A piecewise linear approximation scheme for hereditary optimal control problems
NASA Technical Reports Server (NTRS)
Cliff, E. M.; Burns, J. A.
1977-01-01
An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.
ERIC Educational Resources Information Center
Moses, Tim
2013-01-01
The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of…
1988-03-01
Theories of causal ordering. Artificial Intelli- gence, 29:33-61, 1986. [18] Charles A. Desoer and Ernest S. Kuh. Basic Circuit Theory. McGraw-Hill, New...instance between a and b .................. 31 S 4.1 A circuit governed by van der Pol’s equation ...... .................. 32 4.2 Piecewise Linearization...physical systems with differential equations, including circuits , motors, buildings, chemical reactions, physiology, the motions of celestial bodies
Piecewise linear approximation of protein structures using the principle of minimum message length
Konagurthu, Arun S.; Allison, Lloyd; Stuckey, Peter J.; Lesk, Arthur M.
2011-01-01
Simple and concise representations of protein-folding patterns provide powerful abstractions for visualizations, comparisons, classifications, searching and aligning structural data. Structures are often abstracted by replacing standard secondary structural features—that is, helices and strands of sheet—by vectors or linear segments. Relying solely on standard secondary structure may result in a significant loss of structural information. Further, traditional methods of simplification crucially depend on the consistency and accuracy of external methods to assign secondary structures to protein coordinate data. Although many methods exist automatically to identify secondary structure, the impreciseness of definitions, along with errors and inconsistencies in experimental structure data, drastically limit their applicability to generate reliable simplified representations, especially for structural comparison. This article introduces a mathematically rigorous algorithm to delineate protein structure using the elegant statistical and inductive inference framework of minimum message length (MML). Our method generates consistent and statistically robust piecewise linear explanations of protein coordinate data, resulting in a powerful and concise representation of the structure. The delineation is completely independent of the approaches of using hydrogen-bonding patterns or inspecting local substructural geometry that the current methods use. Indeed, as is common with applications of the MML criterion, this method is free of parameters and thresholds, in striking contrast to the existing programs which are often beset by them. The analysis of results over a large number of proteins suggests that the method produces consistent delineation of structures that encompasses, among others, the segments corresponding to standard secondary structure. Availability: http://www.csse.monash.edu.au/~karun/pmml. Contact: arun.konagurthu@monash.edu; lloyd.allison@monesh.edu PMID
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
NASA Astrophysics Data System (ADS)
Garcia, Andres; Agamennoni, Osvaldo
2010-04-01
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
Métris, Aline; George, Susie M; Ropers, Delphine
2017-01-02
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available
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.
Non-Linear Control Allocation Using Piecewise Linear Functions
2003-08-01
A novel method is presented for the solution of the non- linear control allocation problem. Historically, control allocation has been performed by... linear control allocation problem to be cast as a piecewise linear program. The piecewise linear program is ultimately cast as a mixed-integer linear...piecewise linear control allocation method is shown to be markedly improved when compared to the performance of a more traditional control allocation approach that assumes linearity.
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.
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
Slope Estimation in Noisy Piecewise Linear Functions✩
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
Piecewise linear and Boolean models of chemical reaction networks
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-01-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. PMID:25412739
Continuous Approximations of a Class of Piecewise Continuous Systems
NASA Astrophysics Data System (ADS)
Danca, Marius-F.
In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the underlying piecewise functions can be locally or globally approximated. The approximation results can be used to model piecewise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for differential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
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.
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.
Convergence of the natural approximations of piecewise monotone interval maps.
Haydn, Nicolai
2004-06-01
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.
Convergence of multipoint Pade approximants of piecewise analytic functions
Buslaev, Viktor I
2013-02-28
The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.
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.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
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
Analysis of the Dynamics of Piecewise Linear Memristors
NASA Astrophysics Data System (ADS)
Jiang, Fangfang; Ji, Zhicheng; Wang, Qing-Guo; Sun, Jitao
2016-12-01
In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines |x| = 1 (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results.
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…
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.
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.
Generation of chaotic attractors without equilibria via piecewise linear systems
NASA Astrophysics Data System (ADS)
Escalante-González, R. J.; Campos-Cantón, E.
In this paper, we present a mechanism of generation of a class of switched dynamical system without equilibrium points that generates a chaotic attractor. The switched dynamical systems are based on piecewise linear (PWL) systems. The theoretical results are formally given through a theorem and corollary which give necessary and sufficient conditions to guarantee that a linear affine dynamical system has no equilibria. Numerical results are in accordance with the theory.
The Piecewise Linear Reactive Flow Rate Model
Vitello, P; Souers, P C
2005-07-22
Conclusions are: (1) Early calibrations of the Piece Wise Linear reactive flow model have shown that it allows for very accurate agreement with data for a broad range of detonation wave strengths. (2) The ability to vary the rate at specific pressures has shown that corner turning involves competition between the strong wave that travels roughly in a straight line and growth at low pressure of a new wave that turns corners sharply. (3) The inclusion of a low pressure de-sensitization rate is essential to preserving the dead zone at large times as is observed.
The feasibility of a piecewise-linear dynamic bowtie filter
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.
Neighboring extremal guidance for systems with a piecewise linear control
NASA Technical Reports Server (NTRS)
Hull, David G.; Helfrich, Clifford E.
1991-01-01
The neighboring extremal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied. This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. A simple example, the lunar launch problem, is used to demonstrate the validity of the guidance law. For model errors on the order of 5 percent, the results indicate that 5 percent errors occur in the final conditions.
NASA Astrophysics Data System (ADS)
Zimmermann, Karl-Heinz; Achtziger, Wolfgang
2001-09-01
The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.
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.
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.
Chaotic dynamics and diffusion in a piecewise linear equation
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.
Gravitational backreaction on piecewise linear cosmic string loops
NASA Astrophysics Data System (ADS)
Wachter, Jeremy M.; Olum, Ken D.
2017-01-01
We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational backreaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, backreaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop.
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.
Piecewise-continuous observers for linear systems with sampled and delayed output
NASA Astrophysics Data System (ADS)
Wang, H. P.; Tian, Y.; Christov, N.
2016-06-01
The paper presents a new class of state observers for linear systems with sampled and delayed output measurements. These observers are derived using the theory of a particular class of hybrid systems called piecewise-continuous systems, and can be easily implemented. The performances of the piecewise-continuous observers are compared with the performances of state observers designed using the Lyapunov-Krasovskii techniques. A piecewise-continuous observer is designed and implemented to an experimental visual servoing platform.
Good code sets based on Piecewise Linear FM
NASA Astrophysics Data System (ADS)
Qazi, Farhan Aslam
In this dissertation, classes of good analog and polyphase code sets, based on Piecewise Linear FM (PLFM) are introduced. The analog code sets, designed using pieces of Linear FM waveforms, have good autocorrelation and cross-correlation properties, i.e. they have small autocorrelation sidelobe peaks and cross-correlation peaks. They also possess the ability to both tolerate and detect Doppler shift. By concatenating sections of P3/P4 polyphase codes, new polyphase code sets are constructed, which can be considered as polyphase counterparts of the analog PLFM based code sets. Like the analog code sets, the polyphase PLFM code sets have good correlation properties and stand out in being the only class of polyphase code sets that can both tolerate and detect Doppler shift. The receiver is modeled as a matched filter, decomposed into two parallel parts, in order to extract information on the radial direction of a target in addition to its radial speed. At the cost of a slight degradation in the correlation properties and a small SNR loss, the Doppler properties of the proposed analog and digital code sets can be improved further by extending the matched filter parts in either direction.
Optimal Piecewise Linear Basis Functions in Two Dimensions
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.
Linear response formula for piecewise expanding unimodal maps
NASA Astrophysics Data System (ADS)
Baladi, Viviane; Smania, Daniel
2008-04-01
The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.
Kiani, Vahid; Harati, Ahad; Vahedian, Abedin
2017-02-01
Geometrical wavelets have already proved their strength in approximation, compression, and denoising of piecewise constant and piecewise linear images. In this paper, we extend this family by introducing planelets toward an effective representation of indoor depth images. It uses a linear fractional model to capture non-linearity of depth values in the planar regions of the output images of Kinect-like sensors. A block-based compression framework based on planelet approximation is then presented, which uses quadtree decomposition along with spatial predictions as an effective intra-coding scheme. Compared with both classical geometric wavelets and some state-of-the-art image coding algorithms, our method provides desirable quality by explicitly representing edges and planar patches.
Kiani, Vahid; Harati, Ahad; Vahedian, Abedin
2016-10-26
Geometrical wavelets have already proved their strength in approximation, compression, and denoising of piecewise constant and piecewise linear images. In this paper, we extend this family by introducing planelets toward an effective representation of indoor depth images. It uses linear fractional model to capture non-linearity of depth values in planar regions of the output images of Kinect-like sensors. A block-based compression framework based on planelet approximation is then presented which uses quadtree decomposition along with spatial predictions as an effective intracoding scheme. Compared with both classical geometric wavelets and some state-of-the art image coding algorithms, our method provides desirable quality by explicitly representing edges and planar patches.
NASA Astrophysics Data System (ADS)
Lima, Maurício Firmino Silva; Pessoa, Claudio; Pereira, Weber F.
We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones.
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.
Dose reduction using a dynamic, piecewise-linear attenuator
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
A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains
NASA Astrophysics Data System (ADS)
Guzina, Bojan B.; Madyarov, Andrew I.
2007-08-01
The focus of this study is a 3D inverse scattering problem underlying non-invasive reconstruction of piecewise-homogeneous (PH) defects in a layered semi-infinite solid from near-field, surface elastic waveforms. The solution approach revolves around the use of Green's function for the layered reference domain and a generalization of the linear sampling method to deal with the featured class of PH configurations. For a rigorous treatment of the full-waveform integral equation that is used as a basis for obstacle reconstruction, the developments include an extension of the Holmgren's uniqueness theorem to piecewise-homogeneous domains and an in-depth analysis of the situation when the sampling point is outside the support of the obstacle that employs the method of topological sensitivity. Owing to the ill-posed nature of the featured integral equation, a stable approximate solution is sought via Tikhonov regularization. A set of numerical examples is included to demonstrate the feasibility of 3D obstacle reconstruction when the defects are buried in a multi-layered elastic solid.
Gadgets, approximation, and linear programming
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.
Yu, Guoshen; Sapiro, Guillermo; Mallat, Stéphane
2012-05-01
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.
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).
Application of Piecewise Linear Control Allocation to Reusable Launch Vehicle Guidance and Control
2006-02-01
Reklaitis , et.al. [7]. Without loss of generality, we begin by considering a single variable function, f(x), defined on an interval, [a, b]. Begin by...Piecewise Linear Functions,” Journal of Guidance, Control, and Dynamics, vol. 27, no. 6, pp. 1017–1027, Nov./Dec. 2004. [7] G. Reklaitis , A. Ravindran
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.
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
Akaishi, A; Shudo, A
2009-12-01
We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time T(c)(*) between these two regimes implies T(c)(*) approximately -log[micro(R)] where micro(R) denotes the area of the recurrence region.
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.
Heathcote, Andrew
2016-01-01
In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We use a random-dot motion paradigm along with cognitive modeling to investigate how the decision process is updated when a stimulus changes. Participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. To further investigate the underlying changes in the decision process, we developed a Piecewise Linear Ballistic Accumulator model (PLBA). The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modeling framework using a non-parametric approximate Bayesian algorithm. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Thus, the perceptual decision process was slow to react to, and underestimated, new contrary motion information. PMID:26760448
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.
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.
Reliable H∞ filtering for discrete piecewise linear systems with infinite distributed delays
NASA Astrophysics Data System (ADS)
Wei, Guoliang; Han, Fei; Wang, Licheng; Song, Yan
2014-05-01
This paper is concerned with the reliable H∞ filtering problem for discrete-time piecewise linear systems subject to sensor failures and time delays. The considered sensor failures are depicted by bounded variables taking value on a certain interval. The time delays are assumed to be infinitely distributed in the discrete-time domain. The purpose of the addressed reliable H∞ filtering problem is to design a piecewise linear filter such that, for the admissible sensor failures and possible infinite distributed delays, the augmented dynamics is exponentially stable and the H∞ performance is guaranteed with a prescribed attenuation level γ. With the aid of the convex optimal method, the filter parameters are obtained in terms of the solution to a set of LMIs which can be solved by the Matlab Toolbox. At last, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithms.
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
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
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.
On the nonlinear normal modes of free vibration of piecewise linear systems
NASA Astrophysics Data System (ADS)
Uspensky, B. V.; Avramov, K. V.
2014-07-01
A modification of the Shaw-Pierre nonlinear normal modes is suggested in order to analyze the vibrations of a piecewise linear mechanical systems with finite degrees of freedom. The use of this approach allows one to reduce to twice the dimension of the nonlinear algebraic equations system for nonlinear normal modes calculations in comparison with systems obtained by previous researchers. Two degrees of freedom and fifteen degrees of freedom nonlinear dynamical systems are investigated numerically by using nonlinear normal modes.
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.
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
[Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium].
Zemskov, E P; Loskutov, A Iu
2009-01-01
One-dimensional autowaves (traveling waves) in excitable medium described by a piecewise-linear reaction-diffusion system have been investigated. Two main types of waves have been considered: a single impulse and a periodic sequence of impulses (wave trains). In a two-component system, oscillations appear due to the presence of the second component in the reaction-diffusion system. In a one-component system, oscillations appear owing to external periodic excitation (forcing). Using semianalytical solutions for the wave profile, the shape and velocity of autowaves have been found. It is shown that the dispersion relation for oscillating sequences of impulses has an anomalous character.
Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics.
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.
Simulating piecewise-linear surface water and ground water interactions with MODFLOW.
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.
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.
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.
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.
Hsieh, Scott S; Pelc, Norbert J
2014-06-07
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.
Goreac, Dan; Serea, Oana-Silvia
2012-10-15
We aim at characterizing domains of attraction for controlled piecewise deterministic processes using an occupational measure formulation and Zubov's approach. Firstly, we provide linear programming (primal and dual) formulations of discounted, infinite horizon control problems for PDMPs. These formulations involve an infinite-dimensional set of probability measures and are obtained using viscosity solutions theory. Secondly, these tools allow to construct stabilizing measures and to avoid the assumption of stability under concatenation for controls. The domain of controllability is then characterized as some level set of a convenient solution of the associated Hamilton-Jacobi integral-differential equation. The theoretical results are applied to PDMPs associated to stochastic gene networks. Explicit computations are given for Cook's model for gene expression.
Dynamics of a 2D Piecewise Linear Braess Paradox Model: Effect of the Third Partition
NASA Astrophysics Data System (ADS)
Avrutin, Viktor; Dibak, Christoph; Dal Forno, Arianna; Merlone, Ugo
In this work, we investigate the dynamics of a piecewise linear 2D discontinuous map modeling a simple network showing the Braess paradox. This paradox represents an example in which adding a new route to a specific congested transportation network makes all the travelers worse off in terms of their individual travel time. In the particular case in which the modeled network corresponds to a binary choice situation, the map is defined on two partitions and its dynamics has already been described. In the general case corresponding to a ternary choice, a third partition appears leading to significantly more complex bifurcation structures formed by border collision bifurcations of stable cycles with points located in all three partitions. Considering a map taking a constant value on one of the partitions, we provide a first systematic description of possible dynamics for this case.
Ultra-high-frequency piecewise-linear chaos using delayed feedback loops
NASA Astrophysics Data System (ADS)
Cohen, Seth D.; Rontani, Damien; Gauthier, Daniel J.
2012-12-01
We report on an ultra-high-frequency (>1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar.
NASA Astrophysics Data System (ADS)
Ibáñez, Javier; Hernández, Vicente
2009-11-01
Differential Matrix Riccati Equations play a fundamental role in control theory, for example, in optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a piecewise-linearized method based on the conmutant equation to solve Differential Matrix Riccati Equations (DMREs) is described. This method is applied to develop two algorithms which solve these equations: one for time-varying DMREs and another for time-invariant DMREs, also MATLAB implementations of the above algorithms are developed. Since MATLAB does not have functions which solve DMREs, two algorithms based on a BDF method are also developed. All implemented algorithms have been compared, under equal conditions, at both precision and computational costs. Experimental results show the advantages of solving non-stiff DMREs and in particular stiff DMREs by the proposed algorithms.
Three Definitions of Best Linear Approximation
1976-04-01
Three definitions of best (in the least squares sense) linear approximation to given data points are presented. The relationships between these three area discussed along with their relationship to basic statistics such as mean values, the covariance matrix, and the (linear) correlation coefficient . For each of the three definitions, and best line is solved in closed form in terms of the data centroid and the covariance matrix.
Kohli, Nidhi; Hughes, John; Wang, Chun; Zopluoglu, Cengiz; Davison, Mark L
2015-06-01
A linear-linear piecewise growth mixture model (PGMM) is appropriate for analyzing segmented (disjointed) change in individual behavior over time, where the data come from a mixture of 2 or more latent classes, and the underlying growth trajectories in the different segments of the developmental process within each latent class are linear. A PGMM allows the knot (change point), the time of transition from 1 phase (segment) to another, to be estimated (when it is not known a priori) along with the other model parameters. To assist researchers in deciding which estimation method is most advantageous for analyzing this kind of mixture data, the current research compares 2 popular approaches to inference for PGMMs: maximum likelihood (ML) via an expectation-maximization (EM) algorithm, and Markov chain Monte Carlo (MCMC) for Bayesian inference. Monte Carlo simulations were carried out to investigate and compare the ability of the 2 approaches to recover the true parameters in linear-linear PGMMs with unknown knots. The results show that MCMC for Bayesian inference outperformed ML via EM in nearly every simulation scenario. Real data examples are also presented, and the corresponding computer codes for model fitting are provided in the Appendix to aid practitioners who wish to apply this class of models.
NASA Astrophysics Data System (ADS)
Edwards, C. L.; Edwards, M. L.
2009-05-01
MEMS micro-mirror technology offers the opportunity to replace larger optical actuators with smaller, faster ones for lidar, network switching, and other beam steering applications. Recent developments in modeling and simulation of MEMS two-axis (tip-tilt) mirrors have resulted in closed-form solutions that are expressed in terms of physical, electrical and environmental parameters related to the MEMS device. The closed-form analytical expressions enable dynamic time-domain simulations without excessive computational overhead and are referred to as the Micro-mirror Pointing Model (MPM). Additionally, these first-principle models have been experimentally validated with in-situ static, dynamic, and stochastic measurements illustrating their reliability. These models have assumed that the mirror has a rectangular shape. Because the corners can limit the dynamic operation of a rectangular mirror, it is desirable to shape the mirror, e.g., mitering the corners. Presented in this paper is the formulation of a generalized electrostatic micromirror (GEM) model with an arbitrary convex piecewise linear shape that is readily implemented in MATLAB and SIMULINK for steady-state and dynamic simulations. Additionally, such a model permits an arbitrary shaped mirror to be approximated as a series of linearly tapered segments. Previously, "effective area" arguments were used to model a non-rectangular shaped mirror with an equivalent rectangular one. The GEM model shows the limitations of this approach and provides a pre-fabrication tool for designing mirror shapes.
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.
Development of a piecewise linear omnidirectional 3D image registration method.
Bae, Hyunsoo; Kang, Wonjin; Lee, SukGyu; Kim, Youngwoo
2016-12-01
This paper proposes a new piecewise linear omnidirectional image registration method. The proposed method segments an image captured by multiple cameras into 2D segments defined by feature points of the image and then stitches each segment geometrically by considering the inclination of the segment in the 3D space. Depending on the intended use of image registration, the proposed method can be used to improve image registration accuracy or reduce the computation time in image registration because the trade-off between the computation time and image registration accuracy can be controlled for. In general, nonlinear image registration methods have been used in 3D omnidirectional image registration processes to reduce image distortion by camera lenses. The proposed method depends on a linear transformation process for omnidirectional image registration, and therefore it can enhance the effectiveness of the geometry recognition process, increase image registration accuracy by increasing the number of cameras or feature points of each image, increase the image registration speed by reducing the number of cameras or feature points of each image, and provide simultaneous information on shapes and colors of captured objects.
Development of a piecewise linear omnidirectional 3D image registration method
NASA Astrophysics Data System (ADS)
Bae, Hyunsoo; Kang, Wonjin; Lee, SukGyu; Kim, Youngwoo
2016-12-01
This paper proposes a new piecewise linear omnidirectional image registration method. The proposed method segments an image captured by multiple cameras into 2D segments defined by feature points of the image and then stitches each segment geometrically by considering the inclination of the segment in the 3D space. Depending on the intended use of image registration, the proposed method can be used to improve image registration accuracy or reduce the computation time in image registration because the trade-off between the computation time and image registration accuracy can be controlled for. In general, nonlinear image registration methods have been used in 3D omnidirectional image registration processes to reduce image distortion by camera lenses. The proposed method depends on a linear transformation process for omnidirectional image registration, and therefore it can enhance the effectiveness of the geometry recognition process, increase image registration accuracy by increasing the number of cameras or feature points of each image, increase the image registration speed by reducing the number of cameras or feature points of each image, and provide simultaneous information on shapes and colors of captured objects.
Nie, Xiaobing; Zheng, Wei Xing
2016-03-01
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
NASA Astrophysics Data System (ADS)
Libby, William A.
