameters for which the electron trapping and subsequent acceleration are possible are estimated. The analytical results are verified by numerical simulations in the scope of the piecewise-homogeneous model. The results predicted by this model are also compared to the results given by a more realistic inhomogeneous model.

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

    SciTech Connect

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

    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 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

  4. Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones

    NASA Astrophysics Data System (ADS)

    Euzébio, Rodrigo; Pazim, Rubens; Ponce, Enrique

    2016-06-01

    We consider continuous piecewise-linear differential systems with three zones where the central one is degenerate, that is, the determinant of its linear part vanishes. By moving one parameter which is associated to the equilibrium position, we detect some new bifurcations exhibiting jump transitions both in the equilibrium location and in the appearance of limit cycles. In particular, we introduce the scabbard bifurcation, characterized by the birth of a limit cycle from a continuum of equilibrium points. Some of the studied bifurcations are detected, after an appropriate choice of parameters, in a piecewise linear Morris-Lecar model for the activity of a single neuron activity, which is usually considered as a reduction of the celebrated Hodgkin-Huxley equations.

  5. A Piecewise Linear State Variable Technique for Real Time Propulsion System Simulation

    NASA Technical Reports Server (NTRS)

    Mihaloew, J. R.; Roth, S. P.

    1982-01-01

    The emphasis on increased aircraft and propulsion control system integration and piloted simulation has created a need for higher fidelity real time dynamic propulsion models. A real time propulsion system modeling technique which satisfies this need and which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators was developed and demonstrated using flight simulator facilities at NASA Ames. A piecewise linear state variable technique is used. This technique provides the system accuracy, stability and transient response required for integrated aircraft and propulsion control system studies. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model contains approximately 7.0 K bytes of in-line computational code and 14.7 K of block data. It has an 8.9 ms cycle time on a Xerox Sigma 9 computer. A Pegasus-Harrier propulsion system was used as a baseline for developing the mathematical modeling and simulation technique. A hydromechanical and water injection control system was also simulated. The model was programmed for interfacing with a Harrier aircraft simulation at NASA Ames. Descriptions of the real time methodology and model capabilities are presented.

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

    PubMed

    Holmes, William R; Trueblood, Jennifer S; Heathcote, Andrew

    2016-03-01

    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

  7. 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

  8. Modified hyperspheres algorithm to trace homotopy curves of nonlinear circuits composed by piecewise linear modelled devices.

    PubMed

    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

  9. Piecewise-linear Bonhoeffer-van der Pol dynamics explaining mixed-mode oscillation-incrementing bifurcations

    NASA Astrophysics Data System (ADS)

    Shimizu, Kuniyasu; Inaba, Naohiko

    2016-03-01

    This study investigates mixed-mode oscillations (MMOs) generated by weakly driven piecewise-linear Bonhoeffer-van der Pol and Fitzhugh-Nagumo dynamics. Such a simple piecewise-linear oscillator can generate extremely complex MMO bifurcations such as mixed-mode oscillation-incrementing bifurcations (MMOIBs) and intermittently chaotic MMOs. These remarkable bifurcations are confirmed using explicit solutions of the piecewise-linear differential equation. Moreover, Lorenz plots are introduced, which strongly suggest that MMOIBs occur successively many times, and show that each MMO sequence is surrounded by chaos.

  10. NOTE: Estimation of renal scintigraphy parameters using a linear piecewise-continuous model

    NASA Astrophysics Data System (ADS)

    Zhang, Jeff L.; Zhang, L.; Koh, T. S.; Shuter, B.

    2003-06-01

    Instead of performing a numerical deconvolution, we propose to use a linear piecewise-continuous model of the renal impulse response function for parametric fitting of renal scintigraphy data, to obtain clinically useful renal parameters. The strengths of the present model are its simplicity and speed of computation, while not compromising on accuracy. Preliminary patient case studies show that the estimated parameters are in good agreement with a more elaborate model.

  11. 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. PMID:22370050

  12. Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers.

    PubMed

    Zhao, Lili; Feng, Dai; Neelon, Brian; Buyse, Marc

    2015-05-10

    Prostate-specific antigen (PSA) is a widely used marker in clinical trials for patients with prostate cancer. We develop a mixture model to estimate longitudinal PSA trajectory in response to treatment. The model accommodates subjects responding and not responding to therapy through a mixture of two functions. A responder is described by a piecewise linear function, represented by an intercept, a PSA decline rate, a period of PSA decline, and a PSA rising rate; a nonresponder is described by an increasing linear function with an intercept and a PSA rising rate. Each trajectory is classified as a linear or a piecewise linear function with a certain probability, and the weighted average of these two functions sufficiently characterizes a variety of patterns of PSA trajectories. Furthermore, this mixture structure enables us to derive clinically useful endpoints such as a response rate and time-to-progression, as well as biologically meaningful endpoints such as a cancer cell killing fraction and tumor growth delay. We compare our model with the most commonly used dynamic model in the literature and show its advantages. Finally, we illustrate our approach using data from two multicenter prostate cancer trials. The R code used to produce the analyses reported in this paper is available on request. PMID:25630845

  13. A hybrid approach for the modal analysis of continuous systems with discrete piecewise-linear constraints

    NASA Astrophysics Data System (ADS)

    Brake, M. R.

    2011-06-01

    The analysis of continuous systems with piecewise-linear constraints in their domains have previously been limited to either numerical approaches, or analytical methods that are constrained in the parameter space, boundary conditions, or order of the system. The present analysis develops a robust method for studying continuous systems with arbitrary boundary conditions and discrete piecewise-linear constraints. A superposition method is used to generate homogeneous boundary conditions, and modal analysis is used to find the displacement of the system in each state of the piecewise-linear constraint. In order to develop a mapping across each slope discontinuity in the piecewise-linear force-deflection profile, a variational calculus approach is taken that minimizes the L 2 energy norm between the previous and current states. An approach for calculating the finite-time Lyapunov exponents is presented in order to determine chaotic regimes. To illustrate this method, two examples are presented: a pinned-pinned beam with a deadband constraint, and a leaf spring coupled with a connector pin immersed in a viscous fluid. The pinned-pinned beam example illustrates the method for a non-operator based analysis. Results are used to show that the present method does not necessitate the need of a large number of basis functions to adequately map the displacement and velocity of the system across states. In the second example, the leaf spring is modeled as a clamped-free beam. The interaction between the beam and the connector pin is modeled with a preload and a penalty stiffness. Several experiments are conducted in order to validate aspects of the leaf spring model. From the results of the convergence and parameter studies, a high correlation between the finite-time Lyapunov exponents and the contact time per period of the excitation is observed. The parameter studies also indicate that when the system's parameters are changed in order to reduce the magnitude of the impact

  14. Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics.

    PubMed

    Cao, Qingjie; Wiercigroch, Marian; Pavlovskaia, Ekaterina E; Thompson, J Michael T; Grebogi, Celso

    2008-02-28

    In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement. PMID:17698466

  15. Simulating piecewise-linear surface water and ground water interactions with MODFLOW.

    PubMed

    Zaadnoordijk, Willem Jan

    2009-01-01

    The standard MODFLOW packages offer limited capabilities to model piecewise-linear boundary conditions to describe ground water-surface water interaction. Specifically, MODFLOW is incapable of representing a Cauchy-type boundary with different resistances for discharge or recharge conditions. Such a more sophisticated Cauchy boundary condition is needed to properly represent surface waters alternatively losing water through the bottom (high resistance) or gaining water mostly near the water surface (low resistance). One solution would be to create a new package for MODFLOW to accomplish this. However, it is also possible to combine multiple instances of standard packages in a single cell to the same effect. In this specific example, the general head boundary package is combined with the drain package to arrive at the desired piecewise-linear behavior. In doing so, the standard USGS MODFLOW version can be used without any modifications at the expense of a minor increase in preprocessing and postprocessing and computational effort. The extra preprocessing for creating the input and extra postprocessing to determine the water balance in terms of the physical entities from the MODFLOW cell fluxes per package can be taken care of by a user interface. PMID:19473274

  16. Linear radiosity approximation using vertex radiosities

    SciTech Connect

    Max, N. Lawrence Livermore National Lab., CA ); Allison, M. )

    1990-12-01

    Using radiosities computed at vertices, the radiosity across a triangle can be approximated by linear interpolation. We develop vertex-to-vertex form factors based on this linear radiosity approximation, and show how they can be computed efficiently using modern hardware-accelerated shading and z-buffer technology. 9 refs., 4 figs.

  17. Path-following analysis of the dynamical response of a piecewise-linear capsule system

    NASA Astrophysics Data System (ADS)

    Páez Chávez, Joseph; Liu, Yang; Pavlovskaia, Ekaterina; Wiercigroch, Marian

    2016-08-01

    The dynamical response of a piecewise-linear capsule system is studied by means of path-following techniques in this paper. As the capsule model belongs to the class of piecewise-smooth dynamical systems involving impact and friction, a special care is taken in order to divide the trajectory of the system into a smooth vector field in each disjoint subregion. Specifically we study a two-sided drifting system focusing on directional control and energy consumption. We aim to address two practical problems which are maximizing the rate of progression and directional control of the system by following a typical period-1 trajectory. The one-parameter analysis shows that two types of bifurcations, grazing bifurcation and boundary-intersection crossing bifurcation are found, and the maximal rate of progression is achieved when the capsule performs the oscillations without sticking phases. In our two-parameter study, the control parameters for which the rate of progression is maximal are identified using fixed value of power consumption, and the curves which divide the motion of the capsule between forward and backward progression are obtained.

  18. A wavelet-based method for the forced vibration analysis of piecewise linear single- and multi-DOF systems with application to cracked beam dynamics

    NASA Astrophysics Data System (ADS)

    Joglekar, D. M.; Mitra, M.

    2015-12-01

    The present investigation outlines a method based on the wavelet transform to analyze the vibration response of discrete piecewise linear oscillators, representative of beams with breathing cracks. The displacement and force variables in the governing differential equation are approximated using Daubechies compactly supported wavelets. An iterative scheme is developed to arrive at the optimum transform coefficients, which are back-transformed to obtain the time-domain response. A time-integration scheme, solving a linear complementarity problem at every time step, is devised to validate the proposed wavelet-based method. Applicability of the proposed solution technique is demonstrated by considering several test cases involving a cracked cantilever beam modeled as a bilinear SDOF system subjected to a harmonic excitation. In particular, the presence of higher-order harmonics, originating from the piecewise linear behavior, is confirmed in all the test cases. Parametric study involving the variations in the crack depth, and crack location is performed to bring out their effect on the relative strengths of higher-order harmonics. Versatility of the method is demonstrated by considering the cases such as mixed-frequency excitation and an MDOF oscillator with multiple bilinear springs. In addition to purporting the wavelet-based method as a viable alternative to analyze the response of piecewise linear oscillators, the proposed method can be easily extended to solve inverse problems unlike the other direct time integration schemes.

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

    PubMed

    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. PMID

  20. 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.

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

    PubMed Central

    Hsieh, Scott S.; Pelc, Norbert J.

    2014-01-01

    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, Med Phys 2011). 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 two to three. 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. PMID

  2. Dynamical analysis of periodic bursting in piece-wise linear planar neuron model.

    PubMed

    Ji, Ying; Zhang, Xiaofang; Liang, Minjie; Hua, Tingting; Wang, Yawei

    2015-12-01

    A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well. PMID:26557927

  3. Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps

    NASA Astrophysics Data System (ADS)

    Kowalczyk, P.

    2005-03-01

    This paper investigates border-collision bifurcations in piecewise-linear planar maps that are non-invertible in one region. Maps of this type arise as normal forms for grazing-sliding bifurcations in three-dimensional Filippov-type systems. A possible strategy is presented for classifying fixed and period-2 points, that are involved in such bifurcations. This allows one to determine a region of parameter space where a bifurcation leading to chaos might occur. The main part of the paper contains a careful proof of the onset of attractors which are robust to small parameter changes. An intricate structure is revealed of the limiting set on which the attractor lives, consisting of distinct continuous line segments. As parameters are varied, the attractor on the segments can change from being chaotic to periodic. Also, the mechanism by which the number of line segments can change is uncovered.

  4. Taylor approximations of multidimensional linear differential systems

    NASA Astrophysics Data System (ADS)

    Lomadze, Vakhtang

    2016-06-01

    The Taylor approximations of a multidimensional linear differential system are of importance as they contain a complete information about it. It is shown that in order to construct them it is sufficient to truncate the exponential trajectories only. A computation of the Taylor approximations is provided using purely algebraic means, without requiring explicit knowledge of the trajectories.

  5. Linear Approximation SAR Azimuth Processing Study

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

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

  6. Piecewise linear hamiltonian flows associated to zero-sum games: Transition combinatorics and questions on ergodicity

    NASA Astrophysics Data System (ADS)

    Ostrovski, Georg; van Strien, Sebastian

    2011-02-01

    In this paper we consider a class of piecewise affine Hamiltonian vector fields whose orbits are piecewise straight lines. We give a first classification result of such systems and show that the orbit-structure of the flow of such a differential equation is surprisingly rich.

  7. Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

    NASA Astrophysics Data System (ADS)

    Llibre, Jaume; Ponce, Enrique; Valls, Clàudia

    2015-08-01

    Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators.

  8. Hermite approximation of a hyperbolic Fokker-Planck optimality system to control a piecewise-deterministic process

    NASA Astrophysics Data System (ADS)

    Mohammadi, Masoumeh; Borzì, Alfio

    2016-07-01

    The Hermite spectral approximation of a hyperbolic Fokker-Planck (FP) optimality system arising in the control of an unbounded piecewise-deterministic process (PDP) is discussed. To control the probability density function (PDF) corresponding to the PDP process, an optimal control based on an FP strategy is considered. The resulting optimality system consists of a hyperbolic system with opposite-time orientation and an integral optimality condition equation. A Hermite spectral discretisation is investigated to approximate solutions to the optimality system in unbounded domains. It is proven that the proposed scheme satisfies the conservativity requirement of the PDFs. The spectral convergence rate of the discretisation scheme is proved and validated by numerical experiments.

  9. A failsafe analysis using NASTRAN's piecewise linear analysis and a nine node linear crack element

    NASA Technical Reports Server (NTRS)

    Wilkinson, R. F.; Kelley, J. W.

    1975-01-01

    A two-dimensional crack element was implemented into NASTRAN as a user dummy element and used to study failsafe characteristics of the C5A fuselage. The element is formulated from Reitsner's functional requiring that it satisfy compatability with the linear boundary displacement elements in NASTRAN. Its accuracy is demonstrated by analyzing for the stress intensity factors of two simple crack configurations for which there are classic solutions.

  10. Modified SNOW 3G: Stream cipher algorithm using piecewise linear chaotic map

    NASA Astrophysics Data System (ADS)

    Wasi, Muhammad Arif Ali; Windarta, Susila

    2016-02-01

    SNOW 3G is a synchronous stream cipher developed by Thomas Johansson and Patrik Ekhdal at Lund University. In 2006, it was chosen as the main part of the second set of Universal Mobile Telecommunications System (UMTS) confidentiality and integrity algorithms [2]. In 2008, Patrik Böhm published a report entitled "Statistical Evaluation of Stream Cipher SNOW 3G". He tested the randomness properties of SNOW 3G key stream generator. Böhm using NIST statistical test suite as randomness test tool with three kinds of test, i.e. long key stream data set, short key stream data set, and initialization vector data set. The result of the report shows that from three kind of tests, only short key stream data set has not passed eight randomness tests. He state that the suggests SNOW 3G fail because there is a weakness in the initialization of the cipher. In this paper we modify SNOW 3G algorithm using piecewise linear chaotic map (PLCM) on the key initialization mode and keystream generation mode. We use the same statistical test that have been used by Böhm [5]. The experiment shows that modified SNOW 3G stream cipher algorithm has passed all the statistical test. The results prove that PLCM impact on algorithm's randomness.

  11. Analysis of stable periodic orbits in the one dimensional linear piecewise-smooth discontinuous map.

    PubMed

    Rajpathak, Bhooshan; Pillai, Harish K; Bandyopadhyay, Santanu

    2012-09-01

    In this paper, we consider one dimensional linear piecewise-smooth discontinuous maps. It is well known that stable periodic orbits exist for such maps, in some parameter region. It is also known that the corresponding bifurcation phenomena (termed as period adding bifurcation) exhibit a special structure. In the last couple of years, several authors have analyzed this structure using border collision bifurcation curves and given the characterization for various parameter regions. In this paper, we have analyzed a specific parameter range employing a different approach. We show that this approach enables one to pose some interesting questions like: what is the number of distinct periodic orbits of any given cardinality? We prove that there are precisely φ(n) distinct orbits of period n, where φ is the Euler's totient function. We propose an algorithm which calculates the location of fixed points of all these φ(n) distinct orbits and gives the precise range of existence of these orbits with respect to the parameters. Further, we show how the amount of computations required to find these ranges of existence can be optimized. PMID:23020465

  12. Periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations

    NASA Astrophysics Data System (ADS)

    Narayanan, S.; Sekar, P.

    1995-07-01

    The response of a single-degree-of-freedom (sdf) vibrating system with unsymmetrical piecewise linear stiffness subjected to combined harmonic and flow induced excitations is investigated. Motion limiting stops, different tension and compression behavior, etc., may introduce an unsymmetrical piecewise linear stiffness characteristic. A multi-harmonic balance cum Newton-Raphson procedure in conjunction with an FFT algorithm is adopted to determine the stable and unstable periodic solutions. The stability of the periodic solutions is investigated by using Floquet theory. Digital simulation results reveal periodic, quasi-periodic and chaotic motions of the system in a range of flow velocities. Mode locked oscillations with period 5 motions are found to occur in certain range of flow velocities. Bifurcation diagrams and Lyapunov exponents are also presented.

  13. Application of piecewise hierarchical linear growth modeling to the study of continuity in behavioral development of baboons (Papio hamadryas).

    PubMed

    Hernández-Lloreda, María Victoria; Colmenares, Fernando; Martínez-Arias, Rosario

    2004-09-01

    In behavioral science, developmental discontinuities are thought to arise when the association between an outcome measure and the underlying process changes over time. Sudden changes in behavior across time are often taken to indicate that a reorganization in the outcome-process relationship may have occurred. The authors proposed in this article the use of piecewise hierarchical linear growth modeling as a statistical methodology to search for discontinuities in behavioral development and illustrated its possibilities by applying 2-piece hierarchical linear models to the study of developmental trajectories of baboon (Papio hamadryas) mothers' behavior during their infants' 1st year of life. The authors provided empirical evidence that piecewise growth modeling can be used to determine whether abrupt changes in development trajectories are tied to changes in the underlying process. PMID:15482059

  14. Flexible least squares for approximately linear systems

    NASA Astrophysics Data System (ADS)

    Kalaba, Robert; Tesfatsion, Leigh

    1990-10-01

    A probability-free multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. Consideration is given to applications in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexible-least-squares (FLS) procedure is the cost-efficient frontier, a curve in a two-dimensional cost plane which provides an explicit and systematic way to determine the efficient trade-offs between the separate costs incurred for dynamic and measurement specification errors. The FLS estimates show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A FORTRAN program for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided.

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

    SciTech Connect

    Rajpathak, Bhooshan Pillai, Harish K.; Bandyopadhyay, Santanu

    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.

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

    PubMed

    Rajpathak, Bhooshan; Pillai, Harish K; Bandyopadhyay, Santanu

    2015-10-01

    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. PMID:26520067

  17. A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations.

    PubMed

    Xia, Youshen; Feng, Gang; Wang, Jun

    2004-09-01

    This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications. PMID:15312842

  18. The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations

    NASA Astrophysics Data System (ADS)

    Bailey, Teresa S.

    In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiative-transfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

  19. Robust Unidirectional Airflow through Avian Lungs: New Insights from a Piecewise Linear Mathematical Model.

    PubMed

    Harvey, Emily P; Ben-Tal, Alona

    2016-02-01

    Avian lungs are remarkably different from mammalian lungs in that air flows unidirectionally through rigid tubes in which gas exchange occurs. Experimental observations have been able to determine the pattern of gas flow in the respiratory system, but understanding how the flow pattern is generated and determining the factors contributing to the observed dynamics remains elusive. It has been hypothesized that the unidirectional flow is due to aerodynamic valving during inspiration and expiration, resulting from the anatomical structure and the fluid dynamics involved, however, theoretical studies to back up this hypothesis are lacking. We have constructed a novel mathematical model of the airflow in the avian respiratory system that can produce unidirectional flow which is robust to changes in model parameters, breathing frequency and breathing amplitude. The model consists of two piecewise linear ordinary differential equations with lumped parameters and discontinuous, flow-dependent resistances that mimic the experimental observations. Using dynamical systems techniques and numerical analysis, we show that unidirectional flow can be produced by either effective inspiratory or effective expiratory valving, but that both inspiratory and expiratory valving are required to produce the high efficiencies of flows observed in avian lungs. We further show that the efficacy of the inspiratory and expiratory valving depends on airsac compliances and airflow resistances that may not be located in the immediate area of the valving. Our model provides additional novel insights; for example, we show that physiologically realistic resistance values lead to efficiencies that are close to maximum, and that when the relative lumped compliances of the caudal and cranial airsacs vary, it affects the timing of the airflow across the gas exchange area. These and other insights obtained by our study significantly enhance our understanding of the operation of the avian respiratory

  20. Robust Unidirectional Airflow through Avian Lungs: New Insights from a Piecewise Linear Mathematical Model

    PubMed Central

    Harvey, Emily P.; Ben-Tal, Alona

    2016-01-01

    Avian lungs are remarkably different from mammalian lungs in that air flows unidirectionally through rigid tubes in which gas exchange occurs. Experimental observations have been able to determine the pattern of gas flow in the respiratory system, but understanding how the flow pattern is generated and determining the factors contributing to the observed dynamics remains elusive. It has been hypothesized that the unidirectional flow is due to aerodynamic valving during inspiration and expiration, resulting from the anatomical structure and the fluid dynamics involved, however, theoretical studies to back up this hypothesis are lacking. We have constructed a novel mathematical model of the airflow in the avian respiratory system that can produce unidirectional flow which is robust to changes in model parameters, breathing frequency and breathing amplitude. The model consists of two piecewise linear ordinary differential equations with lumped parameters and discontinuous, flow-dependent resistances that mimic the experimental observations. Using dynamical systems techniques and numerical analysis, we show that unidirectional flow can be produced by either effective inspiratory or effective expiratory valving, but that both inspiratory and expiratory valving are required to produce the high efficiencies of flows observed in avian lungs. We further show that the efficacy of the inspiratory and expiratory valving depends on airsac compliances and airflow resistances that may not be located in the immediate area of the valving. Our model provides additional novel insights; for example, we show that physiologically realistic resistance values lead to efficiencies that are close to maximum, and that when the relative lumped compliances of the caudal and cranial airsacs vary, it affects the timing of the airflow across the gas exchange area. These and other insights obtained by our study significantly enhance our understanding of the operation of the avian respiratory

  1. 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.

  2. A Piecewise Linear Discontinuous Finite Element Spatial Discretization of the Transport Equation in 2D Cylindrical Geometry

    SciTech Connect

    Bailey, T S; Adams, M L; Chang, J H

    2008-10-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.

  3. 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

  4. Effective Estimation of Dynamic Metabolic Fluxes Using 13C Labeling and Piecewise Affine Approximation: From Theory to Practical Applicability

    PubMed Central

    Schumacher, Robin; Wahl, S. Aljoscha

    2015-01-01

    The design of microbial production processes relies on rational choices for metabolic engineering of the production host and the process conditions. These require a systematic and quantitative understanding of cellular regulation. Therefore, a novel method for dynamic flux identification using quantitative metabolomics and 13C labeling to identify piecewise-affine (PWA) flux functions has been described recently. Obtaining flux estimates nevertheless still required frequent manual reinitalization to obtain a good reproduction of the experimental data and, moreover, did not optimize on all observables simultaneously (metabolites and isotopomer concentrations). In our contribution we focus on measures to achieve faster and robust dynamic flux estimation which leads to a high dimensional parameter estimation problem. Specifically, we address the following challenges within the PWA problem formulation: (1) Fast selection of sufficient domains for the PWA flux functions, (2) Control of over-fitting in the concentration space using shape-prescriptive modeling and (3) robust and efficient implementation of the parameter estimation using the hybrid implicit filtering algorithm. With the improvements we significantly speed up the convergence by efficiently exploiting that the optimization problem is partly linear. This allows application to larger-scale metabolic networks and demonstrates that the proposed approach is not purely theoretical, but also applicable in practice. PMID:26690237

  5. Hydration thermodynamics beyond the linear response approximation.

    PubMed

    Raineri, Fernando O

    2016-10-19

    The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute

  6. On linear transform design with non-linear approximation

    NASA Astrophysics Data System (ADS)

    Sezer, Osman G.; Guleryuz, Onur G.

    2013-09-01

    In this paper we share our recent observations on methods for sparsity enforced orthogonal transform design. In our previous work on this problem, our target was to design transforms (sparse orthonormal transforms - SOT) that minimize the overall sparsity-distortion cost of a collection of image patches mainly for improving the performance of compression methods. In this paper we go one step further to understand why these transforms achieve better approximation and how different they are from transforms like the DCT or the Karhunen-Loeve transform (KLT). Our study lead us to mathematically validate that for a Gaussian process the KLT is the optimal transform not only in a linear approximation sense but also in a nonlinear approximation sense, the latter forming the basis for sparsity-based regularization. This means that the search for SOTs yields the KLT in Gaussian processes, but results in transforms that are distinctly different from the KLT in non-Gaussian cases by capturing useful structures within the data. Both toy examples and real compression results in various representation domains are presented in this paper to support our observations.

  7. Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids

    NASA Astrophysics Data System (ADS)

    Yang, Xiaofeng; James, Ashley J.

    2006-05-01

    In volume of fluid methods for interfacial flow simulations, one essential process is the so-called interface reconstruction, in which an approximate interface is reconstructed from a given discrete volume fraction field. In [J. Comput. Phys. 164 (2000) 228-237], Scardovelli and Zaleski presented analytical relations connecting linear interfaces and volume fractions in rectangular grids. Here, we present analytical relations connecting linear interfaces and volume fractions in triangular and tetrahedral grids. For computing the volume of fluid in an arbitrary polygonal or polyhedral fluid element, we also cite some of the most efficient formulas for polygon area and polyhedron volume computations. Simple test cases show that this analytic method of interface reconstruction is about 18 times faster than an iterative method in two dimensions, and four to six times faster in three dimensions. The results can be in general applied to other fields as well.

  8. 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.

  9. Border collision bifurcations and power spectral density of chaotic signals generated by one-dimensional discontinuous piecewise linear maps

    NASA Astrophysics Data System (ADS)

    Feltekh, Kais; Jemaa, Zouhair Ben; Fournier-Prunaret, Danièle; Belghith, Safya

    2014-08-01

    Recently, many papers have appeared which study the power spectral density (PSD) of signals issued from some specific maps. This interest in the PSD is due to the importance of frequency in the telecommunications and transmission security. With the large number of wireless systems, the availability of frequencies for transmission and reception is increasingly uncommon for wireless communications. Also, guided media have limitations related to the bandwidth of a signal. In this paper, we investigate some properties associated to the border-collision bifurcations in a one-dimensional piecewise-linear map with three slopes and two parameters. We derive analytical expressions for the autocorrelation sequence, power spectral density (PSD) of chaotic signals generated by our piecewise-linear map. We prove the existence of strong relation between different types of the power spectral density (low-pass, high-pass or band-stop) and the parameters. We also find a relation between the type of spectrum and the order of attractive cycles which are located after the border collision bifurcation between chaos and cycles.

  10. 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. PMID:25746821

  11. On the Number of Invariant Cones and Existence of Periodic Orbits in 3-dim Discontinuous Piecewise Linear Systems

    NASA Astrophysics Data System (ADS)

    Huan, Song-Mei; Yang, Xiao-Song

    For a family of discontinuous 3-dim homogeneous piecewise linear dynamical systems with two zones, we investigate the number of invariant cones and the existence of periodic orbits as a spatial relationship between the invariant manifolds of the subsystem changes. By studying the number of real roots of a quadratic equation induced by slopes of half straight lines starting from the origin in required domain, we obtain complete results on the number and stability of invariant cones. Especially, we prove that the maximum number of invariant cones is two, and obtain complete parameter regions on which there exist one or two invariant cones, on which one or two fake cones (corresponding to real roots of the quadratic equation that are not in the required domain) appear and on which an invariant cone will be foliated by periodic orbits.