1993-05-01
A guidance law for the control of a system in the neighborhood of a nominal suboptimal trajectory is developed. The guidance law is demonstrated using a lunar launch problem with constraints at orbit entry. A set of precomputed gains is used by the guidance law to operate on an extremal path in the neighborhood of the suboptimal trajectory. The guidance law and gains are designed to minimize the change in the desired performance index while still satisfying the final path constraints. In the lunar launch problem, the nominal suboptimal trajectory minimizes the final time using piecewise linear control. This trajectory is obtained to provide a nominal control history. The guidance law is found by minimizing the second variation of the suboptimal trajectory performance index subject to the final constraints being satisfied. For the lunar launch problem, the guidance law leads to a set of gains that relates deviations from the suboptimal trajectory to required changes in the nominal control history. The deviations from the suboptimal trajectory, used together with the precomputed gains, determines the change in the nominal control history required to meet the final constraints while minimizing the change in the final time.
NASA Astrophysics Data System (ADS)
Venkatesh, P. R.; Venkatesan, A.
2016-10-01
We report the occurrence of vibrational resonance in piecewise-linear non-autonomous system. Especially, we show that an optimal amplitude of the high frequency second harmonic driving enhances the response of a piece-wise linear non-autonomous Murali-Lakshmanan-Chua (MLC) system to a low frequency first harmonic signal. This phenomenon is illustrated with the analytical solutions of circuit equations characterising the system and finally compared with the numerical method. Further, it has been enunciated explicitly, the implementation of the fundamental NOR/NAND gate via vibrational resonance, both by numerical and analytical solutions. In addition, these logical behaviours (AND/NAND/OR/NOR) can be decided by the amplitude of the input square waves without altering the system parameters.
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.
Konishi, Keiji; Takeuchi, Masashi; Shimizu, Tsuyoshi
2011-06-01
Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.
The quartic piecewise-linear criterion for the multiaxial yield behavior of human trabecular bone.
Sanyal, Arnav; Scheffelin, Joanna; Keaveny, Tony M
2015-01-01
Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (lCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36),mechanical anisotropy (range of E3/E1¼3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension,compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space.The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal box like shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized strain space combined with a piecewise linear yield criterion in two planes for normalshear loading (mean error SD: 4.660.8% for the finite element data versus the criterion).This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.
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
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.
NASA Astrophysics Data System (ADS)
Farag, Mohammed; Fleckenstein, Matthias; Habibi, Saeid
2017-02-01
Model-order reduction and minimization of the CPU run-time while maintaining the model accuracy are critical requirements for real-time implementation of lithium-ion electrochemical battery models. In this paper, an isothermal, continuous, piecewise-linear, electrode-average model is developed by using an optimal knot placement technique. The proposed model reduces the univariate nonlinear function of the electrode's open circuit potential dependence on the state of charge to continuous piecewise regions. The parameterization experiments were chosen to provide a trade-off between extensive experimental characterization techniques and purely identifying all parameters using optimization techniques. The model is then parameterized in each continuous, piecewise-linear, region. Applying the proposed technique cuts down the CPU run-time by around 20%, compared to the reduced-order, electrode-average model. Finally, the model validation against real-time driving profiles (FTP-72, WLTP) demonstrates the ability of the model to predict the cell voltage accurately with less than 2% error.
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.
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
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
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.
Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.; Densmore, Jeffery D.
2016-02-23
Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examine the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/T^{3}, but we formulate and test a slight extension for opacities ~ 1/T^{3.5}, where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.
Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.; ...
2016-02-23
Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examinemore » the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/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
Li, Chen; Yang, Weitao
2017-02-21
We provide a rigorous proof that the Hartree Fock energy, as a function of the fractional electron number, E(N), is piecewise concave. Moreover, for semi-local density functionals, we show that the piecewise convexity of the E(N) curve, as stated in the literature, is not generally true for all fractions. By an analysis based on exchange-only local density approximation and careful examination of the E(N) curve, we find for some systems, there exists a very small concave region, corresponding to adding a small fraction of electrons to the integer system, while the remaining E(N) curve is convex. Several numerical examples are provided as verification. Although the E(N) curve is not convex everywhere in these systems, the previous conclusions on the consequence of the delocalization error in the commonly used density functional approximations, in particular, the underestimation of ionization potential, and the overestimation of electron affinity, and other related issues, remain unchanged. This suggests that instead of using the term convexity, a modified and more rigorous description for the delocalization error is that the E(N) curve lies below the straight line segment across the neighboring integer points for these approximate functionals.
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.
Polynomial compensation, inversion, and approximation of discrete time linear systems
NASA Technical Reports Server (NTRS)
Baram, Yoram
1987-01-01
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
Approximately Integrable Linear Statistical Models in Non-Parametric Estimation
1990-08-01
OTIC I EL COPY Lfl 0n Cf) NAPPROXIMATELY INTEGRABLE LINEAR STATISTICAL MODELS IN NON- PARAMETRIC ESTIMATION by B. Ya. Levit University of Maryland...Integrable Linear Statistical Models in Non- Parametric Estimation B. Ya. Levit Sumnmary / The notion of approximately integrable linear statistical models...models related to the study of the "next" order optimality in non- parametric estimation . It appears consistent to keep the exposition at present at the
Nie, Xiaobing; Zheng, Wei Xing
2015-05-01
This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3(n) locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results.
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.
ERIC Educational Resources Information Center
Sinclair, Nathalie; Armstrong, Alayne
2011-01-01
Piecewise linear functions and story graphs are concepts usually associated with algebra, but in the authors' classroom, they found success teaching this topic in a distinctly geometrical manner. The focus of the approach was less on learning geometric concepts and more on using spatial and kinetic reasoning. It not only supports the learning of…
Use of a linearization approximation facilitating stochastic model building.
Svensson, Elin M; Karlsson, Mats O
2014-04-01
The objective of this work was to facilitate the development of nonlinear mixed effects models by establishing a diagnostic method for evaluation of stochastic model components. The random effects investigated were between subject, between occasion and residual variability. The method was based on a first-order conditional estimates linear approximation and evaluated on three real datasets with previously developed population pharmacokinetic models. The results were assessed based on the agreement in difference in objective function value between a basic model and extended models for the standard nonlinear and linearized approach respectively. The linearization was found to accurately identify significant extensions of the model's stochastic components with notably decreased runtimes as compared to the standard nonlinear analysis. The observed gain in runtimes varied between four to more than 50-fold and the largest gains were seen for models with originally long runtimes. This method may be especially useful as a screening tool to detect correlations between random effects since it substantially quickens the estimation of large variance-covariance blocks. To expedite the application of this diagnostic tool, the linearization procedure has been automated and implemented in the software package PsN.
Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation.
Cardelli, Luca; Kwiatkowska, Marta; Laurenti, Luca
2016-10-28
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation.
Cardelli, Luca; Kwiatkowska, Marta; Laurenti, Luca
2016-11-01
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
NASA Astrophysics Data System (ADS)
Kong, Xiangxi; Sun, Wei; Wang, Bo; Wen, Bangchun
2015-06-01
The dynamic behaviors and stability of the linear guide considering contact actions are studied by multi-term incremental harmonic balance method (IHBM). Based on fully considering the parameters of the linear guide, a static model is developed and the contact stiffness is calculated according to Hertz contact theory. A generalized time-varying and piecewise-nonlinear dynamic model of the linear guide is formulated to perform an accurate investigation on its dynamic behaviors and stability. The numerical simulation is used to confirm the feasibility of the approach. The effects of excitation force and mean load on the system are analyzed in low-order nonlinearity. Multi-term IHBM and numerical simulation are employed to the effect of high-order nonlinearity and show the transition to chaos. Additionally, the effects of preload, initial contact angle, the number and diameter of balls are discussed.
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.
Biochemical fluctuations, optimisation and the linear noise approximation
2012-01-01
Background Stochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive. Results We implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this
NASA Astrophysics Data System (ADS)
Vjačeslavov, N. S.
1980-02-01
In this paper estimates are found for L_pR_n(f) - the least deviation in the L_p-metric, 0 < p\\leq\\infty, of a piecewise analytic function f from the rational functions of degree at most n. It is shown that these estimates are sharp in a well-defined sense.Bibliography: 12 titles.
Approximate simulation of entanglement with a linear cost of communication
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.
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.
Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde
2015-11-01
The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations.
Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde
2016-12-01
In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5(n) equilibrium points located in ℜ(n), and 3(n) of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.
NASA Astrophysics Data System (ADS)
Simpson, D. J. W.
2017-01-01
The mode-locking regions of a dynamical system are subsets of parameter space within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a distinctive chain structure with points of zero width called shrinking points. In this paper a local analysis about an arbitrary shrinking point is performed. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional centre manifolds in order to build a comprehensive theoretical framework for the local dynamics. The main results are universal quantitative descriptions for the shape of nearby mode-locking regions, the location of nearby shrinking points, and the key properties of these shrinking points. The results are applied to the three-dimensional border-collision normal form, a model of an oscillator subject to dry friction, and a model of a DC/DC power converter.
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.
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
NASA Astrophysics Data System (ADS)
Ledoux, Veerle; van Daele, Marnix
2011-12-01
The piecewise perturbation methods (PPM) have proven to be very efficient for the numerical solution of the linear time-independent Schrödinger equation. The underlying idea is to replace the potential function piecewisely by simpler approximations and then to solve the approximating problem. The accuracy is improved by adding some perturbation corrections. Two types of approximating potentials were considered in the literature, that is piecewise constant and piecewise linear functions, giving rise to the so-called CP methods (CPM) and LP methods (LPM). Piecewise polynomials of higher degree have not been used since the approximating problem is not easy to integrate analytically. As suggested by Ixaru (Comput Phys Commun 177:897-907, 2007), this problem can be circumvented using another perturbative approach to construct an expression for the solution of the approximating problem. In this paper, we show that there is, however, no need to consider PPM based on higher-order polynomials, since these methods are equivalent to the CPM. Also, LPM is equivalent to CPM, although it was sometimes suggested in the literature that an LP method is more suited for problems with strongly varying potentials. We advocate that CP schemes can (and should) be used in all cases, since it forms the most straightforward way of devising PPM and there is no advantage in considering other piecewise polynomial perturbation methods.
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
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.
A Study of Linear Approximation Techniques for SAR Azimuth Processing
NASA Technical Reports Server (NTRS)
Martinson, L. W.; Perry, R. P.; Liu, B.
1979-01-01
The application of the step transform subarray processing techniques to synthetic aperture radar (SAR) was studied. The subarray technique permits the application of efficient digital transform computational techniques such as the fast Fourier transform to be applied while offering an effective tool for range migration compensation. Range migration compensation is applied at the subarray level, and with the subarray size based on worst case range migration conditions, a minimum control system is achieved. A baseline processor was designed for a four-look SAR system covering approximately 4096 by 4096 SAR sample field every 2.5 seconds. Implementation of the baseline system was projected using advanced low power technologies. A 20 swath is implemented with approximately 1000 circuits having a power dissipation of from 70 to 195 watts. The baseline batch step transform processor is compared to a continuous strip processor, and variations of the baseline are developed for a wide range of SAR parameters.
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.
Keith, Scott W; Allison, David B
2014-09-29
This paper details the design, evaluation, and implementation of a framework for detecting and modeling nonlinearity 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 nonparametric bootstrapping. Unlike other nonlinear 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/m(2)) and the complex multi-stage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic nonlinear 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 nonlinearly 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.
Manning, Jeffrey A; Garton, Edward O
2013-07-01
Habitat selection fundamentally drives the distribution of organisms across landscapes; density-dependent habitat selection (DDHS) is considered a central component of ecological theories explaining habitat use and population regulation. A preponderance of DDHS theories is based on ideal distributions, such that organisms select habitat according to either the ideal free, despotic, or pre-emptive distributions. Models that can be used to simultaneously test competing DDHS theories are desirable to help improve our understanding of habitat selection. We developed hierarchical, piecewise linear models that allow for simultaneous testing of DDHS theories and accommodate densities from multiple habitats and regional populations, environmental covariates, and random effects. We demonstrate the use of these models with data on mule deer (Odocoileus hemionus) abundance and net energy costs in different snow depths within winter ranges of five regional populations in western Idaho, USA. Regional population density explained 40% of the variation in population growth, and we found that deer were ideal free in winter ranges. Deer occupied habitats with lowest net energy costs at higher densities and at a higher rate than compared to habitats with intermediate and high energy costs. The proportion of a regional population in low energy cost habitat the previous year accounted for a significant amount of variation in population growth (17%), demonstrating the importance of winter habitat selection in regulating deer populations. These linear models are most appropriate for empirical data collected from centralized habitat patches within the local range of a species where individuals are either year-round residents or migratory (but have already arrived from migration).
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.
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.
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.
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.
Mirzaei, H R; Pitchford, W S; Verbyla, A P
2011-09-27
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.
The algebra of linear functionals on polynomials, with applications to Padé approximation
NASA Astrophysics Data System (ADS)
Brezinski, C.; Maroni, P.
1996-12-01
Some results about the algebra of linear functionals on the vector space of complex polynomials are given. These results have applications to Padé-type and Padé approximation. In particular an expression for the relative error is obtained.
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…
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.
NASA Technical Reports Server (NTRS)
Gunderson, R. W.; George, J. H.
1974-01-01
Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
NASA Astrophysics Data System (ADS)
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2017-01-01
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.
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.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2017-02-01
An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
NASA Astrophysics Data System (ADS)
Derrida, Bernard; Hakim, Vincent; Zeitak, Reuven
1996-09-01
The fraction r\\(t\\) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that r\\(t\\) decays with time like a power law with a nontrivial exponent θ which depends on the space dimension. The dynamics is a special case of a stationary Gaussian process of known correlation function. The exponent θ is given by the asymptotic decay of the probability distribution of intervals between consecutive zero crossings. An approximation based on the assumption that successive zero crossings are independent random variables gives values of θ in close agreement with the results of simulations.
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.
Reinholz, H; Röpke, G
2012-03-01
Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1988-01-01
The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.
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.
Mayorga, René V; Arriaga, Mariano
2007-10-01
In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.
Linearization of a heat-transfer system model with approximation of transport time delay
NASA Astrophysics Data System (ADS)
Shilin, A. A.; Bukreev, V. G.
2014-10-01
A method is proposed for linearizing the nonlinear model of a heat-transfer facility the state variables of which at equilibrium points are determined by numerically solving the initial bilinear system of differential equations for a stationary position of the control valve equipped with a constant-speed electric drive. The considerable transport time delay resulting from the distributed design of the heat-transfer system secondary circuit is approximated by a limited number of first-order inertial sections for obtaining a mathematical model in the Cauchy form. The proposed linearization method is tested on an operating hot-water supply heat-transfer system, and the study results are presented in the form of transient curves.
On vague logics and approximate reasoning based on vague linear transformation
NASA Astrophysics Data System (ADS)
Feng, Zhi-Qiang; Liu, Cun-Gen
2012-09-01
As a generalisation of the Fuzzy Sets theory, vague set has been proven to be a new tool in dealing with vague information. In this article, we attempt to generalise the techniques of fuzzy inference in a vague environment. In the rule-based inference system, an 'if … then …' rule can be considered a transformer that implements information conversion between input-output ends. Thus, according to the logical operations of vague linguistic variables, we introduce an approach to approximation inference based on linear transformation, and then discuss the representations for several inference structures regarding single rule, multi-rules and compound rules. By defining the inclusion function of vague sets, we provide vague rough approximation based on measure of inclusion, and then present a method on rule creation from a decision system. A case study on the prediction for welding deformation is used to illustrate the effectiveness of the proposed approaches.
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.
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
A novel impact identification algorithm based on a linear approximation with maximum entropy
NASA Astrophysics Data System (ADS)
Sanchez, N.; Meruane, V.; Ortiz-Bernardin, A.
2016-09-01
This article presents a novel impact identification algorithm that uses a linear approximation handled by a statistical inference model based on the maximum-entropy principle, termed linear approximation with maximum entropy (LME). Unlike other regression algorithms as artificial neural networks (ANNs) and support vector machines, the proposed algorithm requires only parameter to be selected and the impact is identified after solving a convex optimization problem that has a unique solution. In addition, with LME data is processed in a period of time that is comparable to the one of other algorithms. The performance of the proposed methodology is validated by considering an experimental aluminum plate. Time varying strain data is measured using four piezoceramic sensors bonded to the plate. To demonstrate the potential of the proposed approach over existing ones, results obtained via LME are compared with those of ANN and least square support vector machines. The results demonstrate that with a low number of sensors it is possible to accurately locate and quantify impacts on a structure and that LME outperforms other impact identification algorithms.
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.
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2017-03-02
This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
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.
Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation
Elf, Johan; Ehrenberg, Måns
2003-01-01
Biochemical networks in single cells can display large fluctuations in molecule numbers, making mesoscopic approaches necessary for correct system descriptions. We present a general method that allows rapid characterization of the stochastic properties of intracellular networks. The starting point is a macroscopic description that identifies the system's elementary reactions in terms of rate laws and stoichiometries. From this formulation follows directly the stationary solution of the linear noise approximation (LNA) of the Master equation for all the components in the network. The method complements bifurcation studies of the system's parameter dependence by providing estimates of sizes, correlations, and time scales of stochastic fluctuations. We describe how the LNA can give precise system descriptions also near macroscopic instabilities by suitable variable changes and elimination of fast variables. PMID:14597656
Are Bilinear Quadrilaterals Better Than Linear Triangles?
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.
Helbig, N.; Fuks, J. I.; Verstraete, M. J.; Marques, M. A. L.; Tokatly, I. V.; Rubio, A.
2011-03-15
We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations obtained by exploiting the mapping of an N-electron system in d dimensions onto a single electron in Nxd dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.
Linear-scaling implementation of the direct random-phase approximation
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.
Jia, X.; Mang, H.A.
2015-01-01
The consistently linearized eigenproblem (CLE) plays an important role in stability analysis of structures. Solution of the CLE requires computation of the tangent stiffness matrix K∼T and of its first derivative with respect to a dimensionless load parameter λ, denoted as K∼˙T. In this paper, three approaches of computation of K∼˙T are discussed. They are based on (a) an analytical expression for the derivative of the element tangent stiffness matrix K∼Te, (b) a load-based finite difference approximation (LBFDA), and (c) a displacement-based finite difference approximation (DBFDA). The convergence rate, the accuracy, and the computing time of the LBFDA and the DBFDA are compared, using the analytical solution as the benchmark result. The numerical investigation consists of the analysis of a circular arch subjected to a vertical point load at the vertex, and of a thrust-line arch under a uniformly distributed load. The main conclusion drawn from this work is that the DBFDA is superior to the LBFDA. PMID:25892827
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.
Chen, Zikuan; Calhoun, Vince
2015-05-01
The underlying source of brain imaging by T2*-weighted magnetic resonance imaging (T2*MRI) is the intracranial inhomogeneous tissue magnetic susceptibility (denoted by χ) that causes an inhomogeneous field map (via magnetization) in a main field. By decomposing T2*MRI into two steps, we understand that the 1st step from a χ source to a field map is a linear but non-isomorphic spatial mapping, and the 2nd step from the field map to a T2* image is a nonlinear mapping due to the trigonometric behavior of spin precession signals. The magnitude and phase calculations from a complex T2* image introduce additional nonlinearities. In this report, we look into the magnitude and phase behaviors of a T2* image (signal) by theoretical approximation and Monte Carlo simulation. We perform the 1st-order Taylor expansion on intravoxel dephasing formula of a T2* signal and show that the T2* magnitude is a quadratic mapping of the field map and T2* phase is a linear isomorphic mapping. By Monte Carlo simulation of T2*MRI for a span of echo times (with B0=3T and TE=[0,120] ms), we first confirm the quadratic magnitude and linear phase behaviors in small phase angle regime (via TE <30ms), and then provide more general magnitude and phase nonlinear behaviors in large phase angle scenarios (via TE >30ms). By solving the inverse problem of T2*MRI, we demonstrate χ tomography and conclude that the χ source can be reliably reconstructed from a T2* phase image in a small phase angle regime.
Wallace, E W J; Gillespie, D T; Sanft, K R; Petzold, L R
2012-08-01
The linear noise approximation (LNA) is a way of approximating the stochastic time evolution of a well-stirred chemically reacting system. It can be obtained either as the lowest order correction to the deterministic chemical reaction rate equation (RRE) in van Kampen's system-size expansion of the chemical master equation (CME), or by linearising the two-term-truncated chemical Kramers-Moyal equation. However, neither of those derivations sheds much light on the validity of the LNA. The problematic character of the system-size expansion of the CME for some chemical systems, the arbitrariness of truncating the chemical Kramers-Moyal equation at two terms, and the sometimes poor agreement of the LNA with the solution of the CME, have all raised concerns about the validity and usefulness of the LNA. Here, the authors argue that these concerns can be resolved by viewing the LNA as an approximation of the chemical Langevin equation (CLE). This view is already implicit in Gardiner's derivation of the LNA from the truncated Kramers-Moyal equation, as that equation is mathematically equivalent to the CLE. However, the CLE can be more convincingly derived in a way that does not involve either the truncated Kramers-Moyal equation or the system-size expansion. This derivation shows that the CLE will be valid, at least for a limited span of time, for any system that is sufficiently close to the thermodynamic (large-system) limit. The relatively easy derivation of the LNA from the CLE shows that the LNA shares the CLE's conditions of validity, and it also suggests that what the LNA really gives us is a description of the initial departure of the CLE from the RRE as we back away from the thermodynamic limit to a large but finite system. The authors show that this approach to the LNA simplifies its derivation, clarifies its limitations, and affords an easier path to its solution.