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

    DOE PAGESBeta

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

    2016-05-04

    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/T3, but we formulate and test a slight extension for opacities ~ 1/T3.5, 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

  13. Equations of motion in the linear approximation.

    NASA Technical Reports Server (NTRS)

    Robinson, I.; Robinson, J. R.

    1972-01-01

    Attempt to develop a gauge-invariant theory of the motion of singularities in an n-dimensional Riemannian space. A gauge-invariant theory is developed for a nongeodetic particle represented by a time-like world line in the linearized field theory. The solution of the basic algebraic and differential equations is to be constructed from the source line, the future null cones emanating from it, a scale factor, and nothing else, and the leading term of the solution is the Schwarzschild field. A class of possible solutions is examined, and it is shown that this class contains just one acceptable member - namely, a particle in constant acceleration.

  14. Construction of Substitution Box Based on Piecewise Linear Chaotic Map and S8 Group

    NASA Astrophysics Data System (ADS)

    Hussain, Iqtadar; Gondal, Muhammad Asif; Hussain, Azkar

    2015-03-01

    In this paper, a scheme for the construction of substitution boxes (S-boxes) based on chaotic map and S8 (symmetric group of permutation) is presented. The properties such as nonlinearity, strict avalanche and resistance against the differential cryptanalysis are analyzed in detail. The result shows that the criterion for designing good S-box can be met approximately. As a result, our approach is suitable for practical application in designing block cryptosystem.

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

    SciTech Connect

    Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.

    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 on 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.

  16. An approximation theory for the identification of linear thermoelastic systems

    NASA Technical Reports Server (NTRS)

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

    1990-01-01

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

  17. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    NASA Technical Reports Server (NTRS)

    Fabiano, R. H.; Ito, K.

    1990-01-01

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

  18. Rational approximations to solutions of linear differential equations

    PubMed Central

    Chudnovsky, D. V.; Chudnovsky, G. V.

    1983-01-01

    Rational approximations of Padé and Padé type to solutions of differential equations are considered. One of the main results is a theorem stating that a simultaneous approximation to arbitrary solutions of linear differential equations over C(x) cannot be “better” than trivial ones implied by the Dirichlet box principle. This constitutes, in particular, the solution in the linear case of Kolchin's problem that the “Roth's theorem” holds for arbitrary solutions of algebraic differential equations. Complete effective proofs for several valuations are presented based on the Wronskian methods and graded subrings of Picard-Vessiot extensions. PMID:16593357

  19. How to Solve Schroedinger Problems by Approximating the Potential Function

    SciTech Connect

    Ledoux, Veerle; Van Daele, Marnix

    2010-09-30

    We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.

  20. Some approximations in the linear dynamic equations of thin cylinders

    NASA Technical Reports Server (NTRS)

    El-Raheb, M.; Babcock, C. D., Jr.

    1981-01-01

    Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valid at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wavelengths, independent of shell thickness and boundary conditions.

  1. Quantitative structure-antibacterial activity relationship modeling using a combination of piecewise linear regression-discriminant analysis (I): Quantum chemical, topographic, and topological descriptors

    NASA Astrophysics Data System (ADS)

    Molina, Enrique; Estrada, Ernesto; Nodarse, Delvin; Torres, Luis A.; González, Humberto; Uriarte, Eugenio

    Time-dependent antibacterial activity of 2-furylethylenes using quantum chemical, topographic, and topological indices is described as inhibition of respiration in E. coli. A QSAR strategy based on the combination of the linear piecewise regression and the discriminant analysis is used to predict the biological activity values of strong and moderates antibacterial furylethylenes. The breakpoint in the values of the biological activity was detected. The biological activities of the compounds are described by two linear regression equations. A discriminant analysis is carried out to classify the compounds in one of the biological activity two groups. The results showed using different kind of descriptors were compared. In all cases the piecewise linear regression - discriminant analysis (PLR-DA) method produced significantly better QSAR models than the linear regression analysis. The QSAR models were validated using an external validation previously extracted from the original data. A prediction of reported antibacterial activity analysis was carried out showing dependence between the probability of a good classification and the experimental antibacterial activity. Statistical parameters showed the quality of quantum-chemical descriptors based models prediction in LDA having an accuracy of 0.9 and a C of 0.9. The best PLR-DA model explains more than 92% of the variance of experimental activity. Models with best prediction results were those based on quantum-chemical descriptors. An interpretation of quantum-chemical descriptors entered in models was carried out.

  2. Approximate Linearization Control of 2-DOF Underactuated-by-1 Systems Using Higher Order Linearization Coordinate

    NASA Astrophysics Data System (ADS)

    Hoshino, Tasuku

    This paper deals with an approximate linearization control of 2-DOF underactuated-by-1 nonlinear systems, proposing a novel linearization coordinate which reduces the approximation error over the state space around the operating point. The coordinate is analytically constructed in a systematic way by solving two first order linear partial differential equations and the solution is given in an infinite series of configuration variables. The resulting linearization feedback is highly nonlinear and the basin of attraction of the stabilized system using proposed coordinate is large, comparing with those of a conventional first order or other lower order linearization coordinates. The approximate linearization control based on the proposed coordinate is applied to the stabilization of a rotational inverted pendulum; the advantage is verified in simulations and experiments. Some perspectives on availability of the linearization coordinate are discussed and they are computed also for a mobile inverted pendulum, Acrobot, and for Pendubot as examples.

  3. Approximate solutions for non-linear iterative fractional differential equations

    NASA Astrophysics Data System (ADS)

    Damag, Faten H.; Kiliçman, Adem; Ibrahim, Rabha W.

    2016-06-01

    This paper establishes approximate solution for non-linear iterative fractional differential equations: d/γv (s ) d sγ =ℵ (s ,v ,v (v )), where γ ∈ (0, 1], s ∈ I := [0, 1]. Our method is based on some convergence tools for analytic solution in a connected region. We show that the suggested solution is unique and convergent by some well known geometric functions.

  4. On approximating hereditary dynamics by systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1978-01-01

    The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

  5. 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. PMID:21997007

  6. A Free-Knot Spline Modeling Framework for Piecewise Linear Logistic Regression in Complex Samples with Body Mass Index and Mortality as an Example

    PubMed Central

    Keith, Scott W.; Allison, David B.

    2014-01-01

    This paper details the design, evaluation, and implementation of a framework for detecting and modeling non-linearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and non-parametric bootstrapping. Unlike other non-linear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI, kg/m2) and the complex multistage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic non-linear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and non-linearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarz’s Bayesian Information Criterion (BIC) and Akaike’s Information Criterion (AIC), in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions. PMID:25610831

  7. Approximate labeling via graph cuts based on linear programming.

    PubMed

    Komodakis, Nikos; Tziritas, Georgios

    2007-08-01

    A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems. PMID:17568146

  8. Approximate simulation of entanglement with a linear cost of communication

    SciTech Connect

    Montina, A.

    2011-10-15

    Bell's theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows exponentially in n. Three simple protocols are presented that provide approximate simulations for low-dimensional entangled systems and require a linearly growing amount of communication. We have tested them by performing some simulations for a family of measurements. The maximal error is less than 1% in three dimensions and grows sublinearly with the number of entangled bits in the range numerically tested. One protocol is the multidimensional generalization of the exact Toner-Bacon [Phys. Rev. Lett. 91, 187904 (2003)] model for a single Bell state. The other two protocols are generalizations of an alternative exact model, which we derive from the Kochen-Specker [J. Math. Mech. 17, 59 (1967)] scheme for simulating single-qubit measurements. These protocols can give some indication for finding optimal one-way communication protocols that classically simulate entanglement and quantum channels. Furthermore they can be useful for deciding if a quantum communication protocol provides an advantage on classical protocols.

  9. Approximate simulation of entanglement with a linear cost of communication

    NASA Astrophysics Data System (ADS)

    Montina, A.

    2011-10-01

    Bell’s theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows exponentially in n. Three simple protocols are presented that provide approximate simulations for low-dimensional entangled systems and require a linearly growing amount of communication. We have tested them by performing some simulations for a family of measurements. The maximal error is less than 1% in three dimensions and grows sublinearly with the number of entangled bits in the range numerically tested. One protocol is the multidimensional generalization of the exact Toner-Bacon [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.91.187904 91, 187904 (2003)] model for a single Bell state. The other two protocols are generalizations of an alternative exact model, which we derive from the Kochen-Specker [J. Math. Mech. 17, 59 (1967)] scheme for simulating single-qubit measurements. These protocols can give some indication for finding optimal one-way communication protocols that classically simulate entanglement and quantum channels. Furthermore they can be useful for deciding if a quantum communication protocol provides an advantage on classical protocols.

  10. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    SciTech Connect

    Benzi, M.; Tuma, M.

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  11. Asymptotic high frequency analysis of the electromagnetic backscattering from an inlet model consisting of piecewise linearly tapered sections

    NASA Technical Reports Server (NTRS)

    Altintas, A.; Pathak, P. H.

    1985-01-01

    Electromagnetic backscattering from an open ended three dimensional inlet model is analyzed and computed patterns are compared with results of experimental measurements. The model is comprised of two sections. The first section consists of a linearly tapered waveguide with a rectangular opening at one end and the other end is connected to the second section which is a uniform rectangular waveguide with a planar perfectly conducting termination. The model is electrically large so that many propagating modes are excited. The method of analysis contains conventional aperture integration and modal techniques combined with high frequency techniques, which employ concepts such as modal rays, geometrical theory of diffraction and equivalent currents. For the cases considered, it is shown that only a few of the many propagating modes contribute appreciably to the backscattered field. These modes are selected according to their modal ray angle directions.

  12. Rational approximations to linear forms of exponentials and binomials

    PubMed Central

    Chudnovsky, G. V.

    1983-01-01

    Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: ǀΣi=0nCieriǀ > H-n-ε for any distinct rational numbers r0,r1,..., rn and rational integers C0,C1,...,Cn with H = max0≤i≤n ǀCiǀ. We improve Mahler's estimate by replacing exponentials eri by linearly independent linear forms Li = Σ Lijesij with rational Lij,siji = 0,1,...,n. Similar results are obtained for binomials (a/b)ri or Σ Lij(a/b)sij with integers a,b and logǀbǀ/logǀaǀ > 1 - ε. The simplest examples of new numbers with the irrationality exponent “2 + ε” are sinh 1 or sin 1. PMID:16593320

  13. Piecing Together Piecewise Functions.

    ERIC Educational Resources Information Center

    King, Sybrina L.

    1997-01-01

    Presents an activity to teach piecewise functions using wax paper and rectangular grids. Helps students understand the idea of different pieces by literally "piecing" together a new type of mathematical function. Also describes a followup activity and explains how piecewise functions can be graphed using graphing calculators. (NB)

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

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1984-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

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

  16. RKH space approximations for the feedback operator in a linear hereditary control system

    NASA Technical Reports Server (NTRS)

    Reneke, J. A.; Fennell, R. E.

    1987-01-01

    Computational implementation of feedback control laws for linear hereditary systems requires the approximation of infinite dimensional feedback operators with finite dimensional operators. The dense subspaces of K-polygonal functions in reproducing kernel Hilbert spaces, RKH spaces, suggest finite dimensional approximations of the matrix representations of the control operators. A convergence theorem is developed for the approximations and the numerical implementation of the approximations is discussed.

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

    NASA Technical Reports Server (NTRS)

    Kowal, Michael T.

    1997-01-01

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

  18. Nonlinear control via approximate input-output linearization - The ball and beam example

    NASA Technical Reports Server (NTRS)

    Hauser, John; Sastry, Shankar; Kokotovic, Petar

    1992-01-01

    A study is made of approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree. For such systems, a method is provided for constructing approximate systems that are input-output linearizable. The analysis presented in this note is motivated through its application to a common undergraduate control laboratory experiment, the ball and beam system, where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization.

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

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

  20. Modeling of crossbred cattle growth, comparison between cubic and piecewise random regression models.

    PubMed

    Mirzaei, H R; Pitchford, W S; Verbyla, A P

    2011-01-01

    Two analyses, cubic and piecewise random regression, were conducted to model growth of crossbred cattle from birth to about two years of age, investigating the ability of a piecewise procedure to fit growth traits without the complications of the cubic model. During a four-year period (1994-1997) of the Australian "Southern Crossbreeding Project", mature Hereford cows (N = 581) were mated to 97 sires of Angus, Belgian Blue, Hereford, Jersey, Limousin, South Devon, and Wagyu breeds, resulting in 1141 steers and heifers born over four years. Data included 13 (for steers) and eight (for heifers) live body weight measurements, made approximately every 50 days from birth until slaughter. The mixed model included fixed effects of sex, sire breed, age (linear, quadratic and cubic), and their interactions between sex and sire breed with age. Random effects were sire, dam, management (birth location, year, post-weaning groups), and permanent environmental effects and for each of these when possible, their interactions with linear, quadratic and cubic growth. In both models, body weights of all breeds increased over pre-weaning period, held fairly steady (slightly flattening) over the dry season then increased again towards the end of the feedlot period. The number of estimated parameters for the cubic model was 22 while for the piecewise model it was 32. It was concluded that the piecewise model was very similar to the cubic model in the fit to the data; with the piecewise model being marginally better. The piecewise model seems to fit the data better at the end of the growth period. PMID:21968730

  1. Piecewise Cubic Interpolation Package

    Energy Science and Technology Software Center (ESTSC)

    1982-04-23

    PCHIP (Piecewise Cubic Interpolation Package) is a set of subroutines for piecewise cubic Hermite interpolation of data. It features software to produce a monotone and "visually pleasing" interpolant to monotone data. Such an interpolant may be more reasonable than a cubic spline if the data contain both 'steep' and 'flat' sections. Interpolation of cumulative probability distribution functions is another application. In PCHIP, all piecewise cubic functions are represented in cubic Hermite form; that is, f(x)more » is determined by its values f(i) and derivatives d(i) at the breakpoints x(i), i=1(1)N. PCHIP contains three routines - PCHIM, PCHIC, and PCHSP to determine derivative values, six routines - CHFEV, PCHFE, CHFDV, PCHFD, PCHID, and PCHIA to evaluate, differentiate, or integrate the resulting cubic Hermite function, and one routine to check for monotonicity. A FORTRAN 77 version and SLATEC version of PCHIP are included.« less

  2. Linear-phase approximation in the triangular facet near-field physical optics computer program

    NASA Technical Reports Server (NTRS)

    Imbriale, W. A.; Hodges, R. E.

    1990-01-01

    Analyses of reflector antenna surfaces use a computer program based on a discrete approximation of the radiation integral. The calculation replaces the actual surface with a triangular facet representation; the physical optics current is assumed to be constant over each facet. Described here is a method of calculation using linear-phase approximation of the surface currents of parabolas, ellipses, and shaped subreflectors and compares results with a previous program that used a constant-phase approximation of the triangular facets. The results show that the linear-phase approximation is a significant improvement over the constant-phase approximation, and enables computation of 100 to 1,000 lambda reflectors within a reasonable time on a Cray computer.

  3. Nonlinear control via approximate input-output linearization - The ball and beam example

    NASA Technical Reports Server (NTRS)

    Hauser, John; Sastry, Shankar; Kokotovic, Petar

    1989-01-01

    This paper presents an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. It is shown that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. Some properties of the accuracy of the approximation are demonstrated and, in the context of the ball and beam example, it is shown to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems.

  4. Piecewise Polynomial Representations of Genomic Tracks

    PubMed Central

    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/. PMID:23166601

  5. 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/. PMID:23166601

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

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

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

  7. Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

    NASA Astrophysics Data System (ADS)

    Rizzato, F. B.

    Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation.

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

    ERIC Educational Resources Information Center

    Vial, Alexandre

    2012-01-01

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

  9. The method of local linear approximation in the theory of nonlinear functional-differential equations

    SciTech Connect

    Slyusarchuk, Vasilii E

    2010-10-06

    Conditions for the existence of solutions to the nonlinear functional-differential equation (d{sup m}x(t))/dt{sup m} + (fx)(t)=h(t), t element of R in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.

  10. Linear Vlasov theory in the shearing sheet approximation with application to the magneto-rotational instability

    SciTech Connect

    Heinemann, Tobias; Quataert, Eliot E-mail: eliot@berkeley.edu

    2014-09-01

    We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or 'kinetic MHD') approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.

  11. Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates

    NASA Astrophysics Data System (ADS)

    Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier

    2016-07-01

    A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.

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

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.; Wall, Johnm W.

    2011-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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

  14. Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes.

    PubMed

    Galtier, Mathieu N; Marini, Camille; Wainrib, Gilles; Jaeger, Herbert

    2014-08-01

    A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Niño phenomenon studied in climate research. PMID:24815743

  15. Challenges within the linear response approximation when studying enzyme catalysis and effects of mutations.

    PubMed

    Sharir-Ivry, Avital; Varatharaj, Rajapandian; Shurki, Avital

    2015-01-13

    Various aspects of the linear response approximation (LRA) approach were examined when calculating reaction barriers within an enzyme and its different mutants. Scaling the electrostatic interactions is shown to slightly affect the absolute values of the barriers but not the overall trend when comparing wild-type and mutants. Convergence of the overall energetics was shown to depend on the sampling. Finally, the contribution of particular residues was shown to be significant, despite its small value. PMID:26574227

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

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1987-01-01

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

  17. Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

    NASA Astrophysics Data System (ADS)

    Atalla, Viktor; Zhang, Igor Ying; Hofmann, Oliver T.; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias

    2016-07-01

    We obtain the exchange parameter of hybrid functionals by imposing the fundamental condition of a piecewise linear total energy with respect to electron number. For the Perdew-Burke-Ernzerhof (PBE) hybrid family of exchange-correlation functionals (i.e., for an approximate generalized Kohn-Sham theory) this implies that (i) the highest occupied molecular orbital corresponds to the ionization potential (I ), (ii) the energy of the lowest unoccupied molecular orbital corresponds to the electron affinity (A ), and (iii) the energies of the frontier orbitals are constant as a function of their occupation. In agreement with a previous study [N. Sai et al., Phys. Rev. Lett. 106, 226403 (2011), 10.1103/PhysRevLett.106.226403], we find that these conditions are met for high values of the exact exchange admixture α and illustrate their importance for the tetrathiafulvalene-tetracyanoquinodimethane complex for which standard density functional theory functionals predict artificial electron transfer. We further assess the performance for atomization energies and weak interaction energies. We find that atomization energies are significantly underestimated compared to PBE or PBE0, whereas the description of weak interaction energies improves significantly if a 1 /R6 van der Waals correction scheme is employed.

  18. Approximate Analytical Solutions for Primary Chatter in the Non-Linear Metal Cutting Model

    NASA Astrophysics Data System (ADS)

    Warmiński, J.; Litak, G.; Cartmell, M. P.; Khanin, R.; Wiercigroch, M.

    2003-01-01

    This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates.

  19. Dynamics of a spinning particle in a linear in spin Hamiltonian approximation

    NASA Astrophysics Data System (ADS)

    Lukes-Gerakopoulos, Georgios; Katsanikas, Matthaios; Patsis, Panos A.; Seyrich, Jonathan

    2016-07-01

    We investigate for order and chaos the dynamical system of a spinning test particle of mass m moving in the spacetime background of a Kerr black hole of mass M . This system is approximated in our investigation by the linear in spin Hamiltonian function [E. Barausse and A. Buonanno, Phys. Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincaré section. Various topological structures coming from the nonintegrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin S /(m M )=10-4 of the particle and below, the impact of the nonintegrability of the system on the motion of the particle seems to be negligible.

  20. S{sub N} Schemes, Linear Infinite-Medium Solutions, and the Diffusion Approximation

    SciTech Connect

    Larsen, E.W.

    2001-06-17

    It is standard practice to require an S{sub N} spatial discretization scheme to preserve the ''flat infinite-medium'' solution of the transport equation. This solution consists of a spatially independent source that gives rise to a spatially independent flux. However, there exist many other exact solutions of the transport equation that are typically not preserved by approximation schemes. Here, we discuss one of these: a source that is linear in space giving rise to an angular flux that is linear in space and angle. For one-group, planar-geometry S{sub N} problems, we show that (a) among the class of weighted-diamond schemes, only one - the diamond-difference scheme - preserves this exact ''linear'' solution; (b) consequently, only the diamond scheme preserves the correct Fick's Law; and (c) as a further consequence, nondiamond schemes can produce significant errors (not observed in the diamond solution) for diffusive problems with spatial cells that are not optically thin. These results demonstrate that it is advantageous for S{sub N} discretization schemes to preserve the ''flat'' and ''linear'' infinite-medium solutions.

  1. Best possible approximation algorithms for single machine scheduling with increasing linear maintenance durations.

    PubMed

    Shi, Xuefei; Xu, Dehua

    2014-01-01

    We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear form f(t) = a+bt with a ≥ 0 and b > 1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem with b ≥ 0 unless P = NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the case b > 1 and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the case b ≤ 1 both from the worst-case bound point of view. PMID:24701177

  2. Fall with linear drag and Wien's displacement law: approximate solution and Lambert function

    NASA Astrophysics Data System (ADS)

    Vial, Alexandre

    2012-07-01

    We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms.

  3. Linear decomposition method for approximating arbitrary magnetic field profiles by optimization of discrete electromagnet currents

    SciTech Connect

    Tejero, E. M.; Gatling, G.

    2009-03-15

    A method for approximating arbitrary axial magnetic field profiles for a given solenoidal electromagnet coil array is described. The method casts the individual contributions from each coil as a truncated orthonormal basis for the space within the array. This truncated basis allows for the linear decomposition of an arbitrary profile function, which returns the appropriate currents for each coil to best reproduce the desired profile. We present the mathematical details of the method along with a detailed example of its use. The results from the method are used in a simulation and compared with magnetic field measuremen0008.

  4. Parallel FE Approximation of the Even/Odd Parity Form of the Linear Boltzmann Equation

    SciTech Connect

    Drumm, Clifton R.; Lorenz, Jens

    1999-07-21

    A novel solution method has been developed to solve the linear Boltzmann equation on an unstructured triangular mesh. Instead of tackling the first-order form of the equation, this approach is based on the even/odd-parity form in conjunction with the conventional mdtigroup discrete-ordinates approximation. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, and the method is well suited for massively parallel computers.

  5. Piecewise-quartics and exponential parameterization for interpolating reduced data

    NASA Astrophysics Data System (ADS)

    Kozera, R.

    2016-06-01

    We examine the asymptotics of a piecewise-quartic Lagrange interpolation used to fit reduced data in arbitrary Euclidean space which are sampled more-or-less uniformly. The unknown interpolation knots are guessed here according to the so-called exponential parameterization which depends on a single parameter λ ∈ [0, 1]. In this work we demonstrate numerically an abrupt discontinuity in the quality of the discussed interpolation scheme yielding a slow linear convergence order for all λ ∈ [0, 1). On the other hand, as well-known the quality of the curve approximation for λ = 1 sharply increases to the fast sharp quartic order which can be further accelerated for special subfamilies of more-or-less uniform samplings.

  6. Structural damage assessment using linear approximation with maximum entropy and transmissibility data

    NASA Astrophysics Data System (ADS)

    Meruane, V.; Ortiz-Bernardin, A.

    2015-03-01

    Supervised learning algorithms have been proposed as a suitable alternative to model updating methods in structural damage assessment, being Artificial Neural Networks the most frequently used. Notwithstanding, the slow learning speed and the large number of parameters that need to be tuned within the training stage have been a major bottleneck in their application. This article presents a new algorithm for real-time damage assessment that uses a linear approximation method in conjunction with antiresonant frequencies that are identified from transmissibility functions. The linear approximation is handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of Neural Networks. The performance of the proposed methodology is validated by considering three experimental structures: an eight-degree-of-freedom (DOF) mass-spring system, a beam, and an exhaust system of a car. To demonstrate the potential of the proposed algorithm over existing ones, the obtained results are compared with those of a model updating method based on parallel genetic algorithms and a multilayer feedforward neural network approach.

  7. A 60-dB linear VGA with novel exponential gain approximation

    NASA Astrophysics Data System (ADS)

    Jiaye, Zhou; Xi, Tan; Junyu, Wang; Zhangwen, Tang; Hao, Min

    2009-06-01

    A CMOS variable gain amplifier (VGA) that adopts a novel exponential gain approximation is presented. No additional exponential gain control circuit is required in the proposed VGA used in a direct conversion receiver. A wide gain control voltage from 0.4 to 1.8 V and a high linearity performance are achieved. The three-stage VGA with automatic gain control (AGC) and DC offset cancellation (DCOC) is fabricated in a 0.18-μm CMOS technology and shows a linear gain range of more than 58-dB with a linearity error less than ±1 dB. The 3-dB bandwidth is over 8 MHz at all gain settings. The measured input-referred third intercept point (IIP3) of the proposed VGA varies from -18.1 to 13.5 dBm, and the measured noise figure varies from 27 to 65 dB at a frequency of 1 MHz. The dynamic range of the closed-loop AGC exceeds 56 dB, where the output signal-to-noise-and-distortion ratio (SNDR) reaches 20 dB. The whole circuit, occupying 0.3 mm2 of chip area, dissipates less than 3.7 mA from a 1.8-V supply.

  8. Are Bilinear Quadrilaterals Better Than Linear Triangles?

    SciTech Connect

    D'Azevedo, E.F.

    1993-01-01

    This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilaterals are more efficient, linear triangles are more accurate and may be preferred in finite element computations; whereas for saddle-shaped functions, quadrilaterals may offer a higher order approximation on a well-designed mesh. A surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy.

  9. Coherent-potential approximation in the tight-binding linear muffin-tin orbital method

    NASA Astrophysics Data System (ADS)

    Singh, Prabhakar P.; Gonis, A.

    1993-07-01

    We describe a consistent approach for applying the coherent-potential approximation (CPA) to the various representations of the linear muffin-tin orbital method. Unlike the previous works of Kudrnovský et al. [Phys. Rev. B 35, 2487 (1987); 41, 7515 (1990)], our results for the ensemble-averaged Green functions in the tight-binding representation yield E- and r-dependent quantities that are consistent with the traditional applications of the single-site CPA. To illustrate the reliability and the usefulness of our approach we compare the nonspherically averaged charge densities, calculated in real space, of ordered NiPt in L10 structure and the substitutionally disordered Ni0.5Pt0.5 on a face-centered-cubic lattice.

  10. Linear-response dynamics from the time-dependent Gutzwiller approximation

    NASA Astrophysics Data System (ADS)

    Bünemann, J.; Capone, M.; Lorenzana, J.; Seibold, G.

    2013-05-01

    Within a Lagrangian formalism, we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent density matrix from which we obtain dynamical correlation functions in the linear-response regime. Our results are illustrated for the one-band model where we show that the interacting system can be mapped to an effective problem of fermionic quasiparticles coupled to ‘doublon’ (double occupancy) bosonic fluctuations. The latter have an energy on the scale of the on-site Hubbard repulsion U in the dilute limit but become soft at the Brinkman-Rice transition, which is shown to be related to an emerging conservation law of doublon charge and the associated gauge invariance. Coupling with the boson mode produces a structure in the charge response and we find that a similar structure appears in dynamical mean-field theory.

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

    SciTech Connect

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

    2015-01-15

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

  12. Linear-scaling implementation of the direct random-phase approximation

    SciTech Connect

    Kállay, Mihály

    2015-05-28

    We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor.

  13. Gaussian functional approximation to 't Hooft's extension of the linear Σ model

    NASA Astrophysics Data System (ADS)

    Nakamura, Issei; Dmitrašinović, V.

    2012-03-01

    We apply a self-consistent relativistic mean-field variational “Gaussian functional” (or optimized one-loop perturbation theory, or Hartree+RPA) approximation to the extended Nf=2 linear σ model with spontaneously and explicitly broken chiral SUR(2)×SUL(2)×UA(1)≡O(4)×O(2) symmetry. We set up the self-consistency, or gap equations that dress up the bare fields with “cactus tree” loop diagrams, and the Bethe-Salpeter equations that provide further dressing with one-loop irreducible diagrams. In a previous publication [V. Dmitrašinović and I. Nakamura, J. Math. Phys. (N.Y.)JMAPAQ0022-2488 44, 2839 (2003).10.1063/1.1576907] we have already shown the ability of this approximation to create composite (i.e., bound and/or resonance) states. With explicit SUR(2)×SUL(2)×UA(1) chiral symmetry breaking first we consider how the UA(1) symmetry induced scalar-pseudoscalar meson mass relation that is known to hold in fermionic chiral models is modified by the bosonic gap equations. Then we solve the gap and Bethe-Salpeter equations numerically and discuss the solutions’ properties and the particle content of the theory. We show that in the strong-coupling regime two, sometimes even three solutions to the η meson channel Bethe-Salpeter equation may coexist.