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.
Boundary parametric approximation to the linearized scalar potential magnetostatic field problem
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.
MAP estimators for piecewise continuous inversion
NASA Astrophysics Data System (ADS)
Dunlop, M. M.; Stuart, A. M.
2016-10-01
We study the inverse problem of estimating a field u a from data comprising a finite set of nonlinear functionals of u a , subject to additive noise; we denote this observed data by y. Our interest is in the reconstruction of piecewise continuous fields u a in which the discontinuity set is described by a finite number of geometric parameters a. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on u a and determining the conditional distribution on u a given the data y. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.
Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter
2003-03-01
In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545-548; Fluct. Noise Lett. 1, L181 (2001)].
A robust SN-DG-approximation for radiation transport in optically thick and diffusive regimes
NASA Astrophysics Data System (ADS)
Ragusa, J. C.; Guermond, J.-L.; Kanschat, G.
2012-02-01
We introduce a new discontinuous Galerkin (DG) method with reduced upwind stabilization for the linear Boltzmann equation applied to particle transport. The asymptotic analysis demonstrates that the new formulation does not suffer from the limitations of standard upwind methods in the thick diffusive regime; in particular, the new method yields the correct diffusion limit for any approximation order, including piecewise constant discontinuous finite elements. Numerical tests on well-established benchmark problems demonstrate the superiority of the new method. The improvement is particularly significant when employing piecewise constant DG approximation for which standard upwinding is known to perform poorly in the thick diffusion limit.
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.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
de Munck, J C
1992-09-01
A method is presented to compute the potential distribution on the surface of a homogeneous isolated conductor of arbitrary shape. The method is based on an approximation of a boundary integral equation as a set linear algebraic equations. The potential is described as a piecewise linear or quadratic function. The matrix elements of the discretized equation are expressed as analytical formulas.
NASA Astrophysics Data System (ADS)
Renac, Florent
2011-06-01
An algorithm for stabilizing linear iterative schemes is developed in this study. The recursive projection method is applied in order to stabilize divergent numerical algorithms. A criterion for selecting the divergent subspace of the iteration matrix with an approximate eigenvalue problem is introduced. The performance of the present algorithm is investigated in terms of storage requirements and CPU costs and is compared to the original Krylov criterion. Theoretical results on the divergent subspace selection accuracy are established. The method is then applied to the resolution of the linear advection-diffusion equation and to a sensitivity analysis for a turbulent transonic flow in the context of aerodynamic shape optimization. Numerical experiments demonstrate better robustness and faster convergence properties of the stabilization algorithm with the new criterion based on the approximate eigenvalue problem. This criterion requires only slight additional operations and memory which vanish in the limit of large linear systems.
Are bilinear quadrilaterals better than linear triangles?
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.
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.
The lens effect of a big spherical inhomogeneity in the linear approximation
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.
Analysis of the linear approximation of seismic inversions for various structural pairs
NASA Astrophysics Data System (ADS)
Buldgen, G.; Reese, D. R.; Dupret, M. A.
2017-01-01
Context. Thanks to the space-based photometry missions CoRoT and Kepler, we now benefit from a wealth of seismic data for stars other than the sun. In the future, K2, Tess, and Plato will complement this data and provide observations in addition to those already at hand. The availability of this data leads to questions on how it is feasible to extend kernel-based, linear structural inversion techniques to stars other than the sun. Linked to the inversion problem is the question of the validity of the linear assumption. In this study, we analyse the limitations of this assumption with respect to changes of structural variables. Aims: We wish to provide a more extended theoretical background to structural linear inversions by doing a study of the validity of the linear assumption for various structural variables. We thus point towards limitations in inversion techniques in the asteroseismic and helioseismic cases. Methods: First, we recall the origins of the linear assumption for structural stellar inversions and explain its importance for asteroseismic studies. We also briefly recall the impact of unknown structural quantities such as the mass and the radius of the star on structural inversion results. We then explain how kernels for new structural variables can be derived using two methods, one suited to asteroseismic targets, the other to helioseismic targets. For this second method, we present a new structural pair, namely the (A,Y) structural kernels. The kernels are then tested in various numerical experiments that enable us to evaluate the weaknesses of different structural pairs and the domains of validity of their respective linear regime. Results: The numerical tests we carry out allow us to disentangle the impact of various uncertainties in stellar models on the verification of the linear integral relations. We show the importance of metallicity, the impact of the equation of state, extra-mixing, and inaccuracies in the microphysics on the verification of
Approximation functions for airblast environments from buried charges
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.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
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.
NASA Technical Reports Server (NTRS)
Green, S.
1978-01-01
The infinite order sudden approximation for excitation of linear rigid rotors by collisions with atom is tested by comparing integral state-to-state cross sections with accurate close coupling and coupled states results. The systems studied are HCl-Ar, HCl-He, CO-He, HCN-He, CS-H2 and OCS-H2. With the exception of diatomic hydrides (e.g., HCl) which have atypically large rotational constants the method is found to be very accurate to remarkably low collision energies. This approximation should generally be extremely useful for thermal energy collisions.
Approximation of periodic functions in the classes H{sub q}{sup {Omega}} by linear methods
Pustovoitov, Nikolai N
2012-01-31
The following result is proved: if approximations in the norm of L{sub {infinity}} (of H{sub 1}) of functions in the classes H{sub {infinity}}{sup {Omega}} (in H{sub 1}{sup {Omega}}, respectively) by some linear operators have the same order of magnitude as the best approximations, then the set of norms of these operators is unbounded. Also Bernstein's and the Jackson-Nikol'skii inequalities are proved for trigonometric polynomials with spectra in the sets Q(N) (in {Gamma}(N,{Omega})). Bibliography: 15 titles.
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.
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.
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.
Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation.
Stathopoulos, Vassilios; Girolami, Mark A
2013-02-13
Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.
Shan, Xiao; Connor, J N L
2012-11-26
A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for
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.
Nonlinear amplitude approximation for bilinear systems
NASA Astrophysics Data System (ADS)
Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I.
2014-06-01
An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.
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
An approximate projection method for incompressible flow
NASA Astrophysics Data System (ADS)
Stevens, David E.; Chan, Stevens T.; Gresho, Phil
2002-12-01
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.
Piecewise quartic polynomial curves with a local shape parameter
NASA Astrophysics Data System (ADS)
Han, Xuli
2006-10-01
Piecewise quartic polynomial curves with a local shape parameter are presented in this paper. The given blending function is an extension of the cubic uniform B-splines. The changes of a local shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. The given curves possess satisfying shape-preserving properties. The given curve can also be used to interpolate locally the control points with GC2 continuity. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. As an application, the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter. The given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse. Some computing examples for curve design are given.
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
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.
Krzyzanowski, Piotr; Wrzosek, Dariusz; Wit, Dominik
2006-10-01
A discontinuous Galerkin approximation of the nonlinear Lotka-McKendrick equation is considered in the frequent case when the solution is only piecewise regular. An O(h(r+1/2)) error estimate for rth order polynomial finite elements is proved, as well as piecewise H(1)-regularity of the exact solution which guarantees the error estimate for r=0. Certain implementational details which improve the robustness of the method are also addressed.
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.
An insight into the behaviour of oscillators with a periodically piecewise-defined time-varying mass
NASA Astrophysics Data System (ADS)
Zukovic, Miodrag; Kovacic, Ivana
2017-01-01
Free vibrations of a linear, single-degree-of-freedom oscillator with a periodic piecewise-defined time-varying mass are studied. Two different cases of this variation are investigated: first, the mass increases and then decreases linearly in time, i.e. it changes triangularly, and the second, when the mass changes trapezoidically, which, unlike the previous case, includes the period when it remains constant. Exact solutions for motion are obtained analytically directly from the equations of motion, and the criteria of stability are derived and used to plot stability charts for different system parameters. In addition, the transformed equation of motion is utilized in conjunction with harmonic balancing to derive approximate analytical expressions for the boundaries of the first and second instability region.
Guidance law based on piecewise constant control for hypersonic gliders
NASA Astrophysics Data System (ADS)
Hull, David G.; Seguin, Jean-Marie
A midcourse guidance law is developed for the descent of a hypersonic glider to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N+1 nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14 percent of the true values are obtained for the downrange and crossranges considered.
Polynomial approximation of Poincare maps for Hamiltonian system
NASA Technical Reports Server (NTRS)
Froeschle, Claude; Petit, Jean-Marc
1992-01-01
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Adcock, T. A. A.; Taylor, P. H.
2016-01-15
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest 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.
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.
Optical spectroscopies of materials from orbital-dependent approximations
NASA Astrophysics Data System (ADS)
Dabo, Ismaila; Ferretti, Andrea; Cococcioni, Matteo; Marzari, Nicola
2013-03-01
Electronic-structure calculations based upon density-functional theory (DFT) have been fruitful in diverse areas of materials science. Despite their exceptional success and widespread use, a range of spectroscopic properties fall beyond the scope of existing DFT approximations. Failures of DFT calculations in describing electronic and optical phenomena take root in the lack of piecewise linearity of approximate functionals. This known deficiency reverberates negatively on the spectroscopic description of systems involving fractionally occupied or spatially delocalized electronic states, such as donor-acceptor organic heterojunctions and heavy-metal organometallic complexes. In this talk, I will present a class of orbital-dependent density-functional theory (OD-DFT) methods that are derived from a multidensity formulation of the electronic-structure problem and that restore the piecewise linearity of the total energy via Koopmans' theorem. Such OD-DFT electronic-structure approximations are apt at describing full orbital spectra within a few tenths of an electron-volt relative to experimental photoemission spectroscopies and with the additional benefit of providing appreciably improved total energies for molecular systems with fractional occupations.
Calculating the derivative of piecewise functions
NASA Astrophysics Data System (ADS)
Tomas Johansson, B.
2016-01-01
Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners' knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.
Regular and chaotic dynamics of a piecewise smooth bouncer
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.
Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
NASA Astrophysics Data System (ADS)
Gouveia, Márcio R. A.; Llibre, Jaume; Novaes, Douglas D.; Pessoa, Claudio
2016-04-01
We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane Σ which admits an invariant hyperplane Ω transversal to Σ containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
NASA Astrophysics Data System (ADS)
Trehan, Sumeet; Durlofsky, Louis J.
2016-12-01
A new reduced-order model based on trajectory piecewise quadratic (TPWQ) approximations and proper orthogonal decomposition (POD) is introduced and applied for subsurface oil-water flow simulation. The method extends existing techniques based on trajectory piecewise linear (TPWL) approximations by incorporating second-derivative terms into the reduced-order treatment. Both the linear and quadratic reduced-order methods, referred to as POD-TPWL and POD-TPWQ, entail the representation of new solutions as expansions around previously simulated high-fidelity (full-order) training solutions, along with POD-based projection into a low-dimensional space. POD-TPWQ entails significantly more offline preprocessing than POD-TPWL as it requires generating and projecting several third-order (Hessian-type) terms. The POD-TPWQ method is implemented for two-dimensional systems. Extensive numerical results demonstrate that it provides consistently better accuracy than POD-TPWL, with speedups of about two orders of magnitude relative to high-fidelity simulations for the problems considered. We demonstrate that POD-TPWQ can be used as an error estimator for POD-TPWL, which motivates the development of a trust-region-based optimization framework. This procedure uses POD-TPWL for fast function evaluations and a POD-TPWQ error estimator to determine when retraining, which entails a high-fidelity simulation, is required. Optimization results for an oil-water problem demonstrate the substantial speedups that can be achieved relative to optimizations based on high-fidelity simulation.
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.
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.
NASA Astrophysics Data System (ADS)
Fernández-Seivane, L.; Oliveira, M. A.; Sanvito, S.; Ferrer, J.
2006-08-01
We propose a computational method that drastically simplifies the inclusion of the spin-orbit interaction in density functional theory when implemented over localized basis sets. Our method is based on a well-known procedure for obtaining pseudopotentials from atomic relativistic ab initio calculations and on an on-site approximation for the spin-orbit matrix elements. We have implemented the technique in the SIESTA (Soler J M et al 2002 J. Phys.: Condens. Matter 14 2745-79) code, and show that it provides accurate results for the overall band-structure and splittings of group IV and III-IV semiconductors as well as for 5d metals.
NASA Astrophysics Data System (ADS)
Cuchí, J. E.; Gil-Rivero, A.; Molina, A.; Ruiz, E.
2013-07-01
We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) ɛ +(1-n)p=ɛ _0. This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois-Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist's metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr's metric.
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).
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.
A piecewise linear approach to volume tracking a triple point
NASA Astrophysics Data System (ADS)
Choi, Benjamin Y.; Bussmann, Markus
2007-02-01
An approach to volume tracking three materials is presented that, in contrast with the so-called onion-skin methodology, assumes the existence of a triple point at which two interfaces between three materials intersect. The reconstruction of any cell that contains three materials is iterative: the approach is to locate a point of intersection between two interfaces that minimizes a given error expression. The advantages and limitations of the algorithm are presented via a series of advection tests that demonstrate that triple points can be reconstructed and advected just as well as simpler interfaces in typical applications.
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.
NASA Astrophysics Data System (ADS)
Ferranti, Francesco; Rolain, Yves
2017-01-01
This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results.
Schurkus, Henry F.; Ochsenfeld, Christian
2016-01-21
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. .
Near constant-time optimal piecewise LDR to HDR inverse tone mapping
NASA Astrophysics Data System (ADS)
Chen, Qian; Su, Guan-Ming; Yin, Peng
2015-02-01
In a backward compatible HDR image/video compression, it is a general approach to reconstruct HDR from compressed LDR as a prediction to original HDR, which is referred to as inverse tone mapping. Experimental results show that 2- piecewise 2nd order polynomial has the best mapping accuracy than 1 piece high order or 2-piecewise linear, but it is also the most time-consuming method because to find the optimal pivot point to split LDR range to 2 pieces requires exhaustive search. In this paper, we propose a fast algorithm that completes optimal 2-piecewise 2nd order polynomial inverse tone mapping in near constant time without quality degradation. We observe that in least square solution, each entry in the intermediate matrix can be written as the sum of some basic terms, which can be pre-calculated into look-up tables. Since solving the matrix becomes looking up values in tables, computation time barely differs regardless of the number of points searched. Hence, we can carry out the most thorough pivot point search to find the optimal pivot that minimizes MSE in near constant time. Experiment shows that our proposed method achieves the same PSNR performance while saving 60 times computation time compared to the traditional exhaustive search in 2-piecewise 2nd order polynomial inverse tone mapping with continuous constraint.
Akcelik, Volkan; Flath, Pearl; Ghattas, Omar; Hill, Judith C; Van Bloemen Waanders, Bart; Wilcox, Lucas
2011-01-01
We consider the problem of estimating the uncertainty in large-scale linear statistical inverse problems with high-dimensional parameter spaces within the framework of Bayesian inference. When the noise and prior probability densities are Gaussian, the solution to the inverse problem is also Gaussian, and is thus characterized by the mean and covariance matrix of the posterior probability density. Unfortunately, explicitly computing the posterior covariance matrix requires as many forward solutions as there are parameters, and is thus prohibitive when the forward problem is expensive and the parameter dimension is large. However, for many ill-posed inverse problems, the Hessian matrix of the data misfit term has a spectrum that collapses rapidly to zero. We present a fast method for computation of an approximation to the posterior covariance that exploits the lowrank structure of the preconditioned (by the prior covariance) Hessian of the data misfit. Analysis of an infinite-dimensional model convection-diffusion problem, and numerical experiments on large-scale 3D convection-diffusion inverse problems with up to 1.5 million parameters, demonstrate that the number of forward PDE solves required for an accurate low-rank approximation is independent of the problem dimension. This permits scalable estimation of the uncertainty in large-scale ill-posed linear inverse problems at a small multiple (independent of the problem dimension) of the cost of solving the forward problem.
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.
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.
Piecewise Integration of Differential Variational Inequality
NASA Astrophysics Data System (ADS)
Wang, Zhengyu; Wu, Xinyuan
2009-09-01
Differential variational inequality (DVI) is a new mathematical paradigm consisting of a system of ordinary differential equations and a parametric variational inequality problem as the constraints. The solution of DVI was shown at best piecewise differentiable, for which the existing integrators possess only convergence of order one. In this paper we present an algorithm of finding the pieces where the solution is differentiable, and propose applying the methods in the pieces for a moderate stepsize, while for smaller stepsize around the boundary of the pieces for achieving high accuracy. Numerical example of bridge collapse is given to illustrate the efficiency of our algorithms.
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.
Piecewise power laws in individual learning curves.
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.
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.
Tetsu, Hiroyuki; Nakamoto, Taishi
2016-03-15
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 and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.
Lee, Ming-Wei; Hung, Cheng-Hung; Liao, Jung-Li; Cheng, Nan-Yu; Hou, Ming-Feng; Tseng, Sheng-Hao
2014-10-01
In this paper, we demonstrate that a scanning MEMS mirror can be employed to create a linear gradient line source that is equivalent to a planar source. This light source setup facilitates the use of diffusion models of increased orders of approximation having closed form solution, and thus enhance the efficiency and accuracy in sample optical properties recovery. In addition, compared with a regular planar light source, the linear gradient line source occupies much less source area and has an elevated measurement efficiency. We employed a δ-P1 diffusion equation with a closed form solution and carried out a phantom study to understand the performance of this new method in determining the absorption and scattering properties of turbid samples. Moreover, our Monte Carlo simulation results indicated that this geometry had probing depths comparable to those of the conventional diffuse reflectance measurement geometry with a source-detector separation of 3 mm. We expect that this new source setup would facilitate the investigating of superficial volumes of turbid samples in the wavelength regions where tissue absorption coefficients are comparable to scattering coefficients.
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.
Piecewise nonlinear regression: a statistical look at lamp performance
NASA Astrophysics Data System (ADS)
Halverson, Galen D.; Hamilton, M. Guyene
1996-09-01
Ultraviolet (UV) thickness measurement equipment has little room for variation when determining ultra thin films which are 70 angstroms or less. High lamp performance is critical for measurement validity. A quality conscious semiconductor must have data to verify a vendor claim of 'The lamp performance will perform with no degradation for up to (xxx) hours of normal operation.' In this article we review a real case where data was collected and examined to answer important questions about lamp performance in UV measurement equipment. How long could a lamp be used before performance degraded enough to necessitate a lamp replacement? This article will illustrate how we used standards and actual measurements to collect data for this study. Plots are included showing actual collected data followed by a discussion of alternative methods for statistical examination of the data. This discussion will include an illustration of an original and useful statistical approach for determining the point in time when degradation is noticeable. The method for examining data begins with a well known but not too frequency used concept known as piecewise linear regression with a fixed point of join. Then we enhance the method by turning the join point into a variable that is 'floated' using an iterative non-linear regression approach.
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
NASA Astrophysics Data System (ADS)
Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto
2016-05-01
This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
Weak-noise limit of a piecewise-smooth stochastic differential equation.
Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram
2013-11-01
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.
Jithinraj, P K; Roy, Ushasi; Gopalakrishnan, Manoj
2014-03-07
Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a 'critical point' for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.
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
Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo
2015-08-05
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.
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.
Periodic plasmonic nanoantennas in a piecewise homogeneous background.
Mousavi, Saba Siadat; Berini, Pierre; McNamara, Derek
2012-07-30
Periodic rectangular gold nanomonopoles and nanodipoles in a piecewise inhomogeneous background, consisting of a silicon substrate and a dielectric (aqueous) cover, have been investigated extensively via 3D finite-difference time-domain simulations. The transmittance, reflectance and absorptance response of the nanoantennas were studied as a function of their geometry (length, width, thickness, gap) and found to vary very strongly. The nanoantennas were found to resonate in a single surface plasmon mode supported by the corresponding rectangular cross-section nanowire waveguide, identified as the sa(b)(0) mode [Phys. Rev. B 63, 125417 (2001)]. We determine the propagation characteristics of this mode as a function of nanowire cross-section and wavelength, and we relate the modal results to the performance of the nanoantennas. An approximate expression resting on modal results is proposed for the resonant length of nanomonopoles, and a simple equivalent circuit, also resting on modal results, but involving transmission lines and a capacitor (modelling the gap) is proposed to determine the resonant wavelength of nanodipoles. The expression and the circuit yield results that are in good agreement with the full computations, and thus will prove useful in the design of nanoantennas.
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.
3D linear dispersion relation for arbitrary shear currents
NASA Astrophysics Data System (ADS)
Ellingsen, Simen; Smeltzer, Benjamin
2016-11-01
Dispesion properties of waves can be strongly affected by the presence of a sub-surface shear current. A number of approximation techniques exist to calculate dispersion properties of waves on shear currents, most relying on assumptions such as long wavelength, weak vorticity or near-potentiality. Another approach has been to approximate the shear current by a piecewise linear function, corresponding to dividing the fluid phase into a sequence of layers with constant vorticity in each layer. We discuss the practical implementation of this scheme in 3D for arbitrary wavelengths, and how how it may be applied to 3D linear surface waves problems where the full Fourier spectrum in the horizontal plane is required. Solutions to particular implementation challenges such as optimal choice of layer distribution and the nature and removal of spurious solutions are presented, as are several validation cases and tests of convergence. Applications to ring waves and ship waves are provided as examples. Norwegian Research Council (FRINATEK).