  14. Three-dimensional forward modelling and inversion of complex resistivity based on the improved quasi-linear approximation

    NASA Astrophysics Data System (ADS)

    Liu, Y.; Li, T.; Zhu, C.; Zhang, R.; Wu, Y.

    2015-12-01

    Three-dimensional (3-D) electromagnetic (EM) forward modelling and inversion continues to be an important issue for the correct interpretation of EM data.To this end,approximate solutions have been developed that allow the construction of relatively fast forward modelling and inversion schemes.We have developed an improved quasi-linear approximation which is more appropriate in solving the linear equation for greatly shortening calculation time.We achieved this by using green's function properties.Then we introduced the improved quasi-linear approximation to spectral induced polarization (SIP) to tackle the problem of the resolution and the efficiency.The localized quasi-linear (LQL) approximation theory is appropriate for multisource array-type surveys assuming that the normal field is slowly varying within the inhomogeneity domain.However,the normal field of attenuates severely which dose not satisfy the assumption of the LQL approximation.As a consenquence,the imaginary part is not accurate when LQL approximation is adopted for the simulation.The improved quasi-linear approximation provide a new approach with the same resolution of QL approximation and much less calculation time.We have also constructed three-dimensional SIP forward modeling based on improved quasi-linear approximation method.It only takes 0.8s for forward modeling when inhomogeneity domain is divided into 2000 blocks.Beyond that, we have introduced the Cole-Cole model to the algorithm and complete the three-dimensional complex resistivity conjugate gradient inversion with parameter restraint.The model trial results show that this method can obtain good inversion results in physical parameters such as zero frequency resistivity, polarization.The results demonstrate the stability and the efficiency of the improved quasi-linear approximation and the method may be a practical solution for3-D EM forward modelling and inversion of SIP.

  15. Linear noise approximation for oscillations in a stochastic inhibitory network with delay

    NASA Astrophysics Data System (ADS)

    Dumont, Grégory; Northoff, Georg; Longtin, André

    2014-07-01

    Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm.

  16. Piecewise nonlinear image registration using DCT basis functions

    NASA Astrophysics Data System (ADS)

    Gan, Lin; Agam, Gady

    2015-03-01

    The deformation field in nonlinear image registration is usually modeled by a global model. Such models are often faced with the problem that a locally complex deformation cannot be accurately modeled by simply increasing degrees of freedom (DOF). In addition, highly complex models require additional regularization which is usually ineffective when applied globally. Registering locally corresponding regions addresses this problem in a divide and conquer strategy. In this paper we propose a piecewise image registration approach using Discrete Cosine Transform (DCT) basis functions for a nonlinear model. The contributions of this paper are three-folds. First, we develop a multi-level piecewise registration framework that extends the concept of piecewise linear registration and works with any nonlinear deformation model. This framework is then applied to nonlinear DCT registration. Second, we show how adaptive model complexity and regularization could be applied for local piece registration, thus accounting for higher variability. Third, we show how the proposed piecewise DCT can overcome the fundamental problem of a large curvature matrix inversion in global DCT when using high degrees of freedoms. The proposed approach can be viewed as an extension of global DCT registration where the overall model complexity is increased while achieving effective local regularization. Experimental evaluation results provide comparison of the proposed approach to piecewise linear registration using an affine transformation model and a global nonlinear registration using DCT model. Preliminary results show that the proposed approach achieves improved performance.

  17. Boundary parametric approximation to the linearized scalar potential magnetostatic field problem

    SciTech Connect

    Bramble, J.H.; Pasciak, J.E.

    1984-01-01

    We consider the linearized scalar potential formulation of the magnetostatic field problem in this paper. Our approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary conditions can also be satisfied in the parametric framework. That is, the field in the exterior of a sphere is expanded in a harmonic series of eigenfunctions for the exterior harmonic problem. The approach is essentially a finite element method coupled with a spectral method via a boundary parametric procedure. The reformulated problem is discretized by finite element techniques which lead to a discrete parametric problem which can be solved by well conditioned iteration involving only the solution of decoupled Neumann type elliptic finite element systems and L/sup 2/ projection onto subspaces of spherical harmonics. Error and stability estimates given show exponential convergence in the degree of the spherical harmonics and optimal order convergence with respect to the finite element approximation for the resulting fields in L/sup 2/. 24 references.

  18. Piecewise-Planar Parabolic Reflectarray Antenna

    NASA Technical Reports Server (NTRS)

    Hodges, Richard; Zawadzki, Mark

    2009-01-01

    The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.

  19. Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models

    NASA Astrophysics Data System (ADS)

    Cai, Zhenning; Torrilhon, Manuel

    2015-08-01

    A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence is proven to be convergent to the linearized Boltzmann operator, and it established a connection between the Shakhov model and the linearized collision model. The convergence is demonstrated by solving the spatially homogeneous Boltzmann equation. By observing the magnitudes of the coefficients, simpler models are developed through removing small entries in the coefficient matrices.

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

    PubMed Central

    2013-01-01

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

  1. Image coding with uniform and piecewise-uniform vector quantizers.

    PubMed

    Jeong, D G; Gibson, J D

    1995-01-01

    New lattice vector quantizer design procedures for nonuniform sources that yield excellent performance while retaining the structure required for fast quantization are described. Analytical methods for truncating and scaling lattices to be used in vector quantization are given, and an analytical technique for piecewise-linear multidimensional companding is presented. The uniform and piecewise-uniform lattice vector quantizers are then used to quantize the discrete cosine transform coefficients of images, and their objective and subjective performance and complexity are contrasted with other lattice vector quantizers and with LBG training-mode designs. PMID:18289966

  2. The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations

    NASA Astrophysics Data System (ADS)

    Simpson, D. J. W.

    2016-09-01

    An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical evidence is provided to show that this invariant set can be chaotic. The transition occurs locally (in a neighbourhood of a point) and instantaneously (for a single critical parameter value). This phenomenon is illustrated for the normal form of a boundary equilibrium bifurcation in three dimensions using parameter values adapted from of a piecewise-linear model of a chaotic electrical circuit. The variation of a secondary parameter reveals a period-doubling cascade to chaos with windows of periodicity. The dynamics is well approximated by a one-dimensional unimodal map which explains the bifurcation structure. The robustness of the attractor is also investigated by studying the influence of nonlinear terms.

  3. Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation

    NASA Technical Reports Server (NTRS)

    Kylling, Arve; Stamnes, Knut

    1992-01-01

    The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.

  4. Are bilinear quadrilaterals better than linear triangles?

    SciTech Connect

    D`Azevedo, E.F.

    1993-08-01

    This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. The theory and numerical results suggest triangles may have a slight advantage over quadrilaterals for interpolating convex data function but bilinear approximation may offer a higher order approximation for saddle-shaped functions on a well-designed mesh. This work is a basic study on optimal meshes with the intention of gaining insight into the more complex meshing problems in finite element analysis.

  5. Moment equations for a piecewise deterministic PDE

    NASA Astrophysics Data System (ADS)

    Bressloff, Paul C.; Lawley, Sean D.

    2015-03-01

    We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval Ω with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially discretizing the diffusion equation using finite differences and constructing the Chapman-Kolmogorov (CK) equation for the resulting finite-dimensional stochastic hybrid system. We show how the CK equation can be used to generate a hierarchy of equations for the r-th moments of the stochastic field, which take the form of r-dimensional parabolic PDEs on {{Ω }r} that couple to lower order moments at the boundaries. We explicitly solve the first and second order moment equations (r = 2). We then describe how the r-th moment of the stochastic PDE can be interpreted in terms of the splitting probability that r non-interacting Brownian particles all exit at the same boundary; although the particles are non-interacting, statistical correlations arise due to the fact that they all move in the same randomly switching environment. Hence the stochastic diffusion equation describes two levels of randomness: Brownian motion at the individual particle level and a randomly switching environment. Finally, in the limit of fast switching, we use a quasi-steady state approximation to reduce the piecewise deterministic PDE to an SPDE with multiplicative Gaussian noise in the bulk and a stochastically-driven boundary.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  7. Ergodic theory and Diophantine approximation for translation surfaces and linear forms

    NASA Astrophysics Data System (ADS)

    Athreya, Jayadev; Parrish, Andrew; Tseng, Jimmy

    2016-08-01

    We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619–31, 1964 Trans. Am. Math. Soc. 110 493–518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.

  8. Approximation functions for airblast environments from buried charges

    SciTech Connect

    Reichenbach, H.; Behrens, K.; Kuhl, A.L.

    1993-11-01

    In EMI report E 1/93, ``Airblast Environments from Buried HE-Charges,`` fit functions were used for the compact description of blastwave parameters. The coefficients of these functions were approximated by means of second order polynomials versus DOB. In most cases, the agreement with the measured data was satisfactory; to reduce remaining noticeable deviations, an approximation by polygons (i.e., piecewise-linear approximation) was used instead of polynomials. The present report describes the results of the polygon approximation and compares them to previous data. We conclude that the polygon representation leads to a better agreement with the measured data.

  9. Construction of approximate analytical solutions to a new class of non-linear oscillator equation

    NASA Technical Reports Server (NTRS)

    Mickens, R. E.; Oyedeji, K.

    1985-01-01

    The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).

  10. The lens effect of a big spherical inhomogeneity in the linear approximation

    SciTech Connect

    Moreno, J.; Portilla, M. )

    1990-04-01

    The paper addresses a large gravitational lens, of dimensions comparable with observer-lens-source distances, for arbitrary lens-observer-source angles. The lens is approximated by a small, pressureless, spsherically symmetric perturbation in a Einstein-de Sitter universe. The deflection angle contains essential terms which do not appear when the lens is approximated by an isolated body in a Minkowskian space. These terms should be considered to study the optical appearance of the inhomogeneity. The lens equation explicitly conserves brightness over the whole celestial sphere of the observer. 8 refs.

  11. The validity of the linear-reservoir approximation for various aquifers.

    NASA Astrophysics Data System (ADS)

    de Rooij, Gerrit H.

    2014-05-01

    Aquifers discharging in streams are often modelled as linear reservoirs. A survey of existing solutions explored if this approach has support in groundwater theory. Literature reports based on numerical solutions show that sloping aquifers do not behave linearly. For horizontal aquifers, an analytical solution for the case with the stream water level close to the aquifer bottom can be shown to produce a second-order reservoir. A recent analytical solution for an aquifer of constant thickness (stream water close to the aquifer top) shows that such aquifers can behave like linear reservoirs when the recharge and the stream water level are constant long enough. If the aquifer is leaky, the exponential recession typical for a linear reservoir is superimposed on a constant baseflow. Analytical expressions for the discharge-storage relationships are presented. They are used to demonstrate the consequences of incorrectly assuming recharge to be zero. The characteristic time of the aquifer increases with the square of the aquifer size (distance between the water divide and the stream). Fields with drains or ditches spaced a few tens of meters have characteristic times in the order of a week. Aquifers drained by rivers spaced several kilometers apart can have characteristic times of decades or centuries. The analytical solution shows that the surface water level needs to be constant for about two characteristic times and recharge for about 8 characteristic times before the aquifer behaves like a linear reservoir. In conceptual catchment models, the excess outflow before that time is typically attributed to a separate fast-response reservoir.

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

  13. Approximating electronically excited states with equation-of-motion linear coupled-cluster theory

    SciTech Connect

    Byrd, Jason N. Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.

    2015-10-28

    A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.

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

    PubMed

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

    2016-07-30

    Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of (i) the expected number of complete cases, (ii) the expected number of non-missing pairs of responses, or (iii) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code. Copyright © 2015 John Wiley & Sons, Ltd. PMID:26603500

  15. Boundary conditions for simulations of oscillating bubbles using the non-linear acoustic approximation

    NASA Astrophysics Data System (ADS)

    King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.

    2015-03-01

    We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.

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

    NASA Technical Reports Server (NTRS)

    Tal-Ezer, Hillel

    1987-01-01

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

  17. Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase approximation

    SciTech Connect

    Losa, C.; Doessing, T.; Pastore, A.; Vigezzi, E.; Broglia, R. A.

    2010-06-15

    We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self-consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed {sup 24-26}Mg, {sup 34}Mg isotopes are presented and compared to experimental findings.

  18. Deterministic inference for stochastic systems using multiple shooting and a linear noise approximation for the transition probabilities.

    PubMed

    Zimmer, Christoph; Sahle, Sven

    2015-10-01

    Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the 'multiple shooting for stochastic systems (MSS)' method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least-squares parameter estimation methods. PMID:26405142

  19. Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states

    NASA Astrophysics Data System (ADS)

    Senjean, Bruno; Knecht, Stefan; Jensen, Hans Jørgen Aa.; Fromager, Emmanuel

    2015-07-01

    Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is, in principle, very attractive but has been hard to use in practice. A practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing, as it enables the rigorous formulation of a multideterminant state-averaged DFT method. In the exact theory, the short-range density functional, which complements the long-range wave-function-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears, thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) can be rationalized and that it effectively introduces weight dependence effects. As proof of principle, the LIM has been applied to He, Be, and H2 in both equilibrium and stretched geometries as well as the stretched HeH+ molecule. Very promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semilocal functionals. Even at the Kohn-Sham ensemble DFT level, which is recovered when the range-separation parameter is set to 0, LIM performs better than standard time-dependent DFT.

  20. TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

    SciTech Connect

    Catt, B; Snyder, M

    2014-06-15

    Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not

  1. 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

  2. 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.

  3. Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee–Richards surfaces (PGALRS)

    PubMed Central

    Bernstein, Herbert J.; Craig, Paul A.

    2010-01-01

    The PGALRS (pseudo-Gaussian approximation to Lee–Richards surfaces) algorithm is discussed. By modeling electron density with unphysical pseudo-Gaussian atoms, the Lee–Richards surface can be approximated by a contour level of that density in time approximately linear in the number of atoms. Having that contour level, the atoms and residues closest to that surface can be identified in average time O[n 2/3log(n)] using a NearTree-based nearest neighbor search. If a high-quality Lee–Richards surface is required, then, as a final stage, one of the standard Lee–Richards algorithms can be used but considering only the previously identified surface residues; the typical cost is thereby reduced to O[n 2/3log(n)], making the overall average time for all the steps O(n). For very large macromolecules, such a reduction in computational burden may be essential to being able to render a meaningful molecular surface. This approach extends the feasible range of application for existing molecular surface software, such as MSMS, to larger macromolecules, especially to macromolecules with more than 50 000 atoms, and can be used as a starting point for surface-based (as opposed to backbone-based) motif identification, e.g. using ProMol. PMID:20300495

  4. Improved piecewise orthogonal signal correction algorithm.

    PubMed

    Feudale, Robert N; Tan, Huwei; Brown, Steven D

    2003-10-01

    Piecewise orthogonal signal correction (POSC), an algorithm that performs local orthogonal filtering, was recently developed to process spectral signals. POSC was shown to improve partial leastsquares regression models over models built with conventional OSC. However, rank deficiencies within the POSC algorithm lead to artifacts in the filtered spectra when removing two or more POSC components. Thus, an updated OSC algorithm for use with the piecewise procedure is reported. It will be demonstrated how the mathematics of this updated OSC algorithm were derived from the previous version and why some OSC versions may not be as appropriate to use with the piecewise modeling procedure as the algorithm reported here. PMID:14639746

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

    NASA Astrophysics Data System (ADS)

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

    2008-06-01

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

  6. Comparing the full time-dependent Bogoliubov-de-Gennes equations to their linear approximation: a numerical investigation

    NASA Astrophysics Data System (ADS)

    Hainzl, Christian; Seyrich, Jonathan

    2016-05-01

    In this paper we report on the results of a numerical study of the nonlinear time-dependent Bardeen-Cooper-Schrieffer (BCS) equations, often also denoted as Bogoliubov-de-Gennes (BdG) equations, for a one-dimensional system of fermions with contact interaction. We show that, even above the critical temperature, the full equations and their linear approximation give rise to completely different evolutions. In contrast to its linearization, the full nonlinear equation does not show any diffusive behavior in the order parameter. This means that the order parameter does not follow a Ginzburg-Landau-type of equation, in accordance with a recent theoretical result in [R.L. Frank, C. Hainzl, B. Schlein, R. Seiringer, to appear in Lett. Math. Phys., arXiv:1504.05885 (2016)]. We include a full description on the numerical implementation of the partial differential BCS/BdG equations.

  7. Linearized Semiclassical Initial Value Time Correlation FunctionsUsing the Thermal Gaussian Approximation: Applications to Condensed PhaseSystems

    SciTech Connect

    Liu, Jian; Miller, William H.

    2007-07-10

    The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne13 Lennard-Jones (LJ) cluster in its liquid-solid phase transition region (temperature from 4 K to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquid-like) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 K and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo (PIMC) results at 25 K. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.

  8. Multivariate piecewise exponential survival modeling.

    PubMed

    Li, Yan; Panagiotou, Orestis A; Black, Amanda; Liao, Dandan; Wacholder, Sholom

    2016-06-01

    In this article, we develop a piecewise Poisson regression method to analyze survival data from complex sample surveys involving cluster-correlated, differential selection probabilities, and longitudinal responses, to conveniently draw inference on absolute risks in time intervals that are prespecified by investigators. Extensive simulations evaluate the developed methods with extensions to multiple covariates under various complex sample designs, including stratified sampling, sampling with selection probability proportional to a measure of size (PPS), and a multi-stage cluster sampling. We applied our methods to a study of mortality in men diagnosed with prostate cancer in the Prostate, Lung, Colorectal, and Ovarian (PLCO) cancer screening trial to investigate whether a biomarker available from biospecimens collected near time of diagnosis stratifies subsequent risk of death. Poisson regression coefficients and absolute risks of mortality (and the corresponding 95% confidence intervals) for prespecified age intervals by biomarker levels are estimated. We conclude with a brief discussion of the motivation, methods, and findings of the study. PMID:26583951

  9. Multivariate Piecewise Exponential Survival Modeling

    PubMed Central

    Li, Yan; Panagiotou, Orestis A.; Black, Amanda; Liao, Dandan; Wacholder, Sholom

    2016-01-01

    Summary In this article, we develop a piecewise Poisson regression method to analyze survival data from complex sample surveys involving cluster-correlated, differential selection probabilities, and longitudinal responses, to conveniently draw inference on absolute risks in time intervals that are prespecified by investigators. Extensive simulations evaluate the developed methods with extensions to multiple covariates under various complex sample designs, including stratified sampling, sampling with selection probability proportional to a measure of size (PPS), and a multi-stage cluster sampling. We applied our methods to a study of mortality in men diagnosed with prostate cancer in the Prostate, Lung, Colorectal, and Ovarian (PLCO) cancer screening trial to investigate whether a biomarker available from biospecimens collected near time of diagnosis stratifies subsequent risk of death. Poisson regression coefficients and absolute risks of mortality (and the corresponding 95% confidence intervals) for prespecified age intervals by biomarker levels are estimated. We conclude with a brief discussion of the motivation, methods, and findings of the study. PMID:26583951

  10. Approximate solutions of the hyperbolic Kepler equation

    NASA Astrophysics Data System (ADS)

    Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge

    2015-12-01

    We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,∞ ). We prove, by using Smale's α -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S( g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then |S_n-S|≤ 0.5^{2^n-1}|widetilde{S}-S|. The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,∞ ) that exclude a small neighborhood of g=1, L=0, we also provide a method to construct simpler starters involving only constants.

  11. A nonlinear modeling approach using weighted piecewise series and its applications to predict unsteady flows

    NASA Astrophysics Data System (ADS)

    Yao, Weigang; Liou, Meng-Sing

    2016-08-01

    To preserve nonlinearity of a full-order system over a range of parameters of interest, we propose an accurate and robust nonlinear modeling approach by assembling a set of piecewise linear local solutions expanded about some sampling states. The work by Rewienski and White [1] on micromachined devices inspired our use of piecewise linear local solutions to study nonlinear unsteady aerodynamics. These local approximations are assembled via nonlinear weights of radial basis functions. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving with different pitching motions, specifically AGARD's CT2 and CT5 problems [27], in which the flows exhibit different nonlinear behaviors. Furthermore, application of the developed aerodynamic model to a two-dimensional aero-elastic system proves the approach is capable of predicting limit cycle oscillations (LCOs) by using AGARD's CT6 [28] as a benchmark test. All results, based on inviscid solutions, confirm that our nonlinear model is stable and accurate, against the full model solutions and measurements, and for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robust for inputs that considerably depart from the base trajectory in form and magnitude. This modeling provides a very efficient way for predicting unsteady flowfields with varying parameters because it needs only a tiny fraction of the cost of a full-order modeling for each new condition-the more cases studied, the more savings rendered. Hence, the present approach is especially useful for parametric studies, such as in the case of design optimization and exploration of flow phenomena.

  12. Identifying parameters of multi-degree-of-freedom nonlinear structural dynamic systems using linear time periodic approximations

    NASA Astrophysics Data System (ADS)

    Sracic, Michael W.; Allen, Matthew S.

    2014-06-01

    The authors recently presented a new nonlinear system identification method, here dubbed the NL-LTP method, in which the system of interest is forced harmonically so that it responds in a stable periodic orbit, and then it is perturbed slightly and its response is recorded as it returns to the orbit. Under mild assumptions the response about the periodic orbit can be approximated using a linear time periodic system model, which can be identified from the measurements using techniques that are akin to linear modal analysis. While the prior work focused on simulated measurements from single degree-of-freedom systems, this work presents several tools that are needed in order to use this approach on multi-degree-of-freedom systems and focuses on applying the method to experimental hardware. The proposed system identification methodology is unique in that it identifies both the order of the nonlinear system and a mathematical model for the nonlinear restoring forces without assuming the mathematical form for the nonlinearities a priori. Towards these ends, this work explains how to extract the underlying nonlinear system model, or nonlinear restoring force versus displacement relationships, from the time periodic model that governs deviations of the system from its periodic orbit, and presents various metrics that can be used to determine which terms in the model are meaningful. These new tools are used to apply the identification method to a continuous, multi-degree-of-freedom structure with a discrete geometric nonlinearity, using both simulated and experimental measurements. The experimental hardware consists of a cantilever beam with a nonlinear spring attached to its tip, which is driven in a periodic limit cycle by an electromagnetic shaker.

  13. Orbital-optimized linearized coupled-cluster doubles with density-fitting and Cholesky decomposition approximations: an efficient implementation.

    PubMed

    Bozkaya, Uğur

    2016-04-20

    An efficient implementation of the orbital-optimized linearized coupled-cluster double method with the density-fitting (DF-OLCCD) and Cholesky decomposition (CD-OLCCD) approximations is presented. The DF-OLCCD and CD-OLCCD methods are applied to a set of alkanes to compare the computational cost with the conventional orbital-optimized linearized coupled-cluster doubles (OLCCD) [U. Bozkaya and C. D. Sherrill, J. Chem. Phys., 2013, 139, 054104]. Our results demonstrate that the DF-OLCCD method provides substantially lower computational costs than OLCCD, and there are more than 9-fold reductions in the computational time for the largest member of the alkane set (C8H18). For barrier heights of hydrogen transfer reaction energies, the DF-OLCCD method again exhibits a substantially better performance than DF-LCCD, providing a mean absolute error of 0.9 kcal mol(-1), which is 7 times lower than that of DF-LCCD (6.2 kcal mol(-1)), and compared to MP2 (9.6 kcal mol(-1)) there is a more than 10-fold reduction in errors. Furthermore, the MAE value of DF-OLCCD is also lower than that of CCSD (1.2 kcal mol(-1)). For open-shell noncovalent interactions, the performance of DF-OLCCD is significantly better than that of MP2, DF-LCCD, and CCSD. Overall, the present application results indicate that the DF-OLCCD and CD-OLCCD methods are very promising for challenging open-shell systems as well as closed-shell molecular systems. PMID:27056800

  14. Mixing with piecewise isometries on a hemispherical shell

    NASA Astrophysics Data System (ADS)

    Park, Paul P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

    2016-07-01

    We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.

  15. Meta-Analysis for Linear and Nonlinear Dose-Response Relations: Examples, an Evaluation of Approximations, and Software

    PubMed Central

    Orsini, Nicola; Li, Ruifeng; Wolk, Alicja; Khudyakov, Polyna; Spiegelman, Donna

    2012-01-01

    Two methods for point and interval estimation of relative risk for log-linear exposure-response relations in meta-analyses of published ordinal categorical exposure-response data have been proposed. The authors compared the results of a meta-analysis of published data using each of the 2 methods with the results that would be obtained if the primary data were available and investigated the circumstances under which the approximations required for valid use of each meta-analytic method break down. They then extended the methods to handle nonlinear exposure-response relations. In the present article, methods are illustrated using studies of the relation between alcohol consumption and colorectal and lung cancer risks from the ongoing Pooling Project of Prospective Studies of Diet and Cancer. In these examples, the differences between the results of a meta-analysis of summarized published data and the pooled analysis of the individual original data were small. However, incorrectly assuming no correlation between relative risk estimates for exposure categories from the same study gave biased confidence intervals for the trend and biased P values for the tests for nonlinearity and between-study heterogeneity when there was strong confounding by other model covariates. The authors illustrate the use of 2 publicly available user-friendly programs (Stata and SAS) to implement meta-analysis for dose-response data. PMID:22135359

  16. Meta-analysis for linear and nonlinear dose-response relations: examples, an evaluation of approximations, and software.

    PubMed

    Orsini, Nicola; Li, Ruifeng; Wolk, Alicja; Khudyakov, Polyna; Spiegelman, Donna

    2012-01-01

    Two methods for point and interval estimation of relative risk for log-linear exposure-response relations in meta-analyses of published ordinal categorical exposure-response data have been proposed. The authors compared the results of a meta-analysis of published data using each of the 2 methods with the results that would be obtained if the primary data were available and investigated the circumstances under which the approximations required for valid use of each meta-analytic method break down. They then extended the methods to handle nonlinear exposure-response relations. In the present article, methods are illustrated using studies of the relation between alcohol consumption and colorectal and lung cancer risks from the ongoing Pooling Project of Prospective Studies of Diet and Cancer. In these examples, the differences between the results of a meta-analysis of summarized published data and the pooled analysis of the individual original data were small. However, incorrectly assuming no correlation between relative risk estimates for exposure categories from the same study gave biased confidence intervals for the trend and biased P values for the tests for nonlinearity and between-study heterogeneity when there was strong confounding by other model covariates. The authors illustrate the use of 2 publicly available user-friendly programs (Stata and SAS) to implement meta-analysis for dose-response data. PMID:22135359

  17. Approximate analytical solutions for the trapped electron distribution due to quasi-linear diffusion by whistler mode waves

    NASA Astrophysics Data System (ADS)

    Mourenas, D.; Artemyev, A. V.; Agapitov, O. V.; Krasnoselskikh, V.; Li, W.

    2014-12-01

    The distribution of trapped energetic electrons inside the Earth's radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the particle distribution function. Here we present for the first time approximate but realistic analytical solutions for the electron distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet time distributions are well recovered, as well as the evolution of energized relativistic electron distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured distributions may allow to infer important bounce- and drift-averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.

  18. Moment inversion problem for piecewise D-finite functions

    NASA Astrophysics Data System (ADS)

    Batenkov, Dmitry

    2009-10-01

    We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in signal processing and other applications. It is somewhat of a 'folklore' that the sequence of the moments of such 'piecewise D-finite' functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of resulting linear systems in the general case, as well as analyse a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise.

  19. Computing Melnikov Curves for Periodically Perturbed Piecewise Smooth Oscillators

    NASA Astrophysics Data System (ADS)

    Dua, Aseem; Marathe, Amol

    Curves dividing the parameter plane into regions according to the presence or absence of homoclinic or heteroclinic tangle corresponding to the periodically perturbed saddle of the piecewise smooth oscillator are studied using Melnikov analysis. The analysis is not simplified by choosing the discontinuity plane at a convenient location. Separatrix of the unperturbed system is parametrized exactly in a piecewise manner. Switching times, i.e. parameter values at which the separatrix crosses the discontinuity plane, are obtained. Switching times split the Melnikov integral into various subintegrals which are evaluated either exactly using term-wise integration of the infinite series of the integrand or approximately using a finite-term series approximation of the integrand, the latter being computationally an extensive task. Integral evaluations though approximate, are purely analytical expressions in terms of special functions such as digamma and hypergeometric. Melnikov plots show that the boundary between three regions in the parameter plane differ qualitatively in case of parametric and external excitations, however; adding self-excitation to the external one does not much alter the boundary qualitatively and quantitatively.