Numerical time-dependent solutions of the Schrödinger equation with piecewise continuous potentials.
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.
Run-Up of Long Waves in Piecewise Sloping U-Shaped Bays
NASA Astrophysics Data System (ADS)
Anderson, Dalton; Harris, Matthew; Hartle, Harrison; Nicolsky, Dmitry; Pelinovsky, Efim; Raz, Amir; Rybkin, Alexei
2017-02-01
We present an analytical study of the propagation and run-up of long waves in piecewise sloping, U-shaped bays using the cross-sectionally averaged shallow water equations. The nonlinear equations are transformed into a linear equation by utilizing the generalized Carrier-Greenspan transform (Rybkin et al. J Fluid Mech 748:416-432, 2014). The solution of the linear wave propagation is taken as the boundary condition at the toe of the last sloping segment, as in Synolakis (J Fluid Mech 185:523-545, 1987). We then consider a piecewise sloping bathymetry, and as in Kanoglu and Synolakis (J Fluid Mech 374:1-28, 1998), find the linear solution in the near shore region, which can be used as the boundary condition for the nonlinear problem. Our primary results are an analytical run-up law for narrow channels and breaking criteria for both monochromatic waves and solitary waves. The derived analytical solutions reduce to well-known solutions for parabolic bays and plane beaches. Our analytical predictions are verified in narrow bays via a comparison to direct numerical simulation of the 2-D shallow water equations.
On uniform approximation of elliptic functions by Padé approximants
NASA Astrophysics Data System (ADS)
Khristoforov, Denis V.
2009-06-01
Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.
A piecewise-focused high DQE detector for MV imaging
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
Specifying Piecewise Latent Trajectory Models for Longitudinal Data
ERIC Educational Resources Information Center
Flora, David B.
2008-01-01
Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when a simple model is needed to describe nonlinear change, or when the purpose of the analysis is to evaluate hypotheses about change occurring during a particular period of time within a model for a longer overall time frame, such as…
Calderón's problem for Lipschitz piecewise smooth conductivities
NASA Astrophysics Data System (ADS)
Eun Kim, Sung
2008-10-01
We consider Lipschitz conductivities which are piecewise smooth across polyhedral boundaries in {\\bb R}^3 . Using complex geometrical optics solutions for Schrödinger operators with certain δ-function potentials, we obtain global uniqueness for Calderón's inverse conductivity problem.
Computation of the anharmonic orbits in two piecewise monotonic maps with a single discontinuity
NASA Astrophysics Data System (ADS)
Li, Yurong; Du, Zhengdong
2017-02-01
In this paper, the bifurcation values for two typical piecewise monotonic maps with a single discontinuity are computed. The variation of the parameter of those maps leads to a sequence of border-collision and period-doubling bifurcations, generating a sequence of anharmonic orbits on the boundary of chaos. The border-collision and period-doubling bifurcation values are computed by the word-lifting technique and the Maple fsolve function or the Newton-Raphson method, respectively. The scaling factors which measure the convergent rates of the bifurcation values and the width of the stable periodic windows, respectively, are investigated. We found that these scaling factors depend on the parameters of the maps, implying that they are not universal. Moreover, if one side of the maps is linear, our numerical results suggest that those quantities converge increasingly. In particular, for the linear-quadratic case, they converge to one of the Feigenbaum constants δ _F= 4.66920160\\cdots.
MAP Estimators for Piecewise Continuous Inversion
2016-08-08
tomography. We take a Bayesian approach, placing a prior distribution on ua and determining the conditional distribution on ua given the data y. It is...with recent work on MAP estimators for linear pro- blems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which...any correspondence should be addressed. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence
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.
Gardini, Laura; Fournier-Prunaret, Danièle; Chargé, Pascal
2011-06-01
In recent years, the study of chaotic and complex phenomena in electronic circuits has been widely developed due to the increasing number of applications. In these studies, associated with the use of chaotic sequences, chaos is required to be robust (not occurring only in a set of zero measure and persistent to perturbations of the system). These properties are not easy to be proved, and numerical simulations are often used. In this work, we consider a simple electronic switching circuit, proposed as chaos generator. The object of our study is to determine the ranges of the parameters at which the dynamics are chaotic, rigorously proving that chaos is robust. This is obtained showing that the model can be studied via a two-dimensional piecewise smooth map in triangular form and associated with a one-dimensional piecewise linear map. The bifurcations in the parameter space are determined analytically. These are the border collision bifurcation curves, the degenerate flip bifurcations, which only are allowed to occur to destabilize the stable cycles, and the homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in 1-piece.
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.
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.
Hergt, Steven; Shah, Abhay; Schäfer, Gerhard
2013-07-12
The orbital motion is derived for a nonspinning test mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods.
Ii, Barry Moore; Autschbach, Jochen
2013-11-12
The lowest-energy/longest-wavelength electronic singlet excitation energies of linear cyanine dyes are examined, using time-dependent density functional theory (TDDFT) and selected wave function methods in comparison with literature data. Variations of the bond-length alternation obtained with different optimized structures produce small differences of the excitation energy in the limit of an infinite chain. Hybrid functionals with range-separated exchange are optimally 'tuned', which is shown to minimize the delocalization error (DE) in the cyanine π systems. Much unlike the case of charge-transfer excitations, small DEs are not strongly correlated with better performance. A representative cyanine is analyzed in detail. Compared with accurate benchmark data, TDDFT with 'pure' local functionals gives too high singlet excitation energies for all systems, but DFT-based ΔSCF calculations with a local functional severely underestimates the energies. TDDFT strongly overestimates the difference between singlet and triplet excitation energies. An analysis points to systematically much too small magnitudes of integrals from the DFT components of the exchange-correlation response kernel as the likely culprit. The findings support previous suggestions that the differential correlation energy between the ground and excited state is not correctly produced by TDDFT with most functionals.
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.
Periodic solutions for nonlinear integro-differential systems with piecewise constant argument.
Chiu, Kuo-Shou
2014-01-01
We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green's function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.
Kumar, R Suresh; Sugumaran, G; Raja, R; Zhu, Quanxin; Raja, U Karthik
2016-02-01
This paper analyzes the global asymptotic stability of a class of neural networks with time delay in the leakage term and time-varying delays under impulsive perturbations. Here the time-varying delays are assumed to be piecewise. In this method, the interval of the variation is divided into two subintervals by its central point. By developing a new Lyapunov-Krasovskii functional and checking its variation in between the two subintervals, respectively, and then we present some sufficient conditions to guarantee the global asymptotic stability of the equilibrium point for the considered neural network. The proposed results which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily verified via the linear matrix inequality (LMI) control toolbox in MATLAB. Finally, a numerical example and its simulation are given to show the conditions obtained are new and less conservative than some existing ones in the literature.
Optimal approximation method to characterize the resource trade-off functions for media servers
NASA Astrophysics Data System (ADS)
Chang, Ray-I.
1999-08-01
We have proposed an algorithm to smooth the transmission of the pre-recorded VBR media stream. It takes O(n) time complexity, where n is large, this algorithm is not suitable for online resource management and admission control in media servers. To resolve this drawback, we have explored the optimal tradeoff among resources by an O(nlogn) algorithm. Based on the pre-computed resource tradeoff function, the resource management and admission control procedure is as simple as table hashing. However, this approach requires O(n) space to store and maintain the resource tradeoff function. In this paper, while giving some extra resources, a linear-time algorithm is proposed to approximate the resource tradeoff function by piecewise line segments. We can prove that the number of line segments in the obtained approximation function is minimized for the given extra resources. The proposed algorithm has been applied to approximate the bandwidth-buffer-tradeoff function of the real-world Star War movie. While an extra 0.1 Mbps bandwidth is given, the storage space required for the approximation function is over 2000 times smaller than that required for the original function. While an extra 10 KB buffer is given, the storage space for the approximation function is over 2200 over times smaller than that required for the original function. The proposed algorithm is really useful for resource management and admission control in real-world media servers.
Isegawa, Miho; Truhlar, Donald G
2013-04-07
Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel
NASA Astrophysics Data System (ADS)
Isegawa, Miho; Truhlar, Donald G.
2013-04-01
Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel
NASA Astrophysics Data System (ADS)
Truong, Tri Quoc; Tsubone, Tadashi; Sekikawa, Munehisa; Inaba, Naohiko
2017-02-01
We analyze the complex quasiperiodic oscillations and chaos generated by two coupled piecewise-constant hysteresis oscillators driven by a rectangular wave force. Oscillations generate Arnol'd resonance webs wherein lower dimensional resonance tongues extend such as that of a web in numerous directions. We provide the fundamental tools for bifurcation analysis of nonautonomous piecewise-constant oscillators. To optimize the outstanding simplicity of piecewise-constant circuits, we formulate a generalized procedure for calculating the Lyapunov exponents in nonautonomous piecewise-constant dynamics. The Lyapunov exponents in these dynamics can be calculated with a precision approximately similar to that of maps. We observe two-parameter Lyapunov diagrams near the fundamental resonance region called Chenciner bubbles, wherein the oscillation frequencies of the two oscillators and the force are synchronized with a ratio of 1:1:1. Inevitably, the hysteresis considerably distorts the Chenciner bubbles. This result suggests that the Chenciner bubbles do not necessarily occur due to simple phase-locking of two-dimensional tori that can be explained by homeomorphism on the circle. Furthermore, we observe the Farey sequence in the experimental measurements.
An algorithm for the numerical solution of linear differential games
Polovinkin, E S; Ivanov, G E; Balashov, M V; Konstantinov, R V; Khorev, A V
2001-10-31
A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented and estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Ultrasonic linear measurement system
NASA Technical Reports Server (NTRS)
Marshall, Scot H. (Inventor)
1991-01-01
An ultrasonic linear measurement system uses the travel time of surface waves along the perimeter of a three-dimensional curvilinear body to determine the perimeter of the curvilinear body. The system can also be used piece-wise to measure distances along plane surfaces. The system can be used to measure perimeters where use of laser light, optical means or steel tape would be extremely difficult, time consuming or impossible. It can also be used to determine discontinuities in surfaces of known perimeter or dimension.
Approximate Linear Regulator and Kalman Filter
1980-09-01
of Equivalent Dominant Poles and Zeros Using Industrial Specifications," IEEE Trans. on Industrial Electronics and Control Instrumentation, Vol. IECI...true. In recent years, the rapid development of powerful minicomputers and microprocessors makes the industrial applications of optimal control...1976, pp. 677-687. [21] Y. Takahashi, M. Tomizuka and D. I. Auslander, Simple discrete control of industrial processes, Trans. on ASME J. of Dynamic
Combining global and local approximations
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.
1991-01-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.
Combining global and local approximations
Haftka, R.T. )
1991-09-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 6 refs.
Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.
1997-01-01
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
NASA Astrophysics Data System (ADS)
Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
2009-10-01
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states ( x, σ)∈Ω×Γ, Ω being a region in ℝ d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3-4):635-675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti-Cohen-type symmetry relation with involution map different from time-reversal.
High resolution A/D conversion based on piecewise conversion at lower resolution
Terwilliger, Steve [Albuquerque, NM
2012-06-05
Piecewise conversion of an analog input signal is performed utilizing a plurality of relatively lower bit resolution A/D conversions. The results of this piecewise conversion are interpreted to achieve a relatively higher bit resolution A/D conversion without sampling frequency penalty.
Fast wavelet based sparse approximate inverse preconditioner
Wan, W.L.
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Regularization of hidden dynamics in piecewise smooth flows
NASA Astrophysics Data System (ADS)
Novaes, Douglas D.; Jeffrey, Mike R.
2015-11-01
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo switches at thresholds in phase space. The canonical convex combination at the discontinuity is only the linear part of a nonlinear combination that more fully explores Filippov's most general problem: the differential inclusion. Here we show how recent work relating discontinuous systems to singular limits of continuous (or regularized) systems extends to nonlinear combinations. We show that if sliding occurs in a discontinuous systems, there exists a differentiable slow-fast system with equivalent slow invariant dynamics. We also show the corresponding result for the pinching method, a converse to regularization which approximates a smooth system by a discontinuous one.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Duality in parameter space and approximation of measures for mixing repellers
NASA Astrophysics Data System (ADS)
Abenda, S.; Turchetti, G.
1990-10-01
For one-dimensional expanding maps T with an invariant measure μ we consider, in a parameter space, the envelope ℰ n of the real lines associated to any couple of points of the orbit, connected by n iterations of T. If the map has s inverses and is piecewise linear, then the sets ℰ n are just the union of s n points and converge to the invariant Cantor set of T. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on ℰ1 to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and has s inverses, the sets ℰ n are homeomorphic to the Cantor set; they converge to the Cantor set of T and their measures converge to the measure of the Cantor set when n→∞. The correspondence between the sets ℰ n allows one to define converging approximation schemes for the map an its measure: one replaces each of the s n disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set ℰ1. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined.
NASA Astrophysics Data System (ADS)
Stenroos, Matti
2016-11-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
Stenroos, Matti
2016-11-21
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
Circular piecewise regression with applications to cell-cycle data.
Rueda, Cristina; Fernández, Miguel A; Barragán, Sandra; Mardia, Kanti V; Peddada, Shyamal D
2016-12-01
Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell-cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology.
Autocalibrating Tiled Projectors on Piecewise Smooth Vertically Extruded Surfaces.
Sajadi, Behzad; Majumder, Aditi
2011-09-01
In this paper, we present a novel technique to calibrate multiple casually aligned projectors on fiducial-free piecewise smooth vertically extruded surfaces using a single camera. Such surfaces include cylindrical displays and CAVEs, common in immersive virtual reality systems. We impose two priors to the display surface. We assume the surface is a piecewise smooth vertically extruded surface for which the aspect ratio of the rectangle formed by the four corners of the surface is known and the boundary is visible and segmentable. Using these priors, we can estimate the display's 3D geometry and camera extrinsic parameters using a nonlinear optimization technique from a single image without any explicit display to camera correspondences. Using the estimated camera and display properties, the intrinsic and extrinsic parameters of each projector are recovered using a single projected pattern seen by the camera. This in turn is used to register the images on the display from any arbitrary viewpoint making it appropriate for virtual reality systems. The fast convergence and robustness of this method is achieved via a novel dimension reduction technique for camera parameter estimation and a novel deterministic technique for projector property estimation. This simplicity, efficiency, and robustness of our method enable several coveted features for nonplanar projection-based displays. First, it allows fast recalibration in the face of projector, display or camera movements and even change in display shape. Second, this opens up, for the first time, the possibility of allowing multiple projectors to overlap on the corners of the CAVE-a popular immersive VR display system. Finally, this opens up the possibility of easily deploying multiprojector displays on aesthetic novel shapes for edutainment and digital signage applications.
Piecewise Mapping in HEVC Lossless Intra-prediction Coding.
Sanchez, Victor; Auli-Llinas, Francesc; Serra-Sagrista, Joan
2016-05-19
The lossless intra-prediction coding modality of the High Efficiency Video Coding (HEVC) standard provides high coding performance while allowing frame-by-frame basis access to the coded data. This is of interest in many professional applications such as medical imaging, automotive vision and digital preservation in libraries and archives. Various improvements to lossless intra-prediction coding have been proposed recently, most of them based on sample-wise prediction using Differential Pulse Code Modulation (DPCM). Other recent proposals aim at further reducing the energy of intra-predicted residual blocks. However, the energy reduction achieved is frequently minimal due to the difficulty of correctly predicting the sign and magnitude of residual values. In this paper, we pursue a novel approach to this energy-reduction problem using piecewise mapping (pwm) functions. Specifically, we analyze the range of values in residual blocks and apply accordingly a pwm function to map specific residual values to unique lower values. We encode appropriate parameters associated with the pwm functions at the encoder, so that the corresponding inverse pwm functions at the decoder can map values back to the same residual values. These residual values are then used to reconstruct the original signal. This mapping is, therefore, reversible and introduces no losses. We evaluate the pwm functions on 4×4 residual blocks computed after DPCM-based prediction for lossless coding of a variety of camera-captured and screen content sequences. Evaluation results show that the pwm functions can attain maximum bit-rate reductions of 5.54% and 28.33% for screen content material compared to DPCM-based and block-wise intra-prediction, respectively. Compared to Intra- Block Copy, piecewise mapping can attain maximum bit-rate reductions of 11.48% for camera-captured material.
Boys, Craig A.; Robinson, Wayne; Miller, Brett; Pflugrath, Brett D.; Baumgartner, Lee J.; Navarro, Anna; Brown, Richard S.; Deng, Zhiqun
2016-05-13
Barotrauma injury can occur when fish are exposed to rapid decompression during downstream passage through river infrastructure. A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species (Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus) following simulated infrastructure passage in barometric chambers. The probability of injuries such as swim bladder rupture; exophthalmia; and haemorrhage and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change RPCE/A) fell. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in RPCE/A that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multi-species precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (RPCE/A of 0.7) should sufficiently protect downstream migrating juveniles of these two physoclistous species. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones.
Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu
2015-12-11
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Boys, C A; Robinson, W; Miller, B; Pflugrath, B; Baumgartner, L J; Navarro, A; Brown, R; Deng, Z
2016-05-01
A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species, Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus, following simulated infrastructure passage in a barometric chamber. The probability of injuries such as swimbladder rupture, exophthalmia and haemorrhage, and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change, R(NE:A) ) reduced. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in R(NE:A) that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multispecies precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (R(NE:A) of 0·7) should protect downstream migrating juveniles of these two physoclistous species sufficiently. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones.
Duan, Junbo; Soussen, Charles; Brie, David; Idier, Jerome; Wang, Yu-Ping; Wan, Mingxi
2015-01-01
To analyze the next generation sequencing data, the so-called read depth signal is often segmented with standard segmentation tools. However, these tools usually assume the signal to be a piecewise constant signal and contaminated with zero mean Gaussian noise, and therefore modeling error occurs. This paper models the read depth signal with piecewise Poisson distribution, which is more appropriate to the next generation sequencing mechanism. Based on the proposed model, an opti- mal dynamic programming algorithm with parallel computing is proposed to segment the piecewise signal, and furthermore detect the copy number variation.
Regularization and Approximation of a Class of Evolution Problems in Applied Mathematics
1991-01-01
32, 663,(1978). -12. P. Lesaint and M. Zlmal, "Superconvergence of the gradient of finite element solutions, ’ RAIRO :-Anal., _13, 139-(1979). :13...problems," - RAIRO -Anal:, 2, 47 (1974). 1. -M.F. Wheeler and J. Whiteman, "Superconvergent recovery of- gradients on subdomains from -piecewise linear
Energy Balance for Random Vibrations of Piecewise-Conservative Systems
NASA Astrophysics Data System (ADS)
IOURTCHENKO, D. V.; DIMENTBERG, M. F.
2001-12-01
Vibrations of systems with instantaneous or stepwise energy losses, e.g., due to impacts with imperfect rebounds, dry friction forces(s) (in which case the losses may be treated as instantaneous ones by appropriate introduction of the response energy) and/or active feedback “bang-bang” control of the systems' response are considered. Response of such (non-linear) systems to a white-noise random excitation is considered for the case where there are no other response energy losses. Thus, a simple linear energy growth with time between “jumps” is observed. Explicit expressions for the expected response energy are derived by direct application of the stochastic differential equations calculus, which contains the expected time interval between two consecutive jumps. The latter may be predicted as a solution to the relevant first-passage problem. Perturbational analysis of the relevant PDE for this problem for a certain vibroimpact system demonstrated the possibility for using the solution to the corresponding free vibration problem as a zero order approximation. The method is applied to an s.d.o.f. system with a feedback inertia control, designed according to a certain previously introduced “generalized reversed swings law”. Extensive Monte-Carlo simulation results are presented for this system as well as for several previously analyzed ones: system with impacts; system with dry friction; system with stiffness control; pendulum with controlled length. The results are compared with those due to the asymptotic stochastic averaging approach. Both methods are shown to provide adequate accuracy far beyond the expected applicability range of the asymptotic approach (which requires both excitation intensity and losses to be small), with direct energy balance being generally superior.
Little, Max A.; Jones, Nick S.
2011-01-01
Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play. PMID:22003312
Little, Max A; Jones, Nick S
2011-11-08
Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.
2010-06-15
of-the-art inpainting [31]. Portilla et al. have shown image denoising impressive results June 15, 2010 DRAFT 2 by assuming Gaussian scale mixture...beta and Dirichlet processes, which leads to excellent results in denoising and inpainting [71]. The now popular sparse signal models, on the other...b) (c) (d) Fig. 2. (a) Some typical dictionary atoms learned from the image Lena (Figure 3-(a)) with K- SVD [2]. (b)-(d) A numerical procedure to
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
NASA Technical Reports Server (NTRS)
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
Hirata, Yoshito; Aihara, Kazuyuki
2012-06-01
We introduce a low-dimensional description for a high-dimensional system, which is a piecewise affine model whose state space is divided by permutations. We show that the proposed model tends to predict wind speeds and photovoltaic outputs for the time scales from seconds to 100 s better than by global affine models. In addition, computations using the piecewise affine model are much faster than those of usual nonlinear models such as radial basis function models.
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
NASA Astrophysics Data System (ADS)
Yang, Jihua; Zhao, Liqin
This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.
On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center
NASA Astrophysics Data System (ADS)
Li, Shimin; Wu, Kuilin
2016-06-01
In this paper, a class of piecewise smooth quasi-homogeneous differential systems are considered. Using the first order Melnikov function derived in [Liu & Han, 2010], we obtain a lower bound of the maximum number of limit cycles which bifurcate from the periodic annulus of the center under polynomial perturbation. The results reveal that piecewise smooth quasi-homogeneous differential systems can bifurcate more limit cycles than the smooth systems.
NASA Technical Reports Server (NTRS)
Hyer, M. W.; Cooper, D. E.; Cohen, D.
1985-01-01
The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less
An approximation technique for jet impingement flow
Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H.
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
NASA Technical Reports Server (NTRS)
Gottlieb, David; Shu, Chi-Wang
1993-01-01
The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment
Straten, Marcel van; Venema, Henk W.; Streekstra, Geert J.; Majoie, Charles B.L.M.; Heeten, Gerard J. den; Grimbergen, Cornelis A.
2004-10-01
In maximum intensity projection (MIP) images of CT angiography (CTA) scans, the arteries are often obscured by bone. A bone removal method is presented that uses an additional, nonenhanced scan to create a mask of the bone by thresholding and dilation. After registration of the CTA scan and the additional scan, the bone in the CTA scan is masked. As the cervical area contains bones that can move with respect to each other, these bones are separated first using a watershed algorithm, and then registered individually. A phantom study was performed to evaluate and quantify the tradeoff between the removal of the bone and the preservation of the arteries contiguous to the bone. The influence of algorithm parameters and scan parameters was studied. The method was clinically evaluated with data sets of 35 patients. Best results were obtained with a threshold of 150 HU and a dilation of 8 in-plane voxels and two out-of-plane voxels. The mean width of the soft tissue layer, which is also masked, was approximately 1 mm. The mAs value of the nonenhanced scan could be reduced from 250 mAs to 65 mAs without a loss of quality. In 32 cases the bones were registered correctly and removed completely. In three cases the bone separation was not completely successful, and consequently the bone was not completely removed. The piecewise matched mask bone elimination method proved to be able to obtain MIP images of the cervical arteries free from overprojecting bone in a fully automatic way and with only a slight increase of radiation dose.
2001-09-01
light weight low recoil machine gun developed by Samuel Neal McClean with later improvement by Colonel USA Issac In reality air combat is far from...Forecast International Radar Forecast Forecast International Newton Conn Fowler Bruce W De Physica Belli An Introduction to
Approximating subtree distances between phylogenies.
Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina
2006-10-01
We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results.
Piecewise Adiabatic Population Transfer in a Molecule via a Wave Packet
Shapiro, Evgeny A.; Peer, Avi; Ye Jun; Shapiro, Moshe
2008-07-11
We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses, thus forming a generalized adiabatic passage via a wave packet. We study piecewise stimulated Raman adiabatic passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possible.
Calculation of the biological effective dose for piecewise defined dose-rate fits
Hobbs, Robert F.; Sgouros, George
2009-03-15
An algorithmic solution to the biological effective dose (BED) calculation from the Lea-Catcheside formula for a piecewise defined function is presented. Data from patients treated for metastatic thyroid cancer were used to illustrate the solution. The Lea-Catcheside formula for the G-factor of the BED is integrated numerically using a large number of small trapezoidal fits to each integral. The algorithmically calculated BED is compatible with an analytic calculation for a similarly valued exponentially fitted dose-rate plot and is the only resolution for piecewise defined dose-rate functions.
Global behaviour of a predator-prey like model with piecewise constant arguments.
Kartal, Senol; Gurcan, Fuat
2015-01-01
The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.
NASA Astrophysics Data System (ADS)
Latchman, J. L.; Morgan, F. D. O.; Aspinall, W. P.
2008-03-01
It is generally found that the relative frequencies of occurrence of earthquakes of different magnitudes in seismogenic zones have a power law distribution. For a long-term dataset, the overall slope of this logarithmically transformed distribution is usually indicated by a best-fit straight line and expressed as a b-value. This slope is stable and normally lies between 0.8 and 1.2, the actual value depending on the region examined, and the threshold selected for data completeness. The linearity of the distribution can be used to make statistical inferences about the potential for larger events over the long run, and with appropriate reservations, may even be extrapolated to magnitudes that are beyond recent experience. We suggest the same information can also be viewed over shorter intervals in terms of an empirical piecewise distribution, with relative frequencies of occurrence at adjacent magnitude steps controlling the local slope of the distribution. An emergence, through time, of an excess number of lower magnitude earthquakes causes temporal changes to appear in the low-end piecewise gradients of this distribution. A marked excursion away from an overall uniform trend for the particular zone may be indicative of an imminent, larger event. On two separate occasions, in 1982 and 1997, such temporal variations were seen in the magnitude distributions of sequences of events near Tobago, West Indies, and used to anticipate subsequent damaging mainshocks. The recognition of temporal departures from overall linearity of the magnitude-frequency relation, in a suitable dataset, may thus provide an evidential element that can contribute to earthquake forecasting. This phenomenological approach was used in the analysis of the NEIC global dataset of earthquakes of magnitude 6.1 and bigger, for the period 1973-2003, to explore its wider applicability. Trends in the piecewise gradients of the global data were interpreted as pointing to an imminent great earthquake
Romeijn, H Edwin; Ahuja, Ravindra K; Dempsey, James F; Kumar, Arvind; Li, Jonathan G
2003-11-07
We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.
Solving Sturm-Liouville problems by piecewise perturbation methods, revisited
NASA Astrophysics Data System (ADS)
Ledoux, V.; Van Daele, M.
2010-08-01
We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the original CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability of the CPM to a wider variety of problems and allows a more efficient solution of many problems. The CPMs are closely related to the second-order coefficient approximation method underlying the SLEDGE software package, but provide for higher order approximations. These higher order approximations can also be obtained by applying a modified Neumann method. The CPM approach, however, leads to simpler formulae in a more convenient form.
ERIC Educational Resources Information Center
Jaggars, Shanna Smith; Xu, Di
2016-01-01
Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this article we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from two popular econometric approaches:…
What Can Tobit-Piecewise Regression Tell Us about the Determinants of Household Educational Debt?
ERIC Educational Resources Information Center
Thipbharos, Titirut
2014-01-01
Educational debt as part of household debt remains a problem for Thailand. The significant factors of household characteristics with regard to educational debt are shown by constructing a Tobit-piecewise regression for three different clusters, namely poor, middle and affluent households in Thailand. It was found that household debt is likely to…
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
NASA Astrophysics Data System (ADS)
Lau, Chun Sing
This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in
Binary Classifier Calibration Using an Ensemble of Linear Trend Estimation
Naeini, Mahdi Pakdaman; Cooper, Gregory F.
2017-01-01
Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called ensemble of linear trend estimation (ELiTE). ELiTE utilizes the recently proposed ℓ1 trend ltering signal approximation method [22] to find the mapping from uncalibrated classification scores to the calibrated probability estimates. ELiTE is designed to address the key limitations of the histogram binning-based calibration methods which are (1) the use of a piecewise constant form of the calibration mapping using bins, and (2) the assumption of independence of predicted probabilities for the instances that are located in different bins. The method post-processes the output of a binary classifier to obtain calibrated probabilities. Thus, it can be applied with many existing classification models. We demonstrate the performance of ELiTE on real datasets for commonly used binary classification models. Experimental results show that the method outperforms several common binary-classifier calibration methods. In particular, ELiTE commonly performs statistically significantly better than the other methods, and never worse. Moreover, it is able to improve the calibration power of classifiers, while retaining their discrimination power. The method is also computationally tractable for large scale datasets, as it is practically O(N log N) time, where N is the number of samples. PMID:28357158
Reliable Function Approximation and Estimation
2016-08-16
Journal on Mathematical Analysis 47 (6), 2015. 4606-4629. (P3) The Sample Complexity of Weighted Sparse Approximation. B. Bah and R. Ward. IEEE...solving systems of quadratic equations. S. Sanghavi, C. White, and R. Ward. Results in Mathematics , 2016. (O5) Relax, no need to round: Integrality of...Theoretical Computer Science. (O6) A unified framework for linear dimensionality reduction in L1. F Krahmer and R Ward. Results in Mathematics , 2014. 1-23
More accurate Talairach coordinates for neuroimaging using non-linear registration.
Lacadie, Cheryl M; Fulbright, Robert K; Rajeevan, Nallakkandi; Constable, R Todd; Papademetris, Xenophon
2008-08-15
While the Talairach atlas remains the most commonly used system for reporting coordinates in neuroimaging studies, the absence of an actual 3-D image of the original brain used in its construction has severely limited the ability of researchers to automatically map locations from 3-D anatomical MRI images to the atlas. Previous work in this area attempted to circumvent this problem by constructing approximate linear and piecewise-linear mappings between standard brain templates (e.g. the MNI template) and Talairach space. These methods are limited in that they can only account for differences in overall brain size and orientation but cannot correct for the actual shape differences between the MNI template and the Talairach brain. In this paper we describe our work to digitize the Talairach atlas and generate a non-linear mapping between the Talairach atlas and the MNI template that attempts to compensate for the actual differences in shape between the two, resulting in more accurate coordinate transformations. We present examples in this paper and note that the method is available freely online as a Java applet.
NASA Astrophysics Data System (ADS)
Guo, Yongfeng; Shen, Yajun; Tan, Jianguo
2016-09-01
The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On piecewise interpolation techniques for estimating solar radiation missing values in Kedah
Saaban, Azizan; Zainudin, Lutfi; Bakar, Mohd Nazari Abu
2014-12-04
This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Error (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.
Low-complexity piecewise-affine virtual sensors: theory and design
NASA Astrophysics Data System (ADS)
Rubagotti, Matteo; Poggi, Tomaso; Oliveri, Alberto; Pascucci, Carlo Alberto; Bemporad, Alberto; Storace, Marco
2014-03-01
This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estimation of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical model. The proposed approach allows one to design estimators which mitigate the effect of the so-called 'curse of dimensionality' of simplicial piecewise-affine functions, and can be therefore applied to relatively high-order systems, enjoying convergence and optimality properties. An automatic toolchain is also presented to generate the VHDL code describing the digital circuit implementing the virtual sensor, starting from the set of measured input and output data. The proposed methodology is applied to generate an FPGA implementation of the virtual sensor for the estimation of vehicle lateral velocity, using a hardware-in-the-loop setting.
NASA Astrophysics Data System (ADS)
Akhmet, M. U.
2007-12-01
In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297-1324 (in Russian); V.A. Pliss, Integral Sets of Periodic Systems of Differential Equations, Nauka, Moskow, 1977 (in Russian)] is proved for EPCAG. The structure of the set of solutions is specified. We establish also the existence of global integral manifolds of quasilinear EPCAG in the so-called critical case and investigate the stability of the zero solution.
NASA Astrophysics Data System (ADS)
Su, Yan; Jun, Xie Cheng
2006-08-01
An algorithm of combining LZC and arithmetic coding algorithm for image compression is presented and both theory deduction and simulation result prove the correctness and feasibility of the algorithm. According to the characteristic of context-based adaptive binary arithmetic coding and entropy, LZC was modified to cooperate the optimized piecewise arithmetic coding, this algorithm improved the compression ratio without any additional time consumption compared to traditional method.
A piecewise modeling approach for climate sensitivity studies: Tests with a shallow-water model
NASA Astrophysics Data System (ADS)
Shao, Aimei; Qiu, Chongjian; Niu, Guo-Yue
2015-10-01
In model-based climate sensitivity studies, model errors may grow during continuous long-term integrations in both the "reference" and "perturbed" states and hence the climate sensitivity (defined as the difference between the two states). To reduce the errors, we propose a piecewise modeling approach that splits the continuous long-term simulation into subintervals of sequential short-term simulations, and updates the modeled states through re-initialization at the end of each subinterval. In the re-initialization processes, this approach updates the reference state with analysis data and updates the perturbed states with the sum of analysis data and the difference between the perturbed and the reference states, thereby improving the credibility of the modeled climate sensitivity. We conducted a series of experiments with a shallow-water model to evaluate the advantages of the piecewise approach over the conventional continuous modeling approach. We then investigated the impacts of analysis data error and subinterval length used in the piecewise approach on the simulations of the reference and perturbed states as well as the resulting climate sensitivity. The experiments show that the piecewise approach reduces the errors produced by the conventional continuous modeling approach, more effectively when the analysis data error becomes smaller and the subinterval length is shorter. In addition, we employed a nudging assimilation technique to solve possible spin-up problems caused by re-initializations by using analysis data that contain inconsistent errors between mass and velocity. The nudging technique can effectively diminish the spin-up problem, resulting in a higher modeling skill.
NASA Technical Reports Server (NTRS)
2006-01-01
[figure removed for brevity, see original site] Context image for PIA03667 Linear Clouds
These clouds are located near the edge of the south polar region. The cloud tops are the puffy white features in the bottom half of the image.
Image information: VIS instrument. Latitude -80.1N, Longitude 52.1E. 17 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
NASA Astrophysics Data System (ADS)
Davies, David L.; Smith, Peter H.; Liutermoza, John F.
1980-06-01
Profile analysis and piecewise correlation techniques for measuring internal machine part clearances by digital processing of industrial radiographs are described in this paper. These methods were developed at the Image and Pattern Analysis Laboratory of Pratt & Whitney Aircraft Group. Profile analysis requires mathematical modeling of the expected optical density of a radiograph as a function of machine part position. Part separations are estimated on the basis of individual image scan lines. A final part separation estimate is produced by fitting a polynominal to the individual estimates and correcting for imaging and processing degradations which are simulated using a mathematical model. Piecewise correlation involves an application of image registration where radiographs are correlated in a piecewise fashion to allow inference of the relative motion of machine parts in a time varying series of images. Each image is divided into segments which are dominated by a small number of features. Segments from one image are cross-correlated with subsequent images to identify machine part motion in image space. Correlation peak magnitude is used in assessing the confidence that a particular motion has occurred between images. The rigid feature motion of machine parts requires image registration by discon-tinuous parts. This method differs from the continuous deformations one encounters in perspective projective transformations characteristic of remote sensing applications.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
NASA Technical Reports Server (NTRS)
Gottlieb, David; Shu, Chi-Wang
1994-01-01
We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.
Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao; and others
2015-04-01
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-10-01
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
Approximate transferability in conjugated polyalkenes
NASA Astrophysics Data System (ADS)
Eskandari, Keiamars; Mandado, Marcos; Mosquera, Ricardo A.
2007-03-01
QTAIM computed atomic and bond properties, as well as delocalization indices (obtained from electron densities computed at HF, MP2 and B3LYP levels) of several linear and branched conjugated polyalkenes and O- and N-containing conjugated polyenes have been employed to assess approximate transferable CH groups. The values of these properties indicate the effects of the functional group extend to four CH groups, whereas those of the terminal carbon affect up to three carbons. Ternary carbons also modify significantly the properties of atoms in α, β and γ.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
Intrinsic Nilpotent Approximation.
1985-06-01
RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E T*M/O. It
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
ON THE PIECEWISE PARABOLIC METHOD FOR COMPRESSIBLE FLOW WITH STELLAR EQUATIONS OF STATE
Zingale, Michael; Katz, Max P.
2015-02-01
The piecewise parabolic method and related schemes are widely used to model stellar flows. Several different methods for extending the validity of these methods to a general equation of state (EOS) have been proposed over time, but direct comparisons among one-another and exact solutions with stellar EOSs are not widely available. We introduce some simple test problems with exact solutions run with a popular stellar EOS and test how two existing codes with different approaches to incorporating general gases perform. The source code for generating the exact solutions is made available.
Steering by transient destabilization in piecewise-holonomic models of legged locomotion
NASA Astrophysics Data System (ADS)
Proctor, J.; Holmes, P.
2008-08-01
We study turning strategies in low-dimensional models of legged locomotion in the horizontal plane. Since the constraints due to foot placement switch from stride to stride, these models are piecewise-holonomic, and this can cause stride-to-stride changes in angular momentum and in the ratio of rotational to translational kinetic energy. Using phase plane analyses and parameter studies based on experimental observations of insects, we investigate how these changes can be harnessed to produce rapid turns, and compare the results with dynamical cockroach data. Qualitative similarities between the model and insect data suggest general strategies that could be implemented in legged robots.
NASA Astrophysics Data System (ADS)
Ricca, Giorgio; Beltrametti, Mauro C.; Massone, Anna Maria
2015-03-01
Many bone shapes in the human skeleton are characterized by profiles that can be associated to equations of algebraic curves. Fixing the parameters in the curve equation, by means of a classical pattern recognition procedure like the Hough transform technique, it is then possible to associate an equation to a specific bone profile. However, most skeleton districts are more accurately described by piecewise defined curves. This paper utilizes an iterative approach of the Hough transform without re-voting, to provide an efficient procedure for describing the profile of a bone in the human skeleton as a collection of different but continuously attached curves.
Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps
NASA Astrophysics Data System (ADS)
Contreras, Fabián; Dolgopyat, Dmitry
2016-09-01
Let f:[0,1]\\to [0,1] be a piecewise expanding unimodal map of class C k+1, with k≥slant 1 , and μ =ρ \\text{d}x the (unique) SRB measure associated to it. We study the regularity of ρ. In particular, points N where ρ is not differentiable has zero Hausdorff dimension, but is uncountable if the critical orbit of f is dense. This improves on a work of Szewc (1984). We also obtain results about higher orders of differentiability of ρ in the sense of Whitney.
Quadtree structured image approximation for denoising and interpolation.
Scholefield, Adam; Dragotti, Pier Luigi
2014-03-01
The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Shukla proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewise polynomial images. In this paper, we adapt this model to the image restoration by changing the rate-distortion penalty to a description-length penalty. In addition, one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree. We address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations. Algorithms are developed to tackle denoising and interpolation. Simulation results indicate that we beat state of the art results when the original signal is in the model (e.g., depth images) and are competitive for natural images when the degradation is high.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
1990-11-19
Cependant, ses r~sultats peuvent 6tre tr~s mauvais. Danis [331, on trouve des exemples ofi le filtre de Kalman e’tendu est ineficace. Dans Ie domaine thi...8217= et TTest d6finie positive. On pose SI =1 = C(lR+;IW) . Soit 11 = f~l X 112 d�ment g~n~rique W = (IW2,F sa tribu bor~Iienne, F = Fr ® F2 , {(XI...nous mon- trons que sous la loi P+, les tribus ),, et u(Alh V ya sont conditionnellernent ind~pendantes sachant o’(M0+) pour t > a. On rappelle que 1
1987-12-01
p.~.,.-****.*. * ** *.ft. -p.-.’.’ ’-% NRI I.. 54 "., 54. -~~~~~~~~.J7r d.2W. .r’ 4. F_ V77 J’, ~~ .2.2PV’.~~~-J *-Jy a, ’., %,50 pil...34" ’*1:’ Z ando: \\,la wlo wl ca co ci c! na no Irans wlo wil wit co cl cg c* no ni soLrc vI v010 tr tl If For example. MODEL nd2 NAND ( 1 0.2 1Of 1Of
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
The stiffness variation of a micro-ring driven by a traveling piecewise-electrode.
Li, Yingjie; Yu, Tao; Hu, Yuh-Chung
2014-09-16
In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.
GRMHD Simulations of Binary Neutron Star Mergers with Piecewise Polytropic Equations of State
NASA Astrophysics Data System (ADS)
Giacomazzo, Bruno
2015-04-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. Our new simulations consider both equal and unequal-mass systems and describe the NS matter via piecewise polytropic equations of state (EOSs). BNS mergers are powerful sources of gravitational waves (GWs) that can be detected by ground based detectors, such as advanced Virgo and LIGO, and they are also thought to be behind the central engine powering short gamma-ray bursts. In our simulations we therefore focus both on the GW emission and on the dynamics of matter and magnetic fields, both in the case a black hole is promptly formed and in the case of the formation of a long-lived magnetized NS. Since the EOS has an important role in both GW emission and matter dynamics, our simulations employ piecewise polytropic EOSs composed by seven pieces, four for the low-density regions (including the crust) and three for the core, in order to more accurately match physically motivated EOSs. Thermal effects are also included in order to more properly describe the post-merger dynamics.
Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application
NASA Astrophysics Data System (ADS)
Li, Shuangbao; Ma, Wensai; Zhang, Wei; Hao, Yuxin
In this paper, we extend the well-known Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth systems, defined in three domains separated by two switching manifolds x = a and x = b. The dynamics in each domain is governed by a smooth system. When an orbit reaches the separation lines, then a reset map describing an impacting rule applies instantaneously before the orbit enters into another domain. We assume that the unperturbed system has a continuum of periodic orbits transversally crossing the separation lines. Then, we wish to study the persistence of the periodic orbits under an autonomous perturbation and the reset map. To achieve this objective, we first choose four appropriate switching sections and build a Poincaré map, after that, we present a displacement function and carry on the Taylor expansion of the displacement function to the first-order in the perturbation parameter ɛ near ɛ = 0. We denote the first coefficient in the expansion as the first-order Melnikov function whose zeros provide us the persistence of periodic orbits under perturbation. Finally, we study periodic orbits of a concrete planar hybrid piecewise-smooth system by the obtained Melnikov function.
Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings
NASA Technical Reports Server (NTRS)
Olson, Erik D.
2015-01-01
Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.
Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.
Kowalczyk, P; Glendinning, P
2011-06-01
In this paper we study the qualitative dynamics of piecewise-smooth slow-fast systems (singularly perturbed systems) which are everywhere continuous. We consider phase space topology of systems with one-dimensional slow dynamics and one-dimensional fast dynamics. The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across the switching surface. In the full system the slow manifold is no longer continuous, and there is an O(ɛ) discontinuity across the switching manifold, but the discontinuity cannot qualitatively alter system dynamics. Revealed phase space topology is used to unfold qualitative dynamics of planar slow-fast systems with an equilibrium point on the switching surface. In this case the local dynamics corresponds to so-called boundary-equilibrium bifurcations, and four qualitative phase portraits are uncovered. Our results are then used to investigate the dynamics of a box model of a thermohaline circulation, and the presence of a boundary-equilibrium bifurcation of a fold type is shown.
NASA Technical Reports Server (NTRS)
Shen, Ji Yao; Abu-Saba, Elias G.; Mcginley, William M.; Sharpe, Lonnie, Jr.; Taylor, Lawrence W., Jr.
1992-01-01
Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.
NASA Astrophysics Data System (ADS)
Sidorin, Anatoly
2010-01-01
In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Approximations of nonlinear systems having outputs
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1985-01-01
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
Information geometry of mean-field approximation.
Tanaka, T
2000-08-01
I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
Analytical approximations for spiral waves
Löber, Jakob Engel, Harald
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Analytical approximations for spiral waves.
Löber, Jakob; Engel, Harald
2013-12-01
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Approximating a nonlinear MTFDE from physiology
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-12-01
This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.
Sensing Position With Approximately Constant Contact Force
NASA Technical Reports Server (NTRS)
Sturdevant, Jay
1996-01-01
Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Approximation of weak solution for the problem of a pH-gradient creation in isoelectrofocusing.
Sakharova, L V; Shiryaeva, E V; Zhukov, M Yu
2014-11-08
The mathematical model describing the stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes is constructed and investigated. The model is a part of a more general model of the isoelectrofocusing process. Investigation is based on the approximation of a weak solution by the piecewise continuous non-smooth functions. The method can be used for solving classes of problems for ordinary differential equations with a small parameter at the highest derivatives and the turning points.
ERIC Educational Resources Information Center
Jaggars, Shanna Smith; Xu, Di
2015-01-01
Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this paper we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from Mincerian and fixed-effects approaches. Our…
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
NASA Astrophysics Data System (ADS)
Kumar, Mano Ranjan; Ghosh, Subhojit; Das, Shantanu
2016-12-01
The usage of ultracapacitors for development of energy storage devices and alternative power sources is increasing at a very rapid rate. However accuracy in selection of ultracapacitor model parameter plays key role in the design of such devices, especially in applications involving wide operating frequency. Ultracapacitors are known to exhibit fractional dynamics and the model parameters vary significantly with frequency. This paper proposes a piecewise modelling and parameter estimation approach for ultracapacitors using a hybrid optimization and fuzzy clustering approach. The proposed modelling technique has been applied over impedance frequency response data acquired from a commercially available ultracapacitor. The model is able to represent the experimental data over different operating points with reduced number of model parameters. Comparative numerical simulations have been carried out to validate the benefits of the proposed approach. The estimated parameters revealed the disparity in the frequency dependent behavior of ultracapacitors and standard electrolytic capacitors.
Locomotion of C. elegans: A Piecewise-Harmonic Curvature Representation of Nematode Behavior
Padmanabhan, Venkat; Khan, Zeina S.; Solomon, Deepak E.; Armstrong, Andrew; Rumbaugh, Kendra P.; Vanapalli, Siva A.; Blawzdziewicz, Jerzy
2012-01-01
Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase. PMID:22792224
Piecewise Smooth Dynamical Systems Theory: The Case of the Missing Boundary Equilibrium Bifurcations
NASA Astrophysics Data System (ADS)
Hogan, S. J.; Homer, M. E.; Jeffrey, M. R.; Szalai, R.
2016-10-01
We present two codimension-one bifurcations that occur when an equilibrium collides with a discontinuity in a piecewise smooth dynamical system. These simple cases appear to have escaped recent classifications. We present them here to highlight some of the powerful results from Filippov's book Differential Equations with Discontinuous Righthand Sides (Kluwer, 1988). Filippov classified the so-called boundary equilibrium collisions without providing their unfolding. We show the complete unfolding here, for the first time, in the particularly interesting case of a node changing its stability as it collides with a discontinuity. We provide a prototypical model that can be used to generate all codimension-one boundary equilibrium collisions, and summarize the elements of Filippov's work that are important in achieving a full classification.
Circular Piecewise Regression with an Application to Cell-cycle Biology
Rueda, Cristina; Fernández, Miguel A.; Barragán, Sandra; Mardia, Kanti V.; Peddada, Shyamal D.
2016-01-01
Summary Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, we need to model the relation among peak expressions of cell-cycle genes in two species with different cell phase lengths. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology. PMID:26991351
Fermion resonances on a thick brane with a piecewise warp factor
Li Haitao; Liu Yuxiao; Zhao Zhenhua; Guo Heng
2011-02-15
In this paper, we mainly investigate the problems of resonances of massive Kaluza-Klein (KK) fermions on a single scalar constructed thick brane with a piecewise warp factor matching smoothly. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling {eta}{Psi}{phi}{sup k{Psi}} with odd k=1,3,5,..., the mass eigenvalue m, width {Gamma}, lifetime {tau}, and maximal probability P{sub max} of fermion resonances are obtained. Our numerical calculations show that the brane without internal structure also favors the appearance of resonant states for both left- and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.
Buckling and vibration analysis of a simply supported column with a piecewise constant cross section
NASA Technical Reports Server (NTRS)
Lake, Mark S.; Mikulas, Martin M., Jr.
1991-01-01
An analysis and sample results for the lateral buckling and vibration of a compressively loaded column is presented whose cross section is piecewise constant along its length. The column is symmetric about its mid-span and consists of three sections, the center section having a stiffer cross section than the two identical end sections. Buckling and vibration characteristics of the column are determined from numerical solution of the exact eigenvalue problems. Parametric structural efficiency analyses are performed using a nondimensionalized set of governing equations to determine the optimum ratio between the lengths of the center section and the outer sections based on both buckling load and vibration frequency requirements. In these analyses, two relationships exist. One is between cross-sectional mass and the cross section, and the other is a high-efficiency scheme. The effect of axial load on vibration frequency is also examined and compared with that of a uniform column.
Improved Survival Modeling in Cancer Research Using a Reduced Piecewise Exponential Approach
Han, Gang; Schell, Michael J.; Kim, Jongphil
2014-01-01
Statistical models for survival data are typically nonparametric, e.g., the Kaplan-Meier curve. Parametric survival modeling, such as exponential modeling, however, can reveal additional insights and be more efficient than nonparametric alternatives. A major constraint of the existing exponential models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is presented to best use the exponential models for arbitrary survival data. This model identifies shifts in the failure rate over time based on an exact likelihood ratio test, a backward elimination procedure, and an optional presumed order restriction on the hazard rate. Such modeling provides a descriptive tool in understanding the patient survival in addition to the Kaplan-Meier curve. This approach is compared with alternative survival models in simulation examples and illustrated in clinical studies. PMID:23900779
Approximate Qualitative Temporal Reasoning
2001-01-01
i.e., their boundaries can be placed in such a way that they coincide with the cell boundaries of the appropriate partition of the time-line. (Think of...respect to some appropriate partition of the time-line. For example, I felt well on Saturday. When I measured my temperature I had a fever on Monday and on...Bittner / Approximate Qualitative Temporal Reasoning 49 [27] I. A. Goralwalla, Y. Leontiev , M. T. Özsu, D. Szafron, and C. Combi. Temporal granularity for
Meta-Regression Approximations to Reduce Publication Selection Bias
ERIC Educational Resources Information Center
Stanley, T. D.; Doucouliagos, Hristos
2014-01-01
Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
Parametric Identification of Systems Via Linear Operators.
1978-09-01
A general parametric identification /approximation model is developed for the black box identification of linear time invariant systems in terms of... parametric identification techniques derive from the general model as special cases associated with a particular linear operator. Some possible
Superconducting linear actuator
NASA Technical Reports Server (NTRS)
Johnson, Bruce; Hockney, Richard
1993-01-01
Special actuators are needed to control the orientation of large structures in space-based precision pointing systems. Electromagnetic actuators that presently exist are too large in size and their bandwidth is too low. Hydraulic fluid actuation also presents problems for many space-based applications. Hydraulic oil can escape in space and contaminate the environment around the spacecraft. A research study was performed that selected an electrically-powered linear actuator that can be used to control the orientation of a large pointed structure. This research surveyed available products, analyzed the capabilities of conventional linear actuators, and designed a first-cut candidate superconducting linear actuator. The study first examined theoretical capabilities of electrical actuators and determined their problems with respect to the application and then determined if any presently available actuators or any modifications to available actuator designs would meet the required performance. The best actuator was then selected based on available design, modified design, or new design for this application. The last task was to proceed with a conceptual design. No commercially-available linear actuator or modification capable of meeting the specifications was found. A conventional moving-coil dc linear actuator would meet the specification, but the back-iron for this actuator would weigh approximately 12,000 lbs. A superconducting field coil, however, eliminates the need for back iron, resulting in an actuator weight of approximately 1000 lbs.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
The Linear KdV Equation with an Interface
NASA Astrophysics Data System (ADS)
Deconinck, Bernard; Sheils, Natalie E.; Smith, David A.
2016-10-01
The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas's Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.
Spline smoothing of histograms by linear programming
NASA Technical Reports Server (NTRS)
Bennett, J. O.
1972-01-01
An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.
Total variation regularization with bounded linear variations
NASA Astrophysics Data System (ADS)
Makovetskii, Artyom; Voronin, Sergei; Kober, Vitaly
2016-09-01
One of the most known techniques for signal denoising is based on total variation regularization (TV regularization). A better understanding of TV regularization is necessary to provide a stronger mathematical justification for using TV minimization in signal processing. In this work, we deal with an intermediate case between one- and two-dimensional cases; that is, a discrete function to be processed is two-dimensional radially symmetric piecewise constant. For this case, the exact solution to the problem can be obtained as follows: first, calculate the average values over rings of the noisy function; second, calculate the shift values and their directions using closed formulae depending on a regularization parameter and structure of rings. Despite the TV regularization is effective for noise removal; it often destroys fine details and thin structures of images. In order to overcome this drawback, we use the TV regularization for signal denoising subject to linear signal variations are bounded.
Approximate learning algorithm in Boltzmann machines.
Yasuda, Muneki; Tanaka, Kazuyuki
2009-11-01
Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments.
Numerical design of FSHL-based approximate cloaks with arbitrary shapes
NASA Astrophysics Data System (ADS)
Wang, Qi; Hou, Yanren; Li, Jingzhi
2017-03-01
This paper considers numerical design of finite sound-hard lining (FSHL)-based approximate cloaks with arbitrary shapes. Regarding the complexity of the shape, two new approaches are proposed to design the transformation map from the virtual space to the physical space via transformation optics. For star-shaped geometry, we propose an explicit global transformation map which can be easily differentiated and inverted. For more general shapes, an Initialize-Untangle-Extend (IUE) approach is initiated to build locally piecewise differentiable deformations, which can be locally inverted with the help of an approximate triangulation. With the locally piecewise-constructed transformation, the parameters of acoustic scattering models in physical space can be determined in both approaches based on the transformation invariance of the Helmholtz system. Then the cloaking effects for an arbitrary shape FSHL-based cloak can be realized following Li et al. (2012) [5]. Extensive numerical experiments are presented to illustrate both the effectiveness of cloak design and the efficiency of the proposed FSHL-based cloaks with arbitrary shapes.
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values.
Vonica-Gligor, Andreea Loredana; Tomuţă, Ioan; Leucuţa, Sorin E
2016-06-01
The aim of this work was to develop a pulsatile release system with metoprolol for chronotherapeutical use by coating swellable mini-tablets with Eudragit RS. To study the influence of the formulation factors (amount of coating polymer, plasticizer percentage in film coating and swelling agent percentage in mini-tablets), a Box-Behnken design of experiment (DoE) was used. To evaluate the influence of the studied factors on the sigmoid shape of the dissolution profile, piecewise function parameters were used as the responses of DoE. The results show that higher concentrations of coating polymer and higher concentrations of plasticizer polymer led to a thicker and more elastic polymeric film, which led to a delay in drug release. Using the parameters of the piecewise function as DoE responses, an optimum formulation with a sigmoid shape dissolution profile and a 2.5-h lag time followed by rapid drug release were obtained.
Identification of piecewise affine systems based on fuzzy PCA-guided robust clustering technique
NASA Astrophysics Data System (ADS)
Khanmirza, Esmaeel; Nazarahari, Milad; Mousavi, Alireza
2016-12-01
Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors. Since a general method for the analysis of hybrid systems is not available, some researchers have focused on specific types of hybrid systems. Piecewise affine (PWA) systems are one of the subsets of hybrid systems. The identification of PWA systems includes the estimation of the parameters of affine subsystems and the coefficients of the hyperplanes defining the partition of the state-input domain. In this paper, we have proposed a PWA identification approach based on a modified clustering technique. By using a fuzzy PCA-guided robust k-means clustering algorithm along with neighborhood outlier detection, the two main drawbacks of the well-known clustering algorithms, i.e., the poor initialization and the presence of outliers, are eliminated. Furthermore, this modified clustering technique enables us to determine the number of subsystems without any prior knowledge about system. In addition, applying the structure of the state-input domain, that is, considering the time sequence of input-output pairs, provides a more efficient clustering algorithm, which is the other novelty of this work. Finally, the proposed algorithm has been evaluated by parameter identification of an IGV servo actuator. Simulation together with experiment analysis has proved the effectiveness of the proposed method.
Piecewise compensation for the nonlinear error of fiber-optic gyroscope scale factor
NASA Astrophysics Data System (ADS)
Zhang, Yonggang; Wu, Xunfeng; Yuan, Shun; Wu, Lei
2013-08-01
Fiber-Optic Gyroscope (FOG) scale factor nonlinear error will result in errors in Strapdown Inertial Navigation System (SINS). In order to reduce nonlinear error of FOG scale factor in SINS, a compensation method is proposed in this paper based on curve piecewise fitting of FOG output. Firstly, reasons which can result in FOG scale factor error are introduced and the definition of nonlinear degree is provided. Then we introduce the method to divide the output range of FOG into several small pieces, and curve fitting is performed in each output range of FOG to obtain scale factor parameter. Different scale factor parameters of FOG are used in different pieces to improve FOG output precision. These parameters are identified by using three-axis turntable, and nonlinear error of FOG scale factor can be reduced. Finally, three-axis swing experiment of SINS verifies that the proposed method can reduce attitude output errors of SINS by compensating the nonlinear error of FOG scale factor and improve the precision of navigation. The results of experiments also demonstrate that the compensation scheme is easy to implement. It can effectively compensate the nonlinear error of FOG scale factor with slightly increased computation complexity. This method can be used in inertial technology based on FOG to improve precision.
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device.
A few remarks on recurrence relations for geometrically continuous piecewise Chebyshevian B-splines
NASA Astrophysics Data System (ADS)
Mazure, Marie-Laurence
2009-08-01
This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457-470, 2008) in which we showed that T. Lyche's recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155-178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences, T. Lyche's approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots. Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603-624, 2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35-78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller supports involved in the recurrence relations.
Piecewise-Constant-Model-Based Interior Tomography Applied to Dentin Tubules
He, Peng; Wei, Biao; Wang, Steve; ...
2013-01-01
Dentin is a hierarchically structured biomineralized composite material, and dentin’s tubules are difficult to study in situ. Nano-CT provides the requisite resolution, but the field of view typically contains only a few tubules. Using a plate-like specimen allows reconstruction of a volume containing specific tubules from a number of truncated projections typically collected over an angular range of about 140°, which is practically accessible. Classical computed tomography (CT) theory cannot exactly reconstruct an object only from truncated projections, needless to say a limited angular range. Recently, interior tomography was developed to reconstruct a region-of-interest (ROI) from truncated data in amore » theoretically exact fashion via the total variation (TV) minimization under the condition that the ROI is piecewise constant. In this paper, we employ a TV minimization interior tomography algorithm to reconstruct interior microstructures in dentin from truncated projections over a limited angular range. Compared to the filtered backprojection (FBP) reconstruction, our reconstruction method reduces noise and suppresses artifacts. Volume rendering confirms the merits of our method in terms of preserving the interior microstructure of the dentin specimen.« less
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?
ERIC Educational Resources Information Center
Oud, Johan H. L.; Folmer, Henk
2011-01-01
This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…
Approximation in LQG control of a thermoelastic rod
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.; Tao, G.
1989-01-01
Control and estimator gains are computed for linear-quadratic-Gaussian (LQG) optimal control of the axial vibrations of a thermoelastic rod. The computations are based on a modal approximation of the partial differential equations representing the rod, and convergence of the approximations to control and estimator gains is the main issue.
Graph-Based Transform for 2D Piecewise Smooth Signals With Random Discontinuity Locations.
Zhang, Dong; Liang, Jie
2017-04-01
The graph-based block transform recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, in existing methods, overheads are required to describe the graph of the block, from which the decoder has to calculate the transform via time-consuming eigendecomposition. To address these problems, in this paper, we aim to develop a single graph-based transform for a class of 2D piecewise smooth signals with similar discontinuity patterns. We first consider the deterministic case with a known discontinuity location in each row. We propose a 2D first-order autoregression (2D AR1) model and a 2D graph for this type of signals. We show that the closed-form expression of the inverse of a biased Laplacian matrix of the proposed 2D graph is exactly the covariance matrix of the proposed 2D AR1 model. Therefore, the optimal transform for the signal are the eigenvectors of the proposed graph Laplacian. Next, we show that similar results hold in the random case, where the locations of the discontinuities in different rows are randomly distributed within a confined region, and we derive the closed-form expression of the corresponding optimal 2D graph Laplacian. The theory developed in this paper can be used to design both pre-computed transforms and signal-dependent transforms with low complexities. Finally, depth image coding experiments demonstrate that our methods can achieve similar performance to the state-of-the-art method, but our complexity is much lower.
Costa, O. L. V.; Dufour, F.
2011-06-15
This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP's) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space Double-Struck-Capital-R {sup n}. The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter {epsilon}>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as {epsilon} goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as {epsilon} goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.
Ranking Support Vector Machine with Kernel Approximation
Dou, Yong
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256
Ranking Support Vector Machine with Kernel Approximation.
Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
CMB-lensing beyond the Born approximation
NASA Astrophysics Data System (ADS)
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Colgate, S.A.
1958-05-27
An improvement is presented in linear accelerators for charged particles with respect to the stable focusing of the particle beam. The improvement consists of providing a radial electric field transverse to the accelerating electric fields and angularly introducing the beam of particles in the field. The results of the foregoing is to achieve a beam which spirals about the axis of the acceleration path. The combination of the electric fields and angular motion of the particles cooperate to provide a stable and focused particle beam.
Impact of using linear optimization models in dose planning for HDR brachytherapy
Holm, Aasa; Larsson, Torbjoern; Carlsson Tedgren, Aasa
2012-02-15
Purpose: Dose plans generated with optimization models hitherto used in high-dose-rate (HDR) brachytherapy have shown a tendency to yield longer dwell times than manually optimized plans. Concern has been raised for the corresponding undesired hot spots, and various methods to mitigate these have been developed. The hypotheses upon this work is based are (a) that one cause for the long dwell times is the use of objective functions comprising simple linear penalties and (b) that alternative penalties, as these are piecewise linear, would lead to reduced length of individual dwell times. Methods: The characteristics of the linear penalties and the piecewise linear penalties are analyzed mathematically. Experimental comparisons between the two types of penalties are carried out retrospectively for a set of prostate cancer patients. Results: When the two types of penalties are compared, significant changes can be seen in the dwell times, while most dose-volume parameters do not differ significantly. On average, total dwell times were reduced by 4.2%, with a reduction of maximum dwell times by 25%, when the alternative penalties were used. Conclusions: The use of linear penalties in optimization models for HDR brachytherapy is one cause for the undesired long dwell times that arise in mathematically optimized plans. By introducing alternative penalties, a significant reduction in dwell times can be achieved for HDR brachytherapy dose plans. Although various measures for mitigating the long dwell times are already available, the observation that linear penalties contribute to their appearance is of fundamental interest.
Phenomenological applications of rational approximants
NASA Astrophysics Data System (ADS)
Gonzàlez-Solís, Sergi; Masjuan, Pere
2016-08-01
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function 1 zln(1 + z) is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract Vub from the semileptonic B → πℓνℓ decays. Finally, the π vector form factor in the TL region is explored using QAs.
NASA Astrophysics Data System (ADS)
Hagedorn, P.
The mathematical pendulum is used to provide a survey of free and forced oscillations in damped and undamped systems. This simple model is employed to present illustrations for and comparisons between the various approximation schemes. A summary of the Liapunov stability theory is provided. The first and the second method of Liapunov are explained for autonomous as well as for nonautonomous systems. Here, a basic familiarity with the theory of linear oscillations is assumed. La Salle's theorem about the stability of invariant domains is explained in terms of illustrative examples. Self-excited oscillations are examined, taking into account such oscillations in mechanical and electrical systems, analytical approximation methods for the computation of self-excited oscillations, analytical criteria for the existence of limit cycles, forced oscillations in self-excited systems, and self-excited oscillations in systems with several degrees of freedom. Attention is given to Hamiltonian systems and an introduction to the theory of optimal control is provided.
Approximate inverse preconditioners for general sparse matrices
Chow, E.; Saad, Y.
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1985-01-01
Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.
Approximate Solution to the Generalized Boussinesq Equation
NASA Astrophysics Data System (ADS)
Telyakovskiy, A. S.; Mortensen, J.
2010-12-01
The traditional Boussinesq equation describes motion of water in groundwater flows. It models unconfined groundwater flow under the Dupuit assumption that the equipotential lines are vertical, making the flowlines horizontal. The Boussinesq equation is a nonlinear diffusion equation with diffusivity depending linearly on water head. Here we analyze a generalization of the Boussinesq equation, when the diffusivity is a power law function of water head. For example polytropic gases moving through porous media obey this equation. Solving this equation usually requires numerical approximations, but for certain classes of initial and boundary conditions an approximate analytical solution can be constructed. This work focuses on the latter approach, using the scaling properties of the equation. We consider one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in case of cylindrical symmetry. Such situation represents the case of an injection well. Solutions would propagate with the finite speed. We construct an approximate scaling function, and we compare the approximate solution with the direct numerical solutions obtained by using the scaling properties of the equations.
Woodward, P. R.
2003-03-26
This report summarizes the results of the project entitled, ''Piecewise-Parabolic Methods for Parallel Computation with Applications to Unstable Fluid Flow in 2 and 3 Dimensions'' This project covers a span of many years, beginning in early 1987. It has provided over that considerable period the core funding to my research activities in scientific computation at the University of Minnesota. It has supported numerical algorithm development, application of those algorithms to fundamental fluid dynamics problems in order to demonstrate their effectiveness, and the development of scientific visualization software and systems to extract scientific understanding from those applications.
NASA Technical Reports Server (NTRS)
Gurin, L. S.; Ivanova, N. P.
1975-01-01
A piecewise-smooth function with discontinuity in the first derivative on a given interval is considered. The values of the function are measured at a sequence of points in the interval and a random error is included in the measurements. A method is proposed to estimate the position of the discontinuity in the derivative. Regression lines are associated with each measurement point and account for k - 1 points preceding or following the point. The estimate for the position of the discontinuity is the measurement point with the largest angle between the regression lines. The error in the estimate is analyzed and the results are verified.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Legendre-Tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1983-01-01
The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.
LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL
NASA Technical Reports Server (NTRS)
Duke, E. L.
1994-01-01
interest, or a full non-linear aerodynamic model as used in simulations. LINEAR is written in FORTRAN and has been implemented on a DEC VAX computer operating under VMS with a virtual memory requirement of approximately 296K of 8 bit bytes. Both an interactive and batch version are included. LINEAR was developed in 1988.
NASA Astrophysics Data System (ADS)
Eymard, Robert; Mercier, Sophie; Prignet, Alain
2008-12-01
We are interested here in the numerical approximation of a family of probability measures, solution of the Chapman-Kolmogorov equation associated to some non-diffusion Markov process with uncountable state space. Such an equation contains a transport term and another term, which implies redistribution of the probability mass on the whole space. An implicit finite volume scheme is proposed, which is intermediate between an upstream weighting scheme and a modified Lax-Friedrichs one. Due to the seemingly unusual probability framework, a new weak bounded variation inequality had to be developed, in order to prove the convergence of the discretised transport term. Such an inequality may be used in other contexts, such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in L1. Also, due to the redistribution term, the tightness of the family of approximate probability measures had to be proven. Numerical examples are provided, showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.
Wu, Ailong; Liu, Ling; Huang, Tingwen; Zeng, Zhigang
2017-01-01
Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results.
Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G Leonard; Parks, Craig; Roll, John
2015-12-01
Researchers often want to examine 2 comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of 2 disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than 2 growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention-deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive-behavioral therapy treatment for a substance use disorder and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these 2 disorders concurrently allowed us to determine whether elevated levels of 1 disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and substance use separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or substance use disorder) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed.
Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G. Leonard; Parks, Craig; Roll, John
2015-01-01
Researchers often want to examine two comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of two disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than two growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive behavioral therapy treatment for a substance use disorder (SUD) and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these two disorders concurrently allowed us to determine whether elevated levels of one disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and SU separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or SUD) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. PMID:26389639
Online segmentation of time series based on polynomial least-squares approximations.
Fuchs, Erich; Gruber, Thiemo; Nitschke, Jiri; Sick, Bernhard
2010-12-01
The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs.
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Using quadratic simplicial elements for hierarchical approximation and visualization
NASA Astrophysics Data System (ADS)
Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson
2002-03-01
Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
NASA Technical Reports Server (NTRS)
Enright, Paul J.; Conway, Bruce A.
1990-01-01
A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.
Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
NASA Astrophysics Data System (ADS)
Enright, Paul J.; Conway, Bruce A.
A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
Burgers approximation for two-dimensional flow past an ellipse
NASA Technical Reports Server (NTRS)
Dorrepaal, J. M.
1982-01-01
A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.
Approximate Bisimulation-Based Reduction of Power System Dynamic Models
Stankovic, AM; Dukic, SD; Saric, AT
2015-05-01
In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential- algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.
Fractional Electron Loss in Approximate DFT and Hartree-Fock Theory.
Peach, Michael J G; Teale, Andrew M; Helgaker, Trygve; Tozer, David J
2015-11-10
Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree-Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree-Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree-Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree-Fock results are presented for the F → F(-) segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne(-).
NASA Astrophysics Data System (ADS)
Hinds, Arianne T.
2011-09-01
Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations.
Approximating a nonlinear advanced-delayed equation from acoustics
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-10-01
We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.
Rational approximations for tomographic reconstructions
NASA Astrophysics Data System (ADS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-06-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image.
Adaptive approximation models in optimization
Voronin, A.N.
1995-05-01
The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions.
Approximating spatially exclusive invasion processes
NASA Astrophysics Data System (ADS)
Ross, Joshua V.; Binder, Benjamin J.
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
Heat pipe transient response approximation.
Reid, R. S.
2001-01-01
A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.
Second Approximation to Conical Flows
1950-12-01
Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . $O’/ + (8) Introducing Eqs
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
ERIC Educational Resources Information Center
Zvoch, Keith
2016-01-01
Piecewise growth models (PGMs) were used to estimate and model changes in the preliteracy skill development of kindergartners in a moderately sized school district in the Pacific Northwest. PGMs were applied to interrupted time-series (ITS) data that arose within the context of a response-to-intervention (RtI) instructional framework. During the…
Gravity modeling: the Jacobian function and its approximation
NASA Astrophysics Data System (ADS)
Strykowski, G.; Lauritsen, N. L. B.
2012-04-01
In mathematics, the elements of a Jacobian matrix are the first-order partial derivatives of a scalar function or a vector function with respect to another vector. In inversion theory of geophysics the elements of a Jacobian matrix are a measure of the change of the output signal caused by a local perturbation of a parameter of a given (Earth) model. The elements of a Jacobian matrix can be determined from the general Jacobian function. In gravity modeling this function consists of the "geometrical part" (related to the relative location in 3D of a field point with respect to the source element) and the "source-strength part" (related to the change of mass density of the source element). The explicit (functional) expressions for the Jacobian function can be quite complicated and depend both on the coordinates used (Cartesian, spherical, ellipsoidal) and on the mathematical parametrization of the source (e.g. the homogenous rectangular prism). In practice, and irrespective of the exact expression for the Jacobian function, its value on a computer will always be rounded to a finite number of digits. In fact, in using the exact formulas such finite representation may cause numerical instabilities. If the Jacobian function is smooth enough, it is an advantage to approximate it by a simpler function, e.g. a piecewise-polynomial, which numerically is more robust than the exact formulas and which is more suitable for the subsequent integration. In our contribution we include a whole family of the Jacobian functions which are associated with all the partial derivatives of the gravitational potential of order 0 to 2, i.e. including all the elements of the gravity gradient tensor. The quality of the support points for the subsequent polynomial approximation of the Jacobian function is ensured by using the exact prism formulas in quadruple precision. We will show some first results. Also, we will discuss how such approximated Jacobian functions can be used for large scale
NASA Technical Reports Server (NTRS)
Barth, TIm
2002-01-01
This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.
Taylor Approximations to Logistic IRT Models and Their Use in Adaptive Testing.
ERIC Educational Resources Information Center
Veerkamp, Wim J. J.
2000-01-01
Showed how Taylor approximation can be used to generate a linear approximation to a logistic item characteristic curve and a linear ability estimator. Demonstrated how, for a specific simulation, this could result in the special case of a Robbins-Monro item selection procedure for adaptive testing. (SLD)
NASA Astrophysics Data System (ADS)
Revenough, Justin
Elastic waves propagating in simple media manifest a surprisingly rich collection of phenomena. Although some can't withstand the complexities of Earth's structure, the majority only grow more interesting and more important as remote sensing probes for seismologists studying the planet's interior. To fully mine the information carried to the surface by seismic waves, seismologists must produce accurate models of the waves. Great strides have been made in this regard. Problems that were entirely intractable a decade ago are now routinely solved on inexpensive workstations. The mathematical representations of waves coded into algorithms have grown vastly more sophisticated and are troubled by many fewer approximations, enforced symmetries, and limitations. They are far from straightforward, and seismologists using them need a firm grasp on wave propagation in simple media. Linear Elastic Waves, by applied mathematician John G. Harris, responds to this need.
An approximation method for configuration optimization of trusses
NASA Technical Reports Server (NTRS)
Hansen, Scott R.; Vanderplaats, Garret N.
1988-01-01
Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.
Wang, Chunyuan; Liu, Xiang; Zhao, Xiaoli; Wang, Yongqi
2016-01-01
Conventional correction approaches are unsuitable for effectively correcting remote sensing images acquired in the seriously oblique condition which has severe distortions and resolution disparity. Considering that the extraction of control points (CPs) and the parameter estimation of the correction model play important roles in correction accuracy, this paper introduces an effective correction method for large angle (LA) images. Firstly, a new CP extraction algorithm is proposed based on multi-view simulation (MVS) to ensure the effective matching of CP pairs between the reference image and the LA image. Then, a new piecewise correction algorithm is advanced with the optimized CPs, where a concept of distribution measurement (DM) is introduced to quantify the CPs distribution. The whole image is partitioned into contiguous subparts which are corrected by different correction formulae to guarantee the accuracy of each subpart. The extensive experimental results demonstrate that the proposed method significantly outperforms conventional approaches. PMID:27763538
NASA Astrophysics Data System (ADS)
Letellier, Christophe; Amaral, Gleison F. V.; Aguirre, Luis A.
2007-06-01
The characterization of chaotic attractors has been a widely addressed problem and there are now many different techniques to define their nature in a rather accurate way, at least in the case of a three-dimensional system. Nevertheless, the link between the structure of the ordinary differential equations and the topology of their solutions is still missing and only a few necessary conditions on the algebraic structure are known today. By using a feedback circuit analysis, it is shown that it is possible to identify the relevant terms of the equations, that is, the terms that really contribute to the structure of the phase portrait. Such analysis also provides some guidelines for constructing piecewise affine models. Moreover, equivalence classes can be defined on the basis of the active feedback circuits involved.
NASA Technical Reports Server (NTRS)
Lee, Jong-Won; Harris, Charles E.
1988-01-01
A mathematical model based on the Euler-Bernoulli beam theory is proposed for predicting the effective Young's moduli of piece-wise isotropic composite laminates with wavy patterns in the main load-carrying layers. Strains in corrugated layers, in-phase layers, and out-of-phase layers are predicted for various geometries and material configurations by assuming matrix layers as elastic foundations. Experimental results obtained from corrugated aluminum specimens and aluminum/epoxy specimens with in-phase and out-of-phase wavy patterns coincide very well with the predictions. The work represents a preliminary effort toward further generalization of the model for two-dimensional anisotropic laminates containing wavy patterns in the main load-carrying layers.
CT reconstruction via denoising approximate message passing
NASA Astrophysics Data System (ADS)
Perelli, Alessandro; Lexa, Michael A.; Can, Ali; Davies, Mike E.
2016-05-01
In this paper, we adapt and apply a compressed sensing based reconstruction algorithm to the problem of computed tomography reconstruction for luggage inspection. Specifically, we propose a variant of the denoising generalized approximate message passing (D-GAMP) algorithm and compare its performance to the performance of traditional filtered back projection and to a penalized weighted least squares (PWLS) based reconstruction method. D-GAMP is an iterative algorithm that at each iteration estimates the conditional probability of the image given the measurements and employs a non-linear "denoising" function which implicitly imposes an image prior. Results on real baggage show that D-GAMP is well-suited to limited-view acquisitions.
NASA Astrophysics Data System (ADS)
Krauze, W.; Makowski, P.; Kujawińska, M.
2015-06-01
Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography - Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.
A note on a linearized approach to gravitational lensing
NASA Astrophysics Data System (ADS)
Walters, S. J.; Forbes, L. K.
2011-10-01
A recent paper by Walters, Forbes and Jarvis presented new kinematic formulae for ray tracing in gravitational lensing models. The approach can generate caustic maps, but is computationally expensive. Here, a linearized approximation to that formulation is presented. Although still complicated, the linearized equations admit a remarkable closed-form solution. As a result, linearized approximations to the caustic patterns may be generated extremely rapidly, and are found to be in good agreement with the results of full non-linear computation. The usual Einstein-angle approximation is derived as a small angle approximation to the solution presented here.
Topics in Multivariate Approximation Theory.
1982-05-01
include tensor products, multivariate polynomial interpolation , esp. Kergin Interpolation , and the recent developments of multivariate B-splines. t1...AMS (MOS) Subject Classifications: 41-02, 41A05, 41A10, 41A15, 41A63, 41A65 Key Words: multivariate, B-splines, Kergin interpolation , linear projectors...splines and in multivariate polynomial interpolation . These developments may well provide the theoretical foundation for efficient methods of
Improved results for linear discrete-time systems with an interval time-varying input delay
NASA Astrophysics Data System (ADS)
Zhang, Jin; Peng, Chen; Zheng, Min
2016-01-01
This paper addresses the problem of delay-dependent stability analysis and controller synthesis for a discrete-time system with an interval time-varying input delay. By dividing delay interval into multiple parts and constructing a novel piecewise Lyapunov-Krasovskii functional, an improved delay-partitioning-dependent stability criterion and a stabilisation criterion are obtained in terms of matrix inequalities. Compared with some existing results, since a tighter bounding inequality is employed to deal with the integral items, our results depend on less number of linear matrix inequality scalar decision variables while obtaining same or better allowable upper delay bound. Numerical examples show the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Wang, Ronghao; Xing, Jianchun; Li, Juelong; Xiang, Zhengrong
2016-10-01
This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results.
Testing the frozen flow approximation
NASA Technical Reports Server (NTRS)
Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro
1993-01-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.
Ab initio dynamical vertex approximation
NASA Astrophysics Data System (ADS)
Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten
2017-03-01
Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.
Potential of the approximation method
Amano, K.; Maruoka, A.
1996-12-31
Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.
Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems
NASA Astrophysics Data System (ADS)
Amaral, Gleison F. V.; Letellier, Christophe; Aguirre, Luis Antonio
2006-03-01
This paper proposes a procedure by which it is possible to synthesize Rössler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.
Nonlinear Filtering and Approximation Techniques
1991-09-01
Shwartz), Academic Press (1991). [191 M.Cl. ROUTBAUD, Fiting lindairc par morceaux avec petit bruit d’obserration, These. Universit6 de Provence ( 1990...Kernel System (GKS), Academic Press (1983). 181 H.J. KUSHNER, Probability methods for approximations in stochastic control and for elliptic equations... Academic Press (1977). [9] F. LE GLAND, Time discretization of nonlinear filtering equations, in: 28th. IEEE CDC, Tampa, pp. 2601-2606. IEEE Press (1989
Calculating Resonance Positions and Widths Using the Siegert Approximation Method
ERIC Educational Resources Information Center
Rapedius, Kevin
2011-01-01
Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
An approximation method for fractional integro-differential equations
NASA Astrophysics Data System (ADS)
Emiroglu, Ibrahim
2015-12-01
In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.
Multidimensional Approximation Operators Generated by Lebesgue-Stieltjes Measures
NASA Astrophysics Data System (ADS)
Volkov, Yu I.
1984-06-01
A general class of sequences of multidimensional positive linear operators is defined and studied; it includes, in particular, sequences of multidimensional Berstein polynomials. The main asymptotic term is obtained in the remainder when derivatives of functions in certain classes are approximated by derivatives of the values of the operators on these functions. Bibliography: 10 titles.
Linearized Functional Minimization for Inverse Modeling
Wohlberg, Brendt; Tartakovsky, Daniel M.; Dentz, Marco
2012-06-21
Heterogeneous aquifers typically consist of multiple lithofacies, whose spatial arrangement significantly affects flow and transport. The estimation of these lithofacies is complicated by the scarcity of data and by the lack of a clear correlation between identifiable geologic indicators and attributes. We introduce a new inverse-modeling approach to estimate both the spatial extent of hydrofacies and their properties from sparse measurements of hydraulic conductivity and hydraulic head. Our approach is to minimize a functional defined on the vectors of values of hydraulic conductivity and hydraulic head fields defined on regular grids at a user-determined resolution. This functional is constructed to (i) enforce the relationship between conductivity and heads provided by the groundwater flow equation, (ii) penalize deviations of the reconstructed fields from measurements where they are available, and (iii) penalize reconstructed fields that are not piece-wise smooth. We develop an iterative solver for this functional that exploits a local linearization of the mapping from conductivity to head. This approach provides a computationally efficient algorithm that rapidly converges to a solution. A series of numerical experiments demonstrates the robustness of our approach.
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
Sensitivity analysis and approximation methods for general eigenvalue problems
NASA Technical Reports Server (NTRS)
Murthy, D. V.; Haftka, R. T.
1986-01-01
Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.
Airborne Linear Array Image Geometric Rectification Method Based on Unequal Segmentation
NASA Astrophysics Data System (ADS)
Li, J. M.; Li, C. R.; Zhou, M.; Hu, J.; Yang, C. M.
2016-06-01
As the linear array sensor such as multispectral and hyperspectral sensor has great potential in disaster monitoring and geological survey, the quality of the image geometric rectification should be guaranteed. Different from the geometric rectification of airborne planar array images or multi linear array images, exterior orientation elements need to be determined for each scan line of single linear array images. Internal distortion persists after applying GPS/IMU data directly to geometrical rectification. Straight lines may be curving and jagged. Straight line feature -based geometrical rectification algorithm was applied to solve this problem, whereby the exterior orientation elements were fitted by piecewise polynomial and evaluated with the straight line feature as constraint. However, atmospheric turbulence during the flight is unstable, equal piecewise can hardly provide good fitting, resulting in limited precision improvement of geometric rectification or, in a worse case, the iteration cannot converge. To solve this problem, drawing on dynamic programming ideas, unequal segmentation of line feature-based geometric rectification method is developed. The angle elements fitting error is minimized to determine the optimum boundary. Then the exterior orientation elements of each segment are fitted and evaluated with the straight line feature as constraint. The result indicates that the algorithm is effective in improving the precision of geometric rectification.
Linear isotherm determination from linear gradient elution experiments.
Pfister, David; Steinebach, Fabian; Morbidelli, Massimo
2015-01-02
A procedure to estimate equilibrium adsorption parameters as a function of the modifier concentration in linear gradient elution chromatography is proposed and its reliability is investigated by comparison with experimental data. Over the past decades, analytical solutions of the so-called equilibrium model under linear gradient elution conditions were derived assuming that proteins and modifier molecules access the same fraction of the pore size distribution of the porous particles. The present approach developed in this work accounts for the size exclusion effect resulting in different exclusions for proteins and modifier. A new analytical solution was derived by applying perturbation theory for differential equations, and the 1st-order approximated solution is presented in this work. Eventually, a turnkey and reliable procedure to efficiently estimate isotherm parameters as a function of modifier concentration from linear gradient elution experiments is proposed.
Jenko, J; Ducrocq, V; Kovač, M
2013-10-01
Piecewise Weibull proportional hazard models were used to investigate the effect of genetic and nongenetic factors on functional and true longevity traits of the Slovenian Brown cattle breed. Records of 37 908 Brown cows from 2401 Slovenian herds were used. As these herds were characterised by a relatively small average herd size starting from 6.7 in 1999 and increasing to 8.7 Brown cows per herd in 2008, milk yield classification was made within different herd size groups. The hazard rate was the lowest in the first part of each lactation and was increasing for later stages. Culling risk was lower for cows from herds increasing in size, for cows with higher milk production and for cows from a region with smaller herd sizes and tougher conditions for cattle breeding. The latter result is surprising and may be related to better attention to maintain the animals, despite their lower milk production. The introduction of the milk quota system and drought was found to have an important effect on culling policy between the last seasons of the years 2001 and 2003. Seasonal effects were not related to the milk quota year (from April to March), but to the effect of shortage in fodder during the winter time. The effect of age at first calving and the interaction between year and milk yield class were not found to be significant. Heritability for functional and for true longevity were similar at around 10% each. Inclusion of a correction for class of milk yield to approximate functional longevity increased the herd-year random effect variance by 53%, whereas the sire variance increased by only 14%. The correlation coefficient between ranks of breeding values for functional and true longevity was high (0.91), whereas genetic trends were not found to be significant. To assess their predictive ability, models were compared looking at the survival rate of 4212 second-crop daughters not included in the initial models. The average correlation between estimated breeding values and
1986-05-01
10O. PROGRAM ELEMENT. 11RO1JECT. TASK * Institute for Physical Science and Technology AREA & WORK UNIT NUMBERS ! ~University of Maryland 1% College...ELLIPTIC EQUATION OF SECOND ORDER I. Babuvka I Institute for Physical Science and Technology University of Maryland B. Guo 2 Department of Mathematics...neighborhood of the Program PROBE of Noetic Technologies, St. Louis. corners of the domain, place where the type of the boundary condition changes, etc
On applications of diophantine approximations
Chudnovsky, G. V.
1984-01-01
This paper is devoted to the study of the arithmetic properties of values of G-functions introduced by Siegel [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1]. One of the main results is a theorem on the linear independence of values of G-functions at rational points close to the origin. In this theorem, no conditions are imposed on the p-adic convergence of a G-function at a generic point. The theorem finally realizes Siegel's program on G-function values outlined in his paper. PMID:16593530
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-15
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Improved non-approximability results
Bellare, M.; Sudan, M.
1994-12-31
We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems.
Morita, Shin-Ya; Nishidate, Yohei; Nagata, Takashi; Yamagata, Yutaka; Teodosiu, Cristian
2010-06-20
We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray-patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10(5) to 10(9) times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.
Laguerre approximation of random foams
NASA Astrophysics Data System (ADS)
Liebscher, André
2015-09-01
Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam's cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.
NASA Astrophysics Data System (ADS)
Chiumenti, M.; Cervera, M.; Agelet de Saracibar, C.; Dialami, N.
2013-05-01
In this work a novel finite element technology based on a three-field mixed formulation is presented. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear piece-wise interpolations for displacement, stress and pressure fields, respectively. The result is an enhanced stress field approximation which enables for stress-accurate results in nonlinear computational mechanics. The use of an independent nodal variable for the pressure field allows for an adhoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the plastic strain in metal forming processes. The highly non-linear stress field typically encountered in the Friction Stir Welding (FSW) process is used as an example to show the performance of this new FE technology. The numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work.piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stirzone (ALE formulation). A fully coupled thermo-mechanical analysis is introduced showing the heat fluxes generated by the plastic dissipation in the stir-zone (Sheppard rigid-viscoplastic constitutive model) as well as the frictional dissipation at the contact interface (Norton frictional contact model). Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. Numerical results are compared with experimental evidence.
The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.
Pang, Haotian; Liu, Han; Vanderbei, Robert
2014-02-01
We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects.
Stabilization of nonlinear systems using linear observers
NASA Technical Reports Server (NTRS)
Strane, R. E.; Vogt, W. G.
1974-01-01
It is shown that a linear observer can always be employed to stabilize a nonlinear system which contains a true Popov type nonlinearity in the closed interval from 0 to k, where k is finite, provided the nonlinear function and a completely observable output of the linear portion are available as inputs to the observer. Taking into consideration the case in which a completely observable output is not available from the linear portion, stabilization is shown to be possible if the original linear approximation of the system is asymptotically stable.
Approximate analytic solutions to the NPDD: Short exposure approximations
NASA Astrophysics Data System (ADS)
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Implementing Linear Algebra Related Algorithms on the TI-92+ Calculator.
ERIC Educational Resources Information Center
Alexopoulos, John; Abraham, Paul
2001-01-01
Demonstrates a less utilized feature of the TI-92+: its natural and powerful programming language. Shows how to implement several linear algebra related algorithms including the Gram-Schmidt process, Least Squares Approximations, Wronskians, Cholesky Decompositions, and Generalized Linear Least Square Approximations with QR Decompositions.…
A quantum relaxation-time approximation for finite fermion systems
Reinhard, P.-G.; Suraud, E.
2015-03-15
We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Femtolensing: Beyond the semiclassical approximation
NASA Technical Reports Server (NTRS)
Ulmer, Andrew; Goodman, Jeremy
1995-01-01
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Moulton, J.D.; Ascher, U.M.; Morel, J.E.
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Mapping biological entities using the longest approximately common prefix method
2014-01-01
Background The significant growth in the volume of electronic biomedical data in recent decades has pointed to the need for approximate string matching algorithms that can expedite tasks such as named entity recognition, duplicate detection, terminology integration, and spelling correction. The task of source integration in the Unified Medical Language System (UMLS) requires considerable expert effort despite the presence of various computational tools. This problem warrants the search for a new method for approximate string matching and its UMLS-based evaluation. Results This paper introduces the Longest Approximately Common Prefix (LACP) method as an algorithm for approximate string matching that runs in linear time. We compare the LACP method for performance, precision and speed to nine other well-known string matching algorithms. As test data, we use two multiple-source samples from the Unified Medical Language System (UMLS) and two SNOMED Clinical Terms-based samples. In addition, we present a spell checker based on the LACP method. Conclusions The Longest Approximately Common Prefix method completes its string similarity evaluations in less time than all nine string similarity methods used for comparison. The Longest Approximately Common Prefix outperforms these nine approximate string matching methods in its Maximum F1 measure when evaluated on three out of the four datasets, and in its average precision on two of the four datasets. PMID:24928653
A test of the adhesion approximation for gravitational clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.
1993-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
Rational-spline approximation with automatic tension adjustment
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Kerr, P. A.
1984-01-01
An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.
NASA Astrophysics Data System (ADS)
Alves, Julio Cesar L.; Poppi, Ronei J.
2013-02-01
This paper reports the application of piecewise direct standardization (PDS) for matrix correction in front face fluorescence spectroscopy of solids when different excipients are used in a pharmaceutical preparation based on a mixture of acetylsalicylic acid (ASA), paracetamol (acetaminophen) and caffeine. As verified in earlier studies, the use of different excipients and their ratio can cause a displacement, change in fluorescence intensity or band profile. To overcome this important drawback, a standardization strategy was adopted to convert all the excitation-emission fluorescence spectra into those used for model development. An excitation-emission matrix (EEM) for which excitation and emission wavelengths ranging from 265 to 405 nm and 300 to 480 nm, respectively, was used. Excellent results were obtained using unfolded partial least squares (U-PLS), with RMSEP values of 8.2 mg/g, 10.9 mg/g and 2.7 mg/g for ASA, paracetamol and caffeine, respectively, and with relative errors lesser than 5% for the three analytes.
NASA Astrophysics Data System (ADS)
Liu, Xuele; Agarwal, G. S.
2017-03-01
Finding new phase of matter is a fundamental task in physics. Generally, various phases or states of matter (for instance solid/liquid/gas phases) have different symmetries, the phase transitions among them can be explained by Landau’s symmetry breaking theory. The topological phases discovered in recent years show that different phases may have the same symmetry. The different topological phases are characterized by different integer values of the Berry phases. By studying one dimensional (1D) trimer lattices we report new phases beyond topological phases. The new phases that we find are characterized by piecewise continuous Berry phases with the discontinuity occurring at the transition point. With time-dependent changes in trimer lattices, we can generate two dimensional (2D) phases, which are characterized by the Berry phase of half period. This half-period Berry phase changes smoothly within one state of the system while changes discontinuously at the transition point. We further demonstrate the existence of adiabatic pumping for each phase and gain assisted enhanced pumping. The non reciprocity of the pumping process makes the system a good optical diode.
NASA Astrophysics Data System (ADS)
Liu, Chen-Chung; Yang, Chih-Chao
2010-09-01
Dusk and dawn are usually the most beautiful moments of the day, and are almost always too short for busy people nowadays to witness their coming. In this work, an efficient strategy for simulating a dusk scene of an outdoor scene image taken at other times before the sunset is presented. The strategy is a hybrid approach combining the piece-wise multiple regression (PMR) of data, discrete cosine transformation (DCT), and a look-up table algorithm. The process begins using a series of color-block images taken in the afternoon of a day. The best fitting functions of PMR for these color block images exist on separate planes (red, green, and blue) in the DCT domain individually. The reference databases of the DCT coefficients varying with respect to time are then established according to the best fitting functions of PMR. Finally, the dusk scene of an outdoor scene taken in the afternoon is synthesized by querying the reference database. The experiment results show that the presented algorithm can precisely simulate the desired dusk scene from a scene image taken in the afternoon.
Terrien, Jérémy; Germain, Guy; Marque, Catherine; Karlsson, Brynjar
2013-08-01
Analysis of synchronization between biological signals can be helpful in characterization of biological functions. Many commonly used measures of synchronicity assume that the signal is stationary. Biomedical signals are however often strongly non stationary. We propose to use a bivariate piecewise stationary pre-segmentation (bPSP) of the signals of interest, before the computation of synchronization measures on biomedical signals to improve the performance of standard synchronization measures. In prior work we have shown how this can be achieved by using the auto-spectrum of either one of the signals under investigation. In this work we show how major improvements of the performance of synchronization measures can be achieved using the cross-spectrum of the signals to detect stationary changes which occur independently in either signal. We show on synthetic as well as on real biological signals (epileptic EEG and uterine EMG) that the proposed bPSP approach increases the accuracy of the measures by making a good tradeoff between the stationarity assumption and the length of the analyzed segments, when compared to the classical windowing method.
Risser, Laurent; Vialard, François-Xavier; Baluwala, Habib Y; Schnabel, Julia A
2013-02-01
In this paper, we propose a new strategy for modelling sliding conditions when registering 3D images in a piecewise-diffeomorphic framework. More specifically, our main contribution is the development of a mathematical formalism to perform Large Deformation Diffeomorphic Metric Mapping registration with sliding conditions. We also show how to adapt this formalism to the LogDemons diffeomorphic registration framework. We finally show how to apply this strategy to estimate the respiratory motion between 3D CT pulmonary images. Quantitative tests are performed on 2D and 3D synthetic images, as well as on real 3D lung images from the MICCAI EMPIRE10 challenge. Results show that our strategy estimates accurate mappings of entire 3D thoracic image volumes that exhibit a sliding motion, as opposed to conventional registration methods which are not capable of capturing discontinuous deformations at the thoracic cage boundary. They also show that although the deformations are not smooth across the location of sliding conditions, they are almost always invertible in the whole image domain. This would be helpful for radiotherapy planning and delivery.
Liu, Xuele; Agarwal, G. S.
2017-01-01
Finding new phase of matter is a fundamental task in physics. Generally, various phases or states of matter (for instance solid/liquid/gas phases) have different symmetries, the phase transitions among them can be explained by Landau’s symmetry breaking theory. The topological phases discovered in recent years show that different phases may have the same symmetry. The different topological phases are characterized by different integer values of the Berry phases. By studying one dimensional (1D) trimer lattices we report new phases beyond topological phases. The new phases that we find are characterized by piecewise continuous Berry phases with the discontinuity occurring at the transition point. With time-dependent changes in trimer lattices, we can generate two dimensional (2D) phases, which are characterized by the Berry phase of half period. This half-period Berry phase changes smoothly within one state of the system while changes discontinuously at the transition point. We further demonstrate the existence of adiabatic pumping for each phase and gain assisted enhanced pumping. The non reciprocity of the pumping process makes the system a good optical diode. PMID:28337994
Imbayarwo-Chikosi, V E; Ducrocq, V; Banga, C B; Halimani, T E; van Wyk, J B; Maiwashe, A; Dzama, K
2017-03-14
Non-genetic factors influencing functional longevity and the heritability of the trait were estimated in South African Holsteins using a piecewise Weibull proportional hazards model. Data consisted of records of 161,222 of daughters of 2,051 sires calving between 1995 and 2013. The reference model included fixed time-independent age at first calving and time-dependent interactions involving lactation number, region, season and age of calving, within-herd class of milk production, fat and protein content, class of annual variation in herd size and the random herd-year effect. Random sire and maternal grandsire effects were added to the model to estimate genetic parameters. The within-lactation Weibull baseline hazards were assumed to change at 0, 270, 380 days and at drying date. Within-herd milk production class had the largest contribution to the relative risk of culling. Relative culling risk increased with lower protein and fat per cent production classes and late age at first calving. Cows in large shrinking herds also had high relative risk of culling. The estimate of the sire genetic variance was 0.0472 ± 0.0017 giving a theoretical heritability estimate of 0.11 in the complete absence of censoring. Genetic trends indicated an overall decrease in functional longevity of 0.014 standard deviation from 1995 to 2007. There are opportunities for including the trait in the breeding objective for South African Holstein cattle.
Wang, Lu; Xu, Lisheng; Zhao, Dazhe; Yao, Yang; Song, Dan
2015-04-01
Because arterial pulse waves contain vital information related to the condition of the cardiovascular system, considerable attention has been devoted to the study of pulse waves in recent years. Accurate acquisition is essential to investigate arterial pulse waves. However, at the stage of developing equipment for acquiring and analyzing arterial pulse waves, specific pulse signals may be unavailable for debugging and evaluating the system under development. To produce test signals that reflect specific physiological conditions, in this paper, an arterial pulse wave generator has been designed and implemented using a field programmable gate array (FPGA), which can produce the desired pulse waves according to the feature points set by users. To reconstruct a periodic pulse wave from the given feature points, a method known as piecewise Gaussian-cosine fitting is also proposed in this paper. Using a test database that contains four types of typical pulse waves with each type containing 25 pulse wave signals, the maximum residual error of each sampling point of the fitted pulse wave in comparison with the real pulse wave is within 8%. In addition, the function for adding baseline drift and three types of noises is integrated into the developed system because the baseline occasionally wanders, and noise needs to be added for testing the performance of the designed circuits and the analysis algorithms. The proposed arterial pulse wave generator can be considered as a special signal generator with a simple structure, low cost and compact size, which can also provide flexible solutions for many other related research purposes.
High Accuracy Attitude Control of a Spacecraft Using Feedback Linearization
1992-05-01
and Spacecraft Body from Gyro Measurements ......... .................................. 119 D.2 An Approximation to Exact Linearization using IPSRU...31 2-4 Attitude Determination and Control System Architecture ................. 33 3-1 Exact Linearization Using Nonlinear Feedback...though basic techniques were adapted from recent references on the use of exact linearization (such as [8] and [27]), the specific control approach
Lanzarotta, Adam
2015-01-01
Theoretical and empirical detection limits have been estimated for aripiprazole (analyte) in alpha lactose monohydrate (matrix model pharmaceutical formulation) using a micro-attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopic imaging instrument equipped with a linear array detector and a 1.5 mm germanium hemisphere internal reflection element (IRE). The instrument yielded a theoretical detection limit of 0.0035% (35 parts per million (ppm)) when operating under diffraction-limited conditions, which was 49 times lower than what was achieved with a traditional macro-ATR instrument operating under practical conditions (0.17%, 1700 ppm). However, these results may not be achievable for most analyses because the detection limits will be particle size limited, rather than diffraction limited, for mixtures with average particle diameters greater than 8.3 μm (most pharmaceutical samples). For example, a theoretical detection limit of 0.028% (280 ppm) was calculated for an experiment operating under particle size-limited conditions where the average particle size was 23.4 μm. These conditions yielded a detection limit of 0.022% (220 ppm) when measured empirically, which was close to the theoretical value and only eight times lower than that of a faster, more simplistic macro-ATR instrument. Considering the longer data acquisition and processing times characteristic of the micro-ATR imaging approach (minutes or even hours versus seconds), the cost-benefit ratio may not often be favorable for the analysis of analytes in matrices that exhibit only a few overlapping absorptions (low-interfering matrices such as alpha lactose monohydrate) using this technique compared to what can be achieved using macro-ATR. However, the advantage was significant for detecting analytes in more complex matrices (those that exhibited several overlapping absorptions with the analyte) because the detection limit of the macro-ATR approach was highly formulation
Approximate Green's function methods for HZE transport in multilayered materials
NASA Technical Reports Server (NTRS)
Wilson, John W.; Badavi, Francis F.; Shinn, Judy L.; Costen, Robert C.
1993-01-01
A nonperturbative analytic solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport in multilayered materials. The code is established to operate on the Langley nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code was found to be highly efficient and compared well with the perturbation approximation.
Nonlinear programming extensions to rational function approximations of unsteady aerodynamics
NASA Technical Reports Server (NTRS)
Tiffany, Sherwood H.; Adams, William M., Jr.
1987-01-01
This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.
NASA Technical Reports Server (NTRS)
Halyo, N.; Caglayan, A. K.
1976-01-01
This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.
Parameterized Linear Longitudinal Airship Model
NASA Technical Reports Server (NTRS)
Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph
2010-01-01
A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics
NASA Astrophysics Data System (ADS)
2001-05-01
the reason for this strange behaviour: the comet's "dirty snowball" nucleus had split into two pieces (IAUC 7616 [1]). During the splitting of the nucleus, fresh material from the interior of this frozen body is suddenly exposed to the sunlight, causing a rapid increase in the evaporation process. More cometary material is released and the overall brightness increases, as more sunlight is reflected off the dust around the nucleus. The VLT observes three fragments But Comet LINEAR has just shown that it is good for another surprise. When astronomers at ESO's Paranal Observatory [2] turned the 8.2-m VLT MELIPAL telescope (UT3) towards that object in the evening of May 14, they noted that one of the two pieces of the nucleus appeared somewhat elongated. The comet is rapidly approaching the Sun - it will pass through its perihelion (the point closest to the Sun) on May 25, and it was quite low in the sky (about 20° above the western horizon). Accordingly, the image quality was not perfect, but there was no doubt that something was going on with the fragment that was closest to the Sun (denoted "B"). And indeed, when the 8.2-m VLT YEPUN telescope (UT4) obtained another image of the comet in the evening of May 16, it was obvious that fragment "B" had split into two, see PR Photos 18a-b/01 . In fact, the astronomers suspect that there may be other, smaller pieces. The distance between the two pieces of nucleus "B" of Comet LINEAR (now denoted "B1" and "B2") was only about 1 arcsec, or approximately 500 km (projected) at the present distance of the comet from the Earth (about 100 million km). The distance between these and the other nucleus ("A") increased from about 6000 km (May 14) to 7000 km (May 16). The ESO astronomers have reported their detailed findings in IAU Circular 7627 [1]. They also note that the shape of the bright cloud (the "coma") around components "B1" and "B2" is quite unsual - this is well visible on the false-colour PR Photo 18b/01 . They interpret this
Hybrid approximate message passing for generalized group sparsity
NASA Astrophysics Data System (ADS)
Fletcher, Alyson K.; Rangan, Sundeep
2013-09-01
We consider the problem of estimating a group sparse vector x ∈ Rn under a generalized linear measurement model. Group sparsity of x means the activity of different components of the vector occurs in groups - a feature common in estimation problems in image processing, simultaneous sparse approximation and feature selection with grouped variables. Unfortunately, many current group sparse estimation methods require that the groups are non-overlapping. This work considers problems with what we call generalized group sparsity where the activity of the different components of x are modeled as functions of a small number of boolean latent variables. We show that this model can incorporate a large class of overlapping group sparse problems including problems in sparse multivariable polynomial regression and gene expression analysis. To estimate vectors with such group sparse structures, the paper proposes to use a recently-developed hybrid generalized approximate message passing (HyGAMP) method. Approximate message passing (AMP) refers to a class of algorithms based on Gaussian and quadratic approximations of loopy belief propagation for estimation of random vectors under linear measurements. The HyGAMP method extends the AMP framework to incorporate priors on x described by graphical models of which generalized group sparsity is a special case. We show that the HyGAMP algorithm is computationally efficient, general and offers superior performance in certain synthetic data test cases.
First and second order convex approximation strategies in structural optimization
NASA Technical Reports Server (NTRS)
Fleury, C.
1989-01-01
In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.
Integral approximants for functions of higher monodromic dimension
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
On current sheet approximations in models of eruptive flares
NASA Technical Reports Server (NTRS)
Bungey, T. N.; Forbes, T. G.
1994-01-01
We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.
NASA Astrophysics Data System (ADS)
Young, T.
This book is intended to be used as a textbook in a one-semester course at a variety of levels. Because of self-study features incorporated, it may also be used by practicing electronic engineers as a formal and thorough introduction to the subject. The distinction between linear and digital integrated circuits is discussed, taking into account digital and linear signal characteristics, linear and digital integrated circuit characteristics, the definitions for linear and digital circuits, applications of digital and linear integrated circuits, aspects of fabrication, packaging, and classification and numbering. Operational amplifiers are considered along with linear integrated circuit (LIC) power requirements and power supplies, voltage and current regulators, linear amplifiers, linear integrated circuit oscillators, wave-shaping circuits, active filters, DA and AD converters, demodulators, comparators, instrument amplifiers, current difference amplifiers, analog circuits and devices, and aspects of troubleshooting.