  20. Determination of borate ion-pair stability constants by potentiometry and non-approximative linearization of titration data.

    PubMed

    Rogers, H R; van den Berg, C M

    1988-04-01

    Borate anions, B(OH)(-)(4), are known to associate with alkali and alkaline-earth metal cations in sea-water. The borate cation ion-pairs are of the general form MB(OH)((n-1)+)(4), where M(n+) is the cation. In this work, the cation borate stability constants (K*(MB)) have been evaluated for Na(+), Li(+), Mg(2+), Ca(2+) and Sr(2+) where K*(MB) = [MB(OH(4))((n-1)+)]/[M(n+)][B(OH)(-)(4)]. The K*(MB) values were obtained from values found for the stability constant of boric acid (K*(B)) in various electrolyte media at 25 degrees and an ionic strength of 0.7. Acid-base potentiometric titrations were performed in the electrolyte media with a standard Pt/H(2) electrode and a junctionless Ag/AgCl reference electrode to monitor the emf. A non-approximative equation was used to linearize the titration data. The values obtained were: K*(Lib) = 0.89 +/- 0.02, K*(NaB) = 0.44 +/- 0.01, K*(MgB) = 13.6 +/- 0.7, K*(CaB) = 11.4 +/- 0.15, K*(SrB) = 3.47 +/- 0.06. The values for K*(MB) correlate with the charge-density parameter z(2)/(r + 0.85), where r is the radius of the cation. The speciation of boron in sea-water was predicted from the K*(MB), data for the major cations present. PMID:18964511

  1. Piecewise lexsegment ideals in exterior algebras

    NASA Astrophysics Data System (ADS)

    Shakin, D. A.

    2005-02-01

    The problem of describing the Hilbert functions of homogeneous ideals of an exterior algebra over a field containing a fixed monomial ideal I is considered. For this purpose the notion of a piecewise lexsegment ideal in an exterior algebra is introduced generalizing the notion of a lexsegment ideal. It is proved that if I is a piecewise lexsegment ideal, then it is possible to describe the Hilbert functions of the homogeneous ideals containing I in a way similar to that suggested by Kruskal and Katona for the situation I=0. Moreover, a generalization of the extremal properties of lexsegment ideals is obtained (the inequality for the Betti numbers).

  2. Regular and chaotic dynamics of a piecewise smooth bouncer

    SciTech Connect

    Langer, Cameron K. Miller, Bruce N.

    2015-07-15

    The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function. We confirm the existence of distinct unbounded orbits (Fermi acceleration) in the elastic model, and investigate regular and chaotic behavior in the inelastic cases. We also examine in the constant restitution model trajectories wherein the particle experiences an infinite number of collisions in a finite time, i.e., the phenomenon of inelastic collapse. We address these so-called “sticking solutions” and their relation to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally, we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. We find the non-smooth nature of the system produces novel bifurcation phenomena not seen in the sinusoidal model, including border-collision bifurcations. The analytical and numerical investigations reveal that although our piecewise linear bouncer is a simplified version of the sinusoidal model, the former not only captures essential features of the latter but also exhibits behavior unique to the discontinuous dynamics.

  3. 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.

  4. Low-dimensional maps for piecewise smooth oscillators

    NASA Astrophysics Data System (ADS)

    Pavlovskaia, Ekaterina; Wiercigroch, Marian

    2007-09-01

    Dynamics of the piecewise smooth nonlinear oscillators is considered, for which, general methodology of reducing multidimensional flows to low-dimensional maps is proposed. This includes a definition of piecewise smooth oscillator and creation of a global iterative map providing an exact solution. The global map is comprised of local maps, which are constructed in the smooth sub-regions of phase space. To construct this low-dimensional map, it is proposed to monitor the points of intersections of a chosen boundary between smooth subspaces by a trajectory. The dimension reduction is directly related to the dimension of the chosen boundary, and the lower its dimension is, the larger dimension reduction can be achieved. Full details are given for a drifting impact oscillator, where the five-dimensional flow is reduced to one-dimensional (1D) approximate analytical map. First an exact two-dimensional map has been formulated and analysed. A further reduction to 1D approximate map is introduced and discussed. Standard nonlinear dynamic analysis reveals a complex behaviour ranging from periodic oscillations to chaos, and co-existence of multiple attractors. Accuracy of the constructed maps is examined by comparing with the exact solutions for a wide range of the system parameters.

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

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  6. Canard-like phenomena in piecewise-smooth Van der Pol systems.

    PubMed

    Roberts, Andrew; Gendinning, Paul

    2014-06-01

    We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard phenomena in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards "with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation-whether leading to canards or super-explosion-can be subcritical. PMID:24985452

  7. Canard-like phenomena in piecewise-smooth Van der Pol systems

    NASA Astrophysics Data System (ADS)

    Roberts, Andrew; Gendinning, Paul

    2014-06-01

    We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard phenomena in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards "with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation—whether leading to canards or super-explosion—can be subcritical.

  8. Fast Fourier Transforms of Piecewise Constant Functions

    NASA Astrophysics Data System (ADS)

    Sorets, Eugene

    1995-02-01

    We present an algorithm for the evaluation of the Fourier transform of piecewise constant functions of two variables. The algorithm overcomes the accuracy problems associated with computing the Fourier transform of discontinuous functions; in fact, its time complexity is O (N2 logN + NP log2 (1/ε) + V log3 (1/ε)), where ε is the accuracy, N is the size of the problem, P is the perimeter of the set of discontinuities, and V is its number of vertices. The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform. It readily generalizes to higher dimensions and to piecewise smooth functions.

  9. Conserved quantities from piecewise Killing vectors

    NASA Astrophysics Data System (ADS)

    Dray, Tevian; Padmanabhan, T.

    1989-07-01

    In the presence of symmetries, conserved quantities can be obtained by contracting the stress-energy tensor with a Killing vector. We generalize this result to piecewise Killing vectors by giving sufficient conditions for the construction of an associated conserved quantity. A typical example, namely, two stationary space-times joined together in such a way that the resulting space-time is not stationary, is treated in detail.

  10. Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

    NASA Technical Reports Server (NTRS)

    Schlesinger, Robert E.

    1990-01-01

    Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

  11. Piecewise Linear Membership Function Generator-Divider Approach

    NASA Technical Reports Server (NTRS)

    Hart, Ron; Martinez, Gene; Yuan, Bo; Zrilic, Djuro; Ramirez, Jaime

    1997-01-01

    In this paper a simple, inexpensive, membership function circuit for fuzzy controllers is presented. The proposed circuit may be used to generate a general trapezoidal membership function. The slope and horizontal shift are fully programmable parameters.

  12. The time course of potassium current following potassium accumulation in frog atrium: analytical solutions using a linear approximation.

    PubMed Central

    DiFrancesco, D; Noble, D

    1980-01-01

    1. Regular perturbation theory was used to obtain analytical solutions for the time course of membrane current decay following voltage-clamp depolarizing pulses when both time-dependent K conductance mechanisms and the process of K accumulation in extracellular spaces are present. These solutions apply when the current and K concentration changes are small enough for linear relations to be assumed between current and K concentration. 2. In the case of a single Hodgkin-Huxley type conductance variable with time constant tau chi the presence of an accumulation process which, by itself, would produce a current decay with time constant tau alpha, induces the appearance of two infinite sets of components with decreasing time constants (1/(n+1/tau chi) and 1/(1/tau alpha + n/tau chi), where n is integer), and decreasing magnitudes. 3. The analytical solutions are used to investigate the range of conditions over which semi-exponential (curve-stripping) analysis of current decay tails may give useful information on the kinetics of current change. It is shown that, except at very large decay tail amplitudes, the method may give a good estimate of the true time constants of conductance decay even when the currents are assumed to be strongly dependent on external K concentration. 4. The method introduces error in current amplitude, but over the range in which curve-stripping gives useful results, the direct distortion of activation curves by variations in external K concentration is fairly small. However, as the current decay becomes grossly distorted in its time course by accumulation, so does the activation curve. The effects are very similar both to those obtained using numerical computation without linearization, and to those obtained experimentally. 5. Even with a large dependence of current on external K concentration the linear model does not reproduce i chi, fast as a perturbation of i chi, slow by K accumulation. PMID:7463358

  13. Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

    NASA Astrophysics Data System (ADS)

    Grima, Ramon

    2015-10-01

    It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.

  14. Dynamic linear response of atoms in plasmas and photo-absorption cross-section in the dipole approximation

    NASA Astrophysics Data System (ADS)

    Caizergues, C.; Blenski, T.; Piron, R.

    2016-03-01

    We report results on the self-consistent linear response theory of quantum average-atoms in plasmas. The approach is based on the two first orders of the cluster expansion of the plasma susceptibility. A change of variable is applied, which allows us to handle the diverging free-free transitions contribution in the self-consistent induced electron density and potential. The method is first tested on the case of rare gas isolated neutral atoms. A test of the Ehrenfest-type sum rule is then performed in a case of an actual average-atom in a plasma. At frequencies much higher than the plasma frequency, the sum rule seems to be fulfilled within the accuracy of the numerical methods. Close to the plasma frequency, the method seems not to account for the cold-plasma dielectric function renormalization in the sum rule, which was correctly reproduced in the case of the Thomas-Fermi-Bloch self-consistent linear response. This suggests the need for a better accounting for the outgoing waves in the asymptotic boundary conditions.

  15. A modified WKB formulation for linear eigenmodes of a collisionless self-gravitating disc in the epicyclic approximation

    NASA Astrophysics Data System (ADS)

    Gulati, Mamta; Saini, Tarun Deep

    2016-04-01

    The short-wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly-wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB theory of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. Although our formulation is general and applies to all discs, we present our analysis only for nearly Keplerian, low-mass, self-gravitating discs revolving around massive central objects, and derive an integral equation governing the slow precessional modes of such discs. For a prograde disc, the integral kernel turns out be real and symmetric, implying that all slow modes are stable. We apply the slow mode integral equation to two unperturbed disc profiles, the Jalali-Tremaine annular discs, and the Kuzmin disc. We determine eigenvalues and eigenfunctions for both m = 1 and m = 2 slow modes for these profiles and discuss their properties. Our results compare well with those of Jalali-Tremaine.

  16. A modified WKB formulation for linear eigenmodes of a collisionless self-gravitating disc in the epicyclic approximation

    NASA Astrophysics Data System (ADS)

    Gulati, Mamta; Saini, Tarun Deep

    2016-07-01

    The short-wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly-wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB theory of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. Although our formulation is general and applies to all discs, we present our analysis only for nearly Keplerian, low-mass, self-gravitating discs revolving around massive central objects, and derive an integral equation governing the slow precessional modes of such discs. For a prograde disc, the integral kernel turns out be real and symmetric, implying that all slow modes are stable. We apply the slow mode integral equation to two unperturbed disc profiles, the Jalali-Tremaine annular discs, and the Kuzmin disc. We determine eigenvalues and eigenfunctions for both m = 1 and m = 2 slow modes for these profiles and discuss their properties. Our results compare well with those of Jalali-Tremaine.

  17. One-dimensional breakdown voltage model of SOI RESURF lateral power device based on lateral linearly graded approximation

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Guo, Yu-Feng; Xu, Yue; Lin, Hong; Yang, Hui; Hong, Yang; Yao, Jia-Fei

    2015-02-01

    A novel one-dimensional (1D) analytical model is proposed for quantifying the breakdown voltage of a reduced surface field (RESURF) lateral power device fabricated on silicon on an insulator (SOI) substrate. We assume that the charges in the depletion region contribute to the lateral PN junctions along the diagonal of the area shared by the lateral and vertical depletion regions. Based on the assumption, the lateral PN junction behaves as a linearly graded junction, thus resulting in a reduced surface electric field and high breakdown voltage. Using the proposed model, the breakdown voltage as a function of device parameters is investigated and compared with the numerical simulation by the TCAD tools. The analytical results are shown to be in fair agreement with the numerical results. Finally, a new RESURF criterion is derived which offers a useful scheme to optimize the structure parameters. This simple 1D model provides a clear physical insight into the RESURF effect and a new explanation on the improvement in breakdown voltage in an SOI RESURF device. Project supported by the National Natural Science Foundation of China (Grant No. 61076073) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20133223110003).

  18. Image segmentation via piecewise constant regression

    NASA Astrophysics Data System (ADS)

    Acton, Scott T.; Bovik, Alan C.

    1994-09-01

    We introduce a novel unsupervised image segmentation technique that is based on piecewise constant (PICO) regression. Given an input image, a PICO output image for a specified feature size (scale) is computed via nonlinear regression. The regression effectively provides the constant region segmentation of the input image that has a minimum deviation from the input image. PICO regression-based segmentation avoids the problems of region merging, poor localization, region boundary ambiguity, and region fragmentation. Additionally, our segmentation method is particularly well-suited for corrupted (noisy) input data. An application to segmentation and classification of remotely sensed imagery is provided.

  19. Renormalizable two-parameter piecewise isometries

    NASA Astrophysics Data System (ADS)

    Lowenstein, J. H.; Vivaldi, F.

    2016-06-01

    We exhibit two distinct renormalization scenarios for two-parameter piecewise isometries, based on 2 π / 5 rotations of a rhombus and parameter-dependent translations. Both scenarios rely on the recently established renormalizability of a one-parameter triangle map, which takes place if and only if the parameter belongs to the algebraic number field K = Q ( √{ 5 }) associated with the rotation matrix. With two parameters, features emerge which have no counterpart in the single-parameter model. In the first scenario, we show that renormalizability is no longer rigid: whereas one of the two parameters is restricted to K , the second parameter can vary continuously over a real interval without destroying self-similarity. The mechanism involves neighbouring atoms which recombine after traversing distinct return paths. We show that this phenomenon also occurs in the simpler context of Rauzy-Veech renormalization of interval exchange transformations, here regarded as parametric piecewise isometries on a real interval. We explore this analogy in some detail. In the second scenario, which involves two-parameter deformations of a three-parameter rhombus map, we exhibit a weak form of rigidity. The phase space splits into several (non-convex) invariant components, on each of which the renormalization still has a free parameter. However, the foliations of the different components are transversal in parameter space; as a result, simultaneous self-similarity of the component maps requires that both of the original parameters belong to the field K .

  20. Piecewise power laws in individual learning curves.

    PubMed

    Donner, Yoni; Hardy, Joseph L

    2015-10-01

    The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning. PMID:25711183

  1. LINEAR INVERSION OF TRANSMITTED ACOUSTIC WAVE FIELDS FOR THREE-DIMENSIONAL MODULUS AND DENSITY PERTURBATIONS USING A BORN-TYPE APPROXIMATION.

    USGS Publications Warehouse

    Stauber, Douglas A.

    1985-01-01

    A Born approximation is used to linearize the relationship, in the horizontal-wavenumber and frequency domains, between lateral perturbations of modulus and density in a layered half-space and the acoustic wave field observed at the surface when a plane wave is incident from below. The resulting equations can be used to perform a linear inversion of observed acoustic wave fields to obtain lateral perturbations in modulus and density. Since modulus and density effects are separated, gravity observations can be included in the inversion procedure without any assumptions about the relationship between density and acoustic velocity. Tests with synthetic data sets reveal that the inversion method gives useful results when the spatial scales of the inhomogeneities are smaller than several acoustic wavelengths. Refs.

  2. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation

    NASA Astrophysics Data System (ADS)

    Schurkus, Henry F.; Ochsenfeld, Christian

    2016-01-01

    An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions.

  3. Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses.

    PubMed

    Xi, Qiang

    2016-01-01

    In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results. PMID:26599709

  4. 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.

  5. Casimir Effect for the Piecewise Uniform String

    NASA Astrophysics Data System (ADS)

    Brevik, Iver

    The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. In its simplest version the string consists of two parts I and II having in general different tension and mass density, but is always obeying the condition that the velocity of sound is equal to the velocity of light. The model, first introduced by Brevik and Nielsen in 1990, possesses attractive formal properties implying that it becomes easily regularizable by several methods, the most powerful one being the contour integration method.We also consider the case where the string is divided into 2N pieces, of alternating type-I and type-II material. The free energy at finite temperature, as well as the Hagedorn temperature, are found. Finally, we make some remarks on the relationship between this kind of theory and the theory of quantum star graphs, recently considered by Fulling et al..

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

    SciTech Connect

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

    2015-11-28

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

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

    PubMed

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

    2015-11-28

    We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment. PMID:26627950

  9. Piece-wise mixed integer programming for optimal sizing of surge control devices in water distribution systems

    NASA Astrophysics Data System (ADS)

    Skulovich, Olya; Bent, Russell; Judi, David; Perelman, Lina Sela; Ostfeld, Avi

    2015-06-01

    Despite their potential catastrophic impact, transients are often ignored or presented ad hoc when designing water distribution systems. To address this problem, we introduce a new piece-wise function fitting model that is integrated with mixed integer programming to optimally place and size surge tanks for transient control. The key features of the algorithm are a model-driven discretization of the search space, a linear approximation nonsmooth system response surface to transients, and a mixed integer linear programming optimization. Results indicate that high quality solutions can be obtained within a reasonable number of function evaluations and demonstrate the computational effectiveness of the approach through two case studies. The work investigates one type of surge control devices (closed surge tank) for a specified set of transient events. The performance of the algorithm relies on the assumption that there exists a smooth relationship between the objective function and tank size. Results indicate the potential of the approach for the optimal surge control design in water systems.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  11. Approximate Analysis of Semiconductor Laser Arrays

    NASA Technical Reports Server (NTRS)

    Marshall, William K.; Katz, Joseph

    1987-01-01

    Simplified equation yields useful information on gains and output patterns. Theoretical method based on approximate waveguide equation enables prediction of lateral modes of gain-guided planar array of parallel semiconductor lasers. Equation for entire array solved directly using piecewise approximation of index of refraction by simple functions without customary approximation based on coupled waveguid modes of individual lasers. Improved results yield better understanding of laser-array modes and help in development of well-behaved high-power semiconductor laser arrays.

  12. Comparison of Implicit Schemes to Solve Equations of Radiation Hydrodynamics with a Flux-limited Diffusion Approximation: Newton--Raphson, Operator Splitting, and Linearization

    NASA Astrophysics Data System (ADS)

    Tetsu, Hiroyuki; Nakamoto, Taishi

    2016-03-01

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

  13. Arithmetic exponents in piecewise-affine planar maps

    NASA Astrophysics Data System (ADS)

    Roberts, John A. G.; Vivaldi, Franco

    2015-04-01

    We consider the growth of some indicators of arithmetical complexity of rational orbits of (piecewise) affine maps of the plane, with rational parameters. The exponential growth rates are expressed by a set of exponents; one exponent describes the growth rate of the so-called logarithmic height of the points of an orbit, while the others describe the growth rate of the size of such points, measured with respect to the p-adic metric. Here p is any prime number which divides the parameters of the map. We show that almost all the points in a domain of linearity (such as an elliptic island in an area-preserving map) have the same set of exponents. We also show that the convergence of the p-adic exponents may be non-uniform, with arbitrarily large fluctuations occurring arbitrarily close to any point. We explore numerically the behaviour of these quantities in the chaotic regions, in both area-preserving and dissipative systems. In the former case, we conjecture that wherever the Lyapunov exponent is zero, the arithmetical exponents achieve a local maximum.

  14. 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.

  15. A piecewise lookup table for calculating nonbonded pairwise atomic interactions.

    PubMed

    Luo, Jinping; Liu, Lijun; Su, Peng; Duan, Pengbo; Lu, Daihui

    2015-11-01

    A critical challenge for molecular dynamics simulations of chemical or biological systems is to improve the calculation efficiency while retaining sufficient accuracy. The main bottleneck in improving the efficiency is the evaluation of nonbonded pairwise interactions. We propose a new piecewise lookup table method for rapid and accurate calculation of interatomic nonbonded pairwise interactions. The piecewise lookup table allows nonuniform assignment of table nodes according to the slope of the potential function and the pair interaction distribution. The proposed method assigns the nodes more reasonably than in general lookup tables, and thus improves the accuracy while requiring fewer nodes. To obtain the same level of accuracy, our piecewise lookup table accelerates the calculation via the efficient usage of cache memory. This new method is straightforward to implement and should be broadly applicable. Graphical Abstract Illustration of piecewise lookup table method. PMID:26481475

  16. Contractivity for nonautonomous logistic equation with piecewise constant delays

    NASA Astrophysics Data System (ADS)

    Nakata, Yukihiko; Kuroda, Masataka; Muroya, Yoshiaki

    2009-05-01

    In this paper, we extend the result in [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602-635] to nonautonomous logistic equations with piecewise constant arguments and establish two sufficient conditions for contractivity-like property, from which the global asymptotic stability of the solutions of this equation is derived, even if the effect of delays dominates over the instantaneous feedback. We offer two examples to illustrate our results.

  17. On Languages Piecewise Testable in the Strict Sense

    NASA Astrophysics Data System (ADS)

    Rogers, James; Heinz, Jeffrey; Bailey, Gil; Edlefsen, Matt; Visscher, Molly; Wellcome, David; Wibel, Sean

    In this paper we explore the class of Strictly Piecewise languages, originally introduced to characterize long-distance phonotactic patterns by Heinz [7] as the Precedence Languages. We provide a series of equivalent abstract characterizations, discuss their basic properties, locate them relative to other well-known subregular classes and provide algorithms for translating between the grammars defined here and finite state automata as well as an algorithm for deciding whether a regular language is Strictly Piecewise.

  18. Pressure-induced phase transformations in alkali-metal hydrides calculated using an improved linear-muffin-tin-orbital-atomic-sphere-approximation energy scheme

    NASA Astrophysics Data System (ADS)

    Rodriguez, C. O.; Methfessel, M.

    1992-01-01

    A scheme for the calculation of total energies from first principles is described which is intermediate between the popular linear muffin-tin-orbital method in the atomic-sphere approximation (LMTO-ASA) and an exact full-potential treatment. The local-density total energy is evaluated accurately for the output charge density from the ASA potential. This method is applied to the study of static structural properties and the pressure-induced phase transformation from B1 (NaCl-structure) to B2 (CsCl-structure) phases for the partially ionic alkaki-metal hydrides NaH and KH and the alkali halide NaCl. Good agreement with experimental transition pressures and volumes is obtained. The series NaH, KH, and NaCl shows the observed strong cation and weak anion dependence. Charge densities and band structures are given at zero and high pressure. Calculated energy-volume curves for LiH show no transition up to 1 Mbar, in agreement with experimental data.

  19. Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems

    PubMed Central

    Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo

    2015-01-01

    Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131

  20. Numerical time-dependent solutions of the Schrödinger equation with piecewise continuous potentials

    NASA Astrophysics Data System (ADS)

    van Dijk, Wytse

    2016-06-01

    We consider accurate numerical solutions of the one-dimensional time-dependent Schrödinger equation when the potential is piecewise continuous. Spatial step sizes are defined for each of the regions between the discontinuities and a matching condition at the boundaries of the regions is employed. The Numerov method for spatial integration is particularly appropriate to this approach. By employing Padé approximants for the time-evolution operator, we obtain solutions with significantly improved precision without increased CPU time. This approach is also appropriate for adaptive changes in spatial step size even when there is no discontinuity of the potential.

  1. How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

    SciTech Connect

    Pernal, Katarzyna; Chatterjee, Koushik; Kowalski, Piotr H.

    2014-01-07

    Performance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li{sub 2}, BH, H{sub 2}O, and CH{sub 2}O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li{sub 2}, BH, and H{sub 2}O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long- and short-range terms and employing density functionals to treat the latter is presented.

  2. How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

    NASA Astrophysics Data System (ADS)

    Pernal, Katarzyna; Chatterjee, Koushik; Kowalski, Piotr H.

    2014-01-01

    Performance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li2, BH, H2O, and CH2O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li2, BH, and H2O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long- and short-range terms and employing density functionals to treat the latter is presented.

  3. Design of low-power hybrid digital pulse width modulator with piecewise calibration scheme

    NASA Astrophysics Data System (ADS)

    Zhen, Shaowei; Hou, Sijian; Gan, Wubing; Chen, Jingbo; Luo, Ping; Zhang, Bo

    2015-12-01

    A low-power hybrid digital pulse width modulator (DPWM) is proposed in the paper. Owing to the piecewise calibration scheme, the delay time of delay line is locked to target frequency. The delay line consists of two piecewise lines with different control codes. The delay time of each cell in one sub-delay-line is longer than the last significant bit (LSB) of DPWM, while the delay time of each cell in the other sub-delay-line is shorter than LSB. Optimum linearity is realised with minimum standard cells. Simulation results show that the differential nonlinearity and integral nonlinearity are improved from 5.1 to 0.4 and from 5 to 1.3, respectively. The DPWM is fully synthesised and fabricated in a 90-nm CMOS process. The proposed DPWM occupies a silicon area of 0.01 mm2, with 31.5 μw core power consumption. Experimental results are shown to demonstrate the 2-MHz, 10-bit resolution implementation. Pulse width histogram is firstly introduced to characterise the linearity of the DPWM.

  4. A piecewise-focused high DQE detector for MV imaging

    PubMed Central

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

    2015-01-01

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

  5. 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.

  6. Implementation of nonlinear registration of brain atlas based on piecewise grid system

    NASA Astrophysics Data System (ADS)

    Liu, Rong; Gu, Lixu; Xu, Jianrong

    2007-12-01

    In this paper, a multi-step registration method of brain atlas and clinical Magnetic Resonance Imaging (MRI) data based on Thin-Plate Splines (TPS) and Piecewise Grid System (PGS) is presented. The method can help doctors to determine the corresponding anatomical structure between patient image and the brain atlas by piecewise nonlinear registration. Since doctors mostly pay attention to particular Region of Interest (ROI), and a global nonlinear registration is quite time-consuming which is not suitable for real-time clinical application, we propose a novel method to conduct linear registration in global area before nonlinear registration is performed in selected ROI. The homogenous feature points are defined to calculate the transform matrix between patient data and the brain atlas to conclude the mapping function. Finally, we integrate the proposed approach into an application of neurosurgical planning and guidance system which lends great efficiency in both neuro-anatomical education and guiding of neurosurgical operations. The experimental results reveal that the proposed approach can keep an average registration error of 0.25mm in near real-time manner.

  7. General Boundary-Value Problems for the Heat Conduction Equation with Piecewise-Continuous Coefficients

    NASA Astrophysics Data System (ADS)

    Tatsii, R. M.; Pazen, O. Yu.

    2016-03-01

    A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.

  8. 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.

  9. Stochastic Schrödinger evolution over piecewise enlarged filtrations

    NASA Astrophysics Data System (ADS)

    Mengütürk, Levent Ali

    2016-03-01

    This paper constructs a nonlinear filtering framework that admits appearances of new information processes at random times by introducing piecewise enlargements of filtrations and proposes a new energy-based Schrodinger evolution expressed as a stochastic differential equation on a complex Hilbert space. Each information process is modeled as the sum of a random variable taking the eigenvalues of a Hamiltonian and an independent Brownian bridge noise. It is shown that under a piecewise enlarged filtration, the wave function is a jump-diffusion process until it collapses at some terminal time. In between discontinuities, the dynamics of the state vector are governed by different Wiener processes and diffusion coefficients. This motivates the introduction of an inclusive chain of Kolmogorov probability spaces or a *-isomorphic chain of commutative von Neumann probability spaces, on which the quantum system evolves differently based on the number of active information processes. The expectation of the Hamiltonian at a given state is the solution of a second-order nonlinear differential equation determined by one of the possible regimes that the quantum system belongs to. It is shown that the collapse rate is a submartingale with positive jumps and the Shannon entropy process is a supermartingale with expected negative jumps when passing to higher-order probability spaces. The framework is extended to the case when the Hamiltonian is modeled as a function of a set of commutative operators, where each operator is associated with a different piecewise enlarged filtration.

  10. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation

    NASA Astrophysics Data System (ADS)

    Kilpatrick, Zachary P.; Bressloff, Paul C.

    2010-06-01

    We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather.