Orthogonal functions, discrete variable representation, and generalized gauss quadratures

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2002-01-01

in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions......, the distinction between spectral and grid approaches becomes blurred. In fact, the two approaches can be related by a similarity transformation. By the exploitation of this idea, calculations can be considerably simplified by removing the need to compute difficult matrix elements of the Hamiltonian...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities

Science.gov (United States)

Bauer, Daniel J.; Curran, Patrick J.

2004-01-01

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…

A uniaxial cyclic elastoplastic constitutive law with a discrete memory variable

International Nuclear Information System (INIS)

Taheri, S.

1991-01-01

At present, the study on cyclic elastoplastic constitutive laws is focused on nonproportional loading, but for uniaxial loading, some problems still exist. For example, the possibility for a law to describe simultaneously the ratcheting in nonsymmetrical load-controlled test, elastic and plastic shakedown in symmetrical and nonsymmetrical ones. Here a law is presented, which in addition to previous phenomena, describes the cyclic hardening in a pushpull test, the cyclic softening after overloading and also the dependence of cyclic strain-stress curves on the history of loading. These are the usual properties of 316 stainless steel at room temperature. This law uses an internal discrete memory variable: the plastic strain at the last unloading. On the other hand, the choice of all macroscopic variables is justified by a microscopic analysis. This law has been also extended to a three-dimensional case. Regarding the microstructure under cyclic loading, plastic shakedown and ratcheting are discussed. The definition of macroscopic variables taking account of microstructure and uniaxial constitutive law are described. (K.I.)

Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

Directory of Open Access Journals (Sweden)

Sandvik Leiv

2011-04-01

Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks

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Xing-Fang Huang

2017-03-01

Full Text Available This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and identically distributed positive random variables with a finite upper endpoint, but a general dependence structure exists between each pair of the insurance risks and the financial risks. Following the works of Yang and Yuen in 2016, we derive some asymptotic relations for the finite-time and infinite-time ruin probabilities. As a complement, we demonstrate our obtained result through a Crude Monte Carlo (CMC simulation with asymptotics.

Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

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Yue Wu

2017-01-01

Full Text Available Firefly Algorithm (FA, for short is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

Classifier-guided sampling for discrete variable, discontinuous design space exploration: Convergence and computational performance

Energy Technology Data Exchange (ETDEWEB)

Backlund, Peter B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shahan, David W. [HRL Labs., LLC, Malibu, CA (United States); Seepersad, Carolyn Conner [Univ. of Texas, Austin, TX (United States)

2014-04-22

A classifier-guided sampling (CGS) method is introduced for solving engineering design optimization problems with discrete and/or continuous variables and continuous and/or discontinuous responses. The method merges concepts from metamodel-guided sampling and population-based optimization algorithms. The CGS method uses a Bayesian network classifier for predicting the performance of new designs based on a set of known observations or training points. Unlike most metamodeling techniques, however, the classifier assigns a categorical class label to a new design, rather than predicting the resulting response in continuous space, and thereby accommodates nondifferentiable and discontinuous functions of discrete or categorical variables. The CGS method uses these classifiers to guide a population-based sampling process towards combinations of discrete and/or continuous variable values with a high probability of yielding preferred performance. Accordingly, the CGS method is appropriate for discrete/discontinuous design problems that are ill-suited for conventional metamodeling techniques and too computationally expensive to be solved by population-based algorithms alone. In addition, the rates of convergence and computational properties of the CGS method are investigated when applied to a set of discrete variable optimization problems. Results show that the CGS method significantly improves the rate of convergence towards known global optima, on average, when compared to genetic algorithms.

Discrete rate and variable power adaptation for underlay cognitive networks

KAUST Repository

Abdallah, Mohamed M.; Salem, Ahmed H.; Alouini, Mohamed-Slim; Qaraqe, Khalid A.

2010-01-01

We consider the problem of maximizing the average spectral efficiency of a secondary link in underlay cognitive networks. In particular, we consider the network setting whereby the secondary transmitter employs discrete rate and variable power

Finite element discretization of Darcy's equations with pressure dependent porosity

KAUST Repository

Girault, Vivette

2010-02-23

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.

The discrete spectrum in azimuthally dependent transport theory

International Nuclear Information System (INIS)

Garcia, R.D.M.; Siewert, C.E.

1989-01-01

The discrete spectrum for each component of a Fourier decomposition of the azimuthally dependent transport equation is analyzed. For a non-multiplying medium described by an L th -order scattering law, the problem of determining the zeros of the dispersion function for the m th Fourier component is formulated in terms of Sturm sequences. In particular, a straightforward application of the Sturm-sequence property is used to compute the number of discrete eigenvalue pairs κ m and to show that either κ m = γ m or κ m = γ m + 1, where γ m denotes the number of zeros of the Chandrasekhar polynomial g m L+1 (ξ) which are greater than unity. It is also shown how Sturm sequences can be used to construct effective algorithms to compute and to refine estimates of the discrete eigenvalues. Results are presented for a test problem. (author) [pt

The large discretization step method for time-dependent partial differential equations

Science.gov (United States)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

International Nuclear Information System (INIS)

Yu, Dequan; Cong, Shu-Lin; Sun, Zhigang

2015-01-01

Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

Energy Technology Data Exchange (ETDEWEB)

Yu, Dequan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Cong, Shu-Lin, E-mail: shlcong@dlut.edu.cn [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Sun, Zhigang, E-mail: zsun@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026 (China)

2015-09-08

Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method.

Micro-macro multilevel latent class models with multiple discrete individual-level variables

NARCIS (Netherlands)

Bennink, M.; Croon, M.A.; Kroon, B.; Vermunt, J.K.

2016-01-01

An existing micro-macro method for a single individual-level variable is extended to the multivariate situation by presenting two multilevel latent class models in which multiple discrete individual-level variables are used to explain a group-level outcome. As in the univariate case, the

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

Directory of Open Access Journals (Sweden)

Hideki Katagiri

2017-10-01

Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.

Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.

Science.gov (United States)

Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

2011-10-01

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Pricing of path dependent derivatives with discretely monitored underlying assets

Science.gov (United States)

Choi, Hyomin

This dissertation presents two different approaches to path dependent option pricing with discrete sampling. Provided the underlying asset of a path dependent derivative contract follows an affine process, we use the forward characteristic method to evaluate its fair price. Our study shows that the valuation method is numerically accessible as long as the contract payoff is a linear combination of log return of its underlying asset price. We compute various examples of such contracts and give contract-tailored formulas that we use in these examples. In the second part, we consider variance options under stochastic volatility model. We analyze the difference between variance option prices with discrete and continuous sampling as a function of N, the number of observations made in the former. We find the series expansion of the difference with respect to 1/N and find its leading term. By adding this leading term to the value of continuously sampled variance option, we obtain a simple and well-understood approximation of discretely sample variance option price.

Diabatic potential-optimized discrete variable representation: application to photodissociation process of the CO molecule

International Nuclear Information System (INIS)

Bitencourt, Ana Carla P; Prudente, Frederico V; Vianna, Jose David M

2007-01-01

We propose a new numerically optimized discrete variable representation using eigenstates of diabatic Hamiltonians. This procedure provides an efficient method to solve non-adiabatic coupling problems since the generated basis sets take into account information on the diabatic potentials. The method is applied to the B 1 Σ + - D' 1 Σ + Rydberg-valence predissociation interaction in the CO molecule. Here we give an account of the discrete variable representation and present the procedure for the calculation of its optimized version, which we apply to obtain the total photodissociation cross sections of the CO molecule

A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics

International Nuclear Information System (INIS)

Hoffman, A. J.; Lee, J. C.

2013-01-01

A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependence of the angular flux time derivative. The accuracy of this method is assessed through implementation in the neutron transport code DeCART. The method is employed with variable-order local source representation to model a TWIGL transient. The results demonstrate that this method is accurate and more efficient than the discretized method. (authors)

Discrete diffusion Monte Carlo for frequency-dependent radiative transfer

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.

2011-01-01

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique. (author)

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2010-01-01

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

Discrete dislocation plasticity analysis of loading rate-dependent static friction.

Science.gov (United States)

Song, H; Deshpande, V S; Van der Giessen, E

2016-08-01

From a microscopic point of view, the frictional force associated with the relative sliding of rough surfaces originates from deformation of the material in contact, by adhesion in the contact interface or both. We know that plastic deformation at the size scale of micrometres is not only dependent on the size of the contact, but also on the rate of deformation. Moreover, depending on its physical origin, adhesion can also be size and rate dependent, albeit different from plasticity. We present a two-dimensional model that incorporates both discrete dislocation plasticity inside a face-centred cubic crystal and adhesion in the interface to understand the rate dependence of friction caused by micrometre-size asperities. The friction strength is the outcome of the competition between adhesion and discrete dislocation plasticity. As a function of contact size, the friction strength contains two plateaus: at small contact length [Formula: see text], the onset of sliding is fully controlled by adhesion while for large contact length [Formula: see text], the friction strength approaches the size-independent plastic shear yield strength. The transition regime at intermediate contact size is a result of partial de-cohesion and size-dependent dislocation plasticity, and is determined by dislocation properties, interfacial properties as well as by the loading rate.

Finite element discretization of Darcy's equations with pressure dependent porosity

KAUST Repository

Girault, Vivette; Murat, Franç ois; Salgado, Abner

2010-01-01

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

International Nuclear Information System (INIS)

Liu Yurong; Wang Zidong; Liu Xiaohui

2008-01-01

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions

Reliability-Based Design Optimization of Trusses with Linked-Discrete Design Variables using the Improved Firefly Algorithm

Directory of Open Access Journals (Sweden)

N. M. Okasha

2016-04-01

Full Text Available In this paper, an approach for conducting a Reliability-Based Design Optimization (RBDO of truss structures with linked-discrete design variables is proposed. The sections of the truss members are selected from the AISC standard tables and thus the design variables that represent the properties of each section are linked. Latin hypercube sampling is used in the evaluation of the structural reliability. The improved firefly algorithm is used for the optimization solution process. It was found that in order to use the improved firefly algorithm for efficiently solving problems of reliability-based design optimization with linked-discrete design variables; it needs to be modified as proposed in this paper to accelerate its convergence.

The selection of a mode of urban transportation: Integrating psychological variables to discrete choice models

International Nuclear Information System (INIS)

Cordoba Maquilon, Jorge E; Gonzalez Calderon, Carlos A; Posada Henao, John J

2011-01-01

A study using revealed preference surveys and psychological tests was conducted. Key psychological variables of behavior involved in the choice of transportation mode in a population sample of the Metropolitan Area of the Valle de Aburra were detected. The experiment used the random utility theory for discrete choice models and reasoned action in order to assess beliefs. This was used as a tool for analysis of the psychological variables using the sixteen personality factor questionnaire (16PF test). In addition to the revealed preference surveys, two other surveys were carried out: one with socio-economic characteristics and the other with latent indicators. This methodology allows for an integration of discrete choice models and latent variables. The integration makes the model operational and quantifies the unobservable psychological variables. The most relevant result obtained was that anxiety affects the choice of urban transportation mode and shows that physiological alterations, as well as problems in perception and beliefs, can affect the decision-making process.

Stable Graphical Model Estimation with Random Forests for Discrete, Continuous, and Mixed Variables

OpenAIRE

Fellinghauer, Bernd; Bühlmann, Peter; Ryffel, Martin; von Rhein, Michael; Reinhardt, Jan D.

2011-01-01

A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among mixed-type, i.e. continuous and discrete, variables. The number of edges is a tuning parameter in any graphical model estimator and there is no obvious number that constitutes a good choice. Stability Selection helps choosing this parameter with respect to...

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis.

Science.gov (United States)

Sakhanenko, Nikita A; Kunert-Graf, James; Galas, David J

2017-12-01

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. We present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis-that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. We illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

Truss topology optimization with discrete design variables by outer approximation

DEFF Research Database (Denmark)

Stolpe, Mathias

2015-01-01

Several variants of an outer approximation method are proposed to solve truss topology optimization problems with discrete design variables to proven global optimality. The objective is to minimize the volume of the structure while satisfying constraints on the global stiffness of the structure...... for classical outer approximation approaches applied to optimal design problems. A set of two- and three-dimensional benchmark problems are solved and the numerical results suggest that the proposed approaches are competitive with other special-purpose global optimization methods for the considered class...... under the applied loads. We extend the natural problem formulation by adding redundant force variables and force equilibrium constraints. This guarantees that the designs suggested by the relaxed master problems are capable of carrying the applied loads, a property which is generally not satisfied...

A New Multidisciplinary Design Optimization Method Accounting for Discrete and Continuous Variables under Aleatory and Epistemic Uncertainties

Directory of Open Access Journals (Sweden)

Hong-Zhong Huang

2012-02-01

Full Text Available Various uncertainties are inevitable in complex engineered systems and must be carefully treated in design activities. Reliability-Based Multidisciplinary Design Optimization (RBMDO has been receiving increasing attention in the past decades to facilitate designing fully coupled systems but also achieving a desired reliability considering uncertainty. In this paper, a new formulation of multidisciplinary design optimization, namely RFCDV (random/fuzzy/continuous/discrete variables Multidisciplinary Design Optimization (RFCDV-MDO, is developed within the framework of Sequential Optimization and Reliability Assessment (SORA to deal with multidisciplinary design problems in which both aleatory and epistemic uncertainties are present. In addition, a hybrid discrete-continuous algorithm is put forth to efficiently solve problems where both discrete and continuous design variables exist. The effectiveness and computational efficiency of the proposed method are demonstrated via a mathematical problem and a pressure vessel design problem.

Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

NARCIS (Netherlands)

Wu, Yue; Li, Q.; Hu, Qingjie; Borgart, A.

2017-01-01

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly,

State control of discrete-time linear systems to be bound in state variables by equality constraints

International Nuclear Information System (INIS)

Filasová, Anna; Krokavec, Dušan; Serbák, Vladimír

2014-01-01

The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach

A highly efficient SDRAM controller supporting variable-length burst access and batch process for discrete reads

Science.gov (United States)

Li, Nan; Wang, Junzheng

2016-03-01

A highly efficient Synchronous Dynamic Random Access Memory (SDRAM) controller supporting variable-length burst access and batch process for discrete reads is proposed in this paper. Based on the Principle of Locality, command First In First Out (FIFO) and address range detector are designed within this controller to accelerate its responses to discrete read requests, which dramatically improves the average Effective Bus Utilization Ratio (EBUR) of SDRAM. Our controller is finally verified by driving the Micron 256-Mb SDRAM MT48LC16M16A2. Successful simulation and verification results show that our controller exhibits much higher EBUR than do most existing designs in case of discrete reads.

Peculiar symmetry structure of some known discrete nonautonomous equations

International Nuclear Information System (INIS)

Garifullin, R N; Habibullin, I T; Yamilov, R I

2015-01-01

We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler−Bobenko−Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler−Bobenko−Suris list. (paper)

Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

Directory of Open Access Journals (Sweden)

S. K. Barik

2012-01-01

Full Text Available Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.

Study on the security of discrete-variable quantum key distribution over non-Markovian channels

International Nuclear Information System (INIS)

Huang Peng; Zhu Jun; He Guangqiang; Zeng Guihua

2012-01-01

The dynamic of the secret key rate of the discrete-variable quantum key distribution (QKD) protocol over the non-Markovian quantum channel is investigated. In particular, we calculate the secret key rate for the six-state protocol over non-Markovian depolarizing channels with coloured noise and Markovian depolarizing channels with Gaussian white noise, respectively. We find that the secure secret key rate for the non-Markovian depolarizing channel will be larger than the Markovian one under the same conditions even when their upper bounds of tolerable quantum bit error rate are equal. This indicates that this coloured noise in the non-Markovian depolarizing channel can enhance the security of communication. Moreover, we show that the secret key rate fluctuates near the secure point when the coupling strength of the system with the environment is high. The results demonstrate that the non-Markovian effects of the transmission channel can have a positive impact on the security of discrete-variable QKD. (paper)

A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

KAUST Repository

Zhu, Guangpu

2018-01-26

In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation with the generalized Navier boundary condition. Variable densities and viscosities are incorporated in this model. A rigorous proof of energy stability is provided for the fully discrete scheme based on a semi-implicit temporal discretization and a finite difference method on the staggered grids for the spatial discretization. A splitting method based on the pressure stabilization is implemented to solve the Navier-Stokes equation, while the stabilization approach is also used for the Cahn-Hilliard equation. Numerical results in both 2-D and 3-D demonstrate the accuracy, efficiency and decaying property of discrete energy of the proposed scheme.

Discretized representations of harmonic variables by bilateral Jacobi operators

Directory of Open Access Journals (Sweden)

Andreas Ruffing

2000-01-01

Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

Future-dependent Flow Policies with Prophetic Variables

DEFF Research Database (Denmark)

Li, Ximeng; Nielson, Flemming; Nielson, Hanne Riis

2016-01-01

future-dependent flow policies- policies that can depend on not only the current values of variables, but also their final values. The final values are referred to using what we call prophetic variables, just as the initial values can be referenced using logical variables in Hoare logic. We develop...... and enforce a notion of future-dependent security for open systems, in the spirit of "non-deducibility on strategies". We also illustrate our approach in scenarios where future-dependency has advantages over present-dependency and avoids mixtures of upgradings and downgradings....

The discrete ordinates method for solving the azimuthally dependent transport equation in plane geometry

International Nuclear Information System (INIS)

Chalhoub, Ezzat Selim

1997-01-01

The method of discrete ordinates is applied to the solution of the slab albedo problem with azimuthal dependence in transport theory. A new set of quadratures appropriate to the problem is introduced. In addition to the ANISN code, modified to include the proposed formalism, two new programs, PEESNC and PEESNA, which were created on the basis of the discrete ordinates formalism, using the direct integration method and the analytic solution method respectively, are used in the generation of results for a few sample problems. Program PEESNC was created to validate the results obtained with the discrete ordinates method and the finite difference approximation (ANISN), while program PEESNA was developed in order to implement an analytical discrete ordinates formalism, which provides more accurate results. The obtained results for selected sample problems are compared with highly accurate numerical results published in the literature. Compared to ANISN and PEESNC, program PEESNA presents a greater efficiency in execution time and much more precise numerical results. (author)

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

International Nuclear Information System (INIS)

Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

2014-01-01

The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

Discrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index

International Nuclear Information System (INIS)

Liu, L.H.

2004-01-01

A discrete curved ray-tracing method is developed to analyze the radiative transfer in one-dimensional absorbing-emitting semitransparent slab with variable spatial refractive index. The curved ray trajectory is locally treated as straight line and the complicated and time-consuming computation of ray trajectory is cut down. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example to examine the accuracy of the proposed method. The temperature distributions are determined by the proposed method and compared with the data in references, which are obtained by other different methods. The results show that the discrete curved ray-tracing method has a good accuracy in solving the radiative transfer in one-dimensional semitransparent slab with variable spatial refractive index

Discrete rate and variable power adaptation for underlay cognitive networks

KAUST Repository

Abdallah, Mohamed M.

2010-01-01

We consider the problem of maximizing the average spectral efficiency of a secondary link in underlay cognitive networks. In particular, we consider the network setting whereby the secondary transmitter employs discrete rate and variable power adaptation under the constraints of maximum average transmit power and maximum average interference power allowed at the primary receiver due to the existence of an interference link between the secondary transmitter and the primary receiver. We first find the optimal discrete rates assuming a predetermined partitioning of the signal-to-noise ratio (SNR) of both the secondary and interference links. We then present an iterative algorithm for finding a suboptimal partitioning of the SNR of the interference link assuming a fixed partitioning of the SNR of secondary link selected for the case where no interference link exists. Our numerical results show that the average spectral efficiency attained by using the iterative algorithm is close to that achieved by the computationally extensive exhaustive search method for the case of Rayleigh fading channels. In addition, our simulations show that selecting the optimal partitioning of the SNR of the secondary link assuming no interference link exists still achieves the maximum average spectral efficiency for the case where the average interference constraint is considered. © 2010 IEEE.

Reward-dependent modulation of movement variability.

Science.gov (United States)

Pekny, Sarah E; Izawa, Jun; Shadmehr, Reza

2015-03-04

Movement variability is often considered an unwanted byproduct of a noisy nervous system. However, variability can signal a form of implicit exploration, indicating that the nervous system is intentionally varying the motor commands in search of actions that yield the greatest success. Here, we investigated the role of the human basal ganglia in controlling reward-dependent motor variability as measured by trial-to-trial changes in performance during a reaching task. We designed an experiment in which the only performance feedback was success or failure and quantified how reach variability was modulated as a function of the probability of reward. In healthy controls, reach variability increased as the probability of reward decreased. Control of variability depended on the history of past rewards, with the largest trial-to-trial changes occurring immediately after an unrewarded trial. In contrast, in participants with Parkinson's disease, a known example of basal ganglia dysfunction, reward was a poor modulator of variability; that is, the patients showed an impaired ability to increase variability in response to decreases in the probability of reward. This was despite the fact that, after rewarded trials, reach variability in the patients was comparable to healthy controls. In summary, we found that movement variability is partially a form of exploration driven by the recent history of rewards. When the function of the human basal ganglia is compromised, the reward-dependent control of movement variability is impaired, particularly affecting the ability to increase variability after unsuccessful outcomes. Copyright © 2015 the authors 0270-6474/15/354015-10$15.00/0.

A cyclic constitutive law for metals with a semi-discrete memory variable for description of ratcheting phenomena

International Nuclear Information System (INIS)

Andrieux, S.; Schoenberger, P.; Taheri, S.

1993-01-01

The study of cyclic elastoplastic constitutive laws is, at the moment, focused on non proportional loadings, but for uniaxial loadings some problems remain, as for example the ability for a law to describe simultaneously ratcheting in non symmetrical load-controlled test, elastic and plastic shakedown in symmetrical and non symmetrical ones. We have proposed in a law with a discrete memory variable which, in addition to previous phenomena, describes the cyclic hardening in a pushpull test, and the cyclic softening after overloading. A modified law has been proposed to take into account the dependence of cyclic strain stress curve on the history of loading. The extension to 3D situations of this law is proposed. The discrete nature of the memory leads to discontinuity problems for some loading paths, a modification is then proposed which uses a differential evolution law. For large enough uniaxial cycles, the uniaxial law is nevertheless recovered. In this paper, an incremental form of the implicit evolution problem is given, and we describe the implementation of this model in the Code Aster - a thermomechanical structural software using the finite element method (f.e.m) developed at Electricite de France. Comparison between experiment and numerical results is given for uniaxial ratcheting, non proportional strain controlled test

ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE

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Isaac Yaesh

2013-01-01

Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.

Time-dependent switched discrete-time linear systems control and filtering

CERN Document Server

Zhang, Lixian; Shi, Peng; Lu, Qiugang

2016-01-01

This book focuses on the basic control and filtering synthesis problems for discrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds and motivations of switched systems, the definitions of the typical time-dependent switching signals, the differences and links to other types of systems with hybrid characteristics and a literature review mainly on the control and filtering for the underlying systems. By summarizing the multiple Lyapunov-like functions (MLFs) approach in which different requirements on comparisons of Lyapunov function values at switching instants, a series of methodologies are developed for the issues on stability and stabilization, and l2-gain performance or tube-based robustness for l∞ disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and filtering problems for the time-dependent switched linear systems with either polytopic uncertainties or measurable time-varying...

Discrete model of opinion changes using knowledge and emotions as control variables.

Directory of Open Access Journals (Sweden)

Pawel Sobkowicz

Full Text Available We present a new model of opinion changes dependent on the agents emotional state and their information about the issue in question. Our goal is to construct a simple, yet nontrivial and flexible representation of individual attitude dynamics for agent based simulations, that could be used in a variety of social environments. The model is a discrete version of the cusp catastrophe model of opinion dynamics in which information is treated as the normal factor while emotional arousal (agitation level determining agent receptiveness and rationality is treated as the splitting factor. Both variables determine the resulting agent opinion, which itself can be in favor of the studied position, against it, or neutral. Thanks to the flexibility of implementing communication between the agents, the model is potentially applicable in a wide range of situations. As an example of the model application, we study the dynamics of a set of agents communicating among themselves via messages. In the example, we chose the simplest, fully connected communication topology, to focus on the effects of the individual opinion dynamics, and to look for stable final distributions of agents with different emotions, information and opinions. Even for such simplified system, the model shows complex behavior, including phase transitions due to symmetry breaking by external propaganda.

Discrete model of opinion changes using knowledge and emotions as control variables.

Science.gov (United States)

Sobkowicz, Pawel

2012-01-01

We present a new model of opinion changes dependent on the agents emotional state and their information about the issue in question. Our goal is to construct a simple, yet nontrivial and flexible representation of individual attitude dynamics for agent based simulations, that could be used in a variety of social environments. The model is a discrete version of the cusp catastrophe model of opinion dynamics in which information is treated as the normal factor while emotional arousal (agitation level determining agent receptiveness and rationality) is treated as the splitting factor. Both variables determine the resulting agent opinion, which itself can be in favor of the studied position, against it, or neutral. Thanks to the flexibility of implementing communication between the agents, the model is potentially applicable in a wide range of situations. As an example of the model application, we study the dynamics of a set of agents communicating among themselves via messages. In the example, we chose the simplest, fully connected communication topology, to focus on the effects of the individual opinion dynamics, and to look for stable final distributions of agents with different emotions, information and opinions. Even for such simplified system, the model shows complex behavior, including phase transitions due to symmetry breaking by external propaganda.

Discrete Model of Opinion Changes Using Knowledge and Emotions as Control Variables

Science.gov (United States)

Sobkowicz, Pawel

2012-01-01

We present a new model of opinion changes dependent on the agents emotional state and their information about the issue in question. Our goal is to construct a simple, yet nontrivial and flexible representation of individual attitude dynamics for agent based simulations, that could be used in a variety of social environments. The model is a discrete version of the cusp catastrophe model of opinion dynamics in which information is treated as the normal factor while emotional arousal (agitation level determining agent receptiveness and rationality) is treated as the splitting factor. Both variables determine the resulting agent opinion, which itself can be in favor of the studied position, against it, or neutral. Thanks to the flexibility of implementing communication between the agents, the model is potentially applicable in a wide range of situations. As an example of the model application, we study the dynamics of a set of agents communicating among themselves via messages. In the example, we chose the simplest, fully connected communication topology, to focus on the effects of the individual opinion dynamics, and to look for stable final distributions of agents with different emotions, information and opinions. Even for such simplified system, the model shows complex behavior, including phase transitions due to symmetry breaking by external propaganda. PMID:22984516

Discrete factor approximations in simultaneous equation models: estimating the impact of a dummy endogenous variable on a continuous outcome.

Science.gov (United States)

Mroz, T A

1999-10-01

This paper contains a Monte Carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models. When the true model has bivariate normal disturbances, estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias; these approximation estimators dominate all the other estimators examined when the disturbances are non-normal. The experiments also indicate that one should liberally add points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages.

Multiple and dependent scattering by densely packed discrete spheres: Comparison of radiative transfer and Maxwell theory

International Nuclear Information System (INIS)

Ma, L.X.; Tan, J.Y.; Zhao, J.M.; Wang, F.Q.; Wang, C.A.

2017-01-01

The radiative transfer equation (RTE) has been widely used to deal with multiple scattering of light by sparsely and randomly distributed discrete particles. However, for densely packed particles, the RTE becomes questionable due to strong dependent scattering effects. This paper examines the accuracy of RTE by comparing with the exact electromagnetic theory. For an imaginary spherical volume filled with randomly distributed, densely packed spheres, the RTE is solved by the Monte Carlo method combined with the Percus–Yevick hard model to consider the dependent scattering effect, while the electromagnetic calculation is based on the multi-sphere superposition T-matrix method. The Mueller matrix elements of the system with different size parameters and volume fractions of spheres are obtained using both methods. The results verify that the RTE fails to deal with the systems with a high-volume fraction due to the dependent scattering effects. Apart from the effects of forward interference scattering and coherent backscattering, the Percus–Yevick hard sphere model shows good accuracy in accounting for the far-field interference effects for medium or smaller size parameters (up to 6.964 in this study). For densely packed discrete spheres with large size parameters (equals 13.928 in this study), the improvement of dependent scattering correction tends to deteriorate. The observations indicate that caution must be taken when using RTE in dealing with the radiative transfer in dense discrete random media even though the dependent scattering correction is applied. - Highlights: • The Muller matrix of randomly distributed, densely packed spheres are investigated. • The effects of multiple scattering and dependent scattering are analyzed. • The accuracy of radiative transfer theory for densely packed spheres is discussed. • Dependent scattering correction takes effect at medium size parameter or smaller. • Performance of dependent scattering correction

Intraclass Correlation Coefficients in Hierarchical Design Studies with Discrete Response Variables: A Note on a Direct Interval Estimation Procedure

Science.gov (United States)

Raykov, Tenko; Marcoulides, George A.

2015-01-01

A latent variable modeling procedure that can be used to evaluate intraclass correlation coefficients in two-level settings with discrete response variables is discussed. The approach is readily applied when the purpose is to furnish confidence intervals at prespecified confidence levels for these coefficients in setups with binary or ordinal…

Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays

Directory of Open Access Journals (Sweden)

Yonggang Chen

2008-01-01

Full Text Available This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI. Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

Science.gov (United States)

Schneeloch, James; Dixon, P. Ben; Howland, Gregory A.; Broadbent, Curtis J.; Howell, John C.

2013-03-01

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

The Propagation of Movement Variability in Time: A Methodological Approach for Discrete Movements with Multiple Degrees of Freedom

Science.gov (United States)

Krüger, Melanie; Straube, Andreas; Eggert, Thomas

2017-01-01

In recent years, theory-building in motor neuroscience and our understanding of the synergistic control of the redundant human motor system has significantly profited from the emergence of a range of different mathematical approaches to analyze the structure of movement variability. Approaches such as the Uncontrolled Manifold method or the Noise-Tolerance-Covariance decomposition method allow to detect and interpret changes in movement coordination due to e.g., learning, external task constraints or disease, by analyzing the structure of within-subject, inter-trial movement variability. Whereas, for cyclical movements (e.g., locomotion), mathematical approaches exist to investigate the propagation of movement variability in time (e.g., time series analysis), similar approaches are missing for discrete, goal-directed movements, such as reaching. Here, we propose canonical correlation analysis as a suitable method to analyze the propagation of within-subject variability across different time points during the execution of discrete movements. While similar analyses have already been applied for discrete movements with only one degree of freedom (DoF; e.g., Pearson's product-moment correlation), canonical correlation analysis allows to evaluate the coupling of inter-trial variability across different time points along the movement trajectory for multiple DoF-effector systems, such as the arm. The theoretical analysis is illustrated by empirical data from a study on reaching movements under normal and disturbed proprioception. The results show increased movement duration, decreased movement amplitude, as well as altered movement coordination under ischemia, which results in a reduced complexity of movement control. Movement endpoint variability is not increased under ischemia. This suggests that healthy adults are able to immediately and efficiently adjust the control of complex reaching movements to compensate for the loss of proprioceptive information. Further, it is

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

International Nuclear Information System (INIS)

Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

2013-01-01

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models.

Science.gov (United States)

Franke, John E; Yakubu, Abdul-Aziz

2008-12-01

The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors. In addition, we use a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark-Sacker) cycle attractor coexisting with a fixed point attractor. The basin boundaries of the coexisting attractors are fractal in nature, and the example exhibits sensitive dependence of the long-term disease dynamics on initial conditions. Furthermore, we show that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics.

TIMEX: a time-dependent explicit discrete ordinates program for the solution of multigroup transport equations with delayed neutrons

International Nuclear Information System (INIS)

Hill, T.R.; Reed, W.H.

1976-01-01

TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures

Discrete scale-free distributions and associated limit theorems

International Nuclear Information System (INIS)

Hopcraft, K I; Jakeman, E; Matthews, J O

2004-01-01

Consideration is given to the convergence properties of sums of identical, independently distributed random variables drawn from a class of discrete distributions with power-law tails, which are relevant to scale-free networks. Different limiting distributions, and rates of convergence to these limits, are identified and depend on the index of the tail. For indices ≥2, the topology evolves to a random Poisson network, but the rate of convergence can be extraordinarily slow and unlikely to be yet evident for the current size of the WWW for example. It is shown that treating discrete scale-free behaviour with continuum or mean-field approximations can lead to incorrect results. (letter to the editor)

Implementation of continuous-variable quantum key distribution with discrete modulation

Science.gov (United States)

Hirano, Takuya; Ichikawa, Tsubasa; Matsubara, Takuto; Ono, Motoharu; Oguri, Yusuke; Namiki, Ryo; Kasai, Kenta; Matsumoto, Ryutaroh; Tsurumaru, Toyohiro

2017-06-01

We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

International Nuclear Information System (INIS)

Guo, Z.; Lin, P.; Lowengrub, J.S.

2014-01-01

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C 0 finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C 0 finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme

An analytical nodal method for time-dependent one-dimensional discrete ordinates problems

International Nuclear Information System (INIS)

Barros, R.C. de

1992-01-01

In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids

Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays

International Nuclear Information System (INIS)

Karaoglu, Esra; Merdan, Huseyin

2014-01-01

Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations

TDTORT: Time-Dependent, 3-D, Discrete Ordinates, Neutron Transport Code System with Delayed Neutrons

International Nuclear Information System (INIS)

2002-01-01

1 - Description of program or function: TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation. TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. TDTORT reads ANISN-format cross-section libraries, which are not included in the package. Users may choose from several available in RSICC's data library collection which can be identified by the keyword 'ANISN FORMAT'. 2 - Methods:The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function. The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal

Validity of a Residualized Dependent Variable after Pretest Covariance Adjustments: Still the Same Variable?

Science.gov (United States)

Nimon, Kim; Henson, Robin K.

2015-01-01

The authors empirically examined whether the validity of a residualized dependent variable after covariance adjustment is comparable to that of the original variable of interest. When variance of a dependent variable is removed as a result of one or more covariates, the residual variance may not reflect the same meaning. Using the pretest-posttest…

Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials

International Nuclear Information System (INIS)

Tratnik, M.V.

1990-01-01

Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

Improved method for solving the neutron transport problem by discretization of space and energy variables

International Nuclear Information System (INIS)

Bosevski, T.

1971-01-01

The polynomial interpolation of neutron flux between the chosen space and energy variables enabled transformation of the integral transport equation into a system of linear equations with constant coefficients. Solutions of this system are the needed values of flux for chosen values of space and energy variables. The proposed improved method for solving the neutron transport problem including the mathematical formalism is simple and efficient since the number of needed input data is decreased both in treating the spatial and energy variables. Mathematical method based on this approach gives more stable solutions with significantly decreased probability of numerical errors. Computer code based on the proposed method was used for calculations of one heavy water and one light water reactor cell, and the results were compared to results of other very precise calculations. The proposed method was better concerning convergence rate, decreased computing time and needed computer memory. Discretization of variables enabled direct comparison of theoretical and experimental results

A discrete stress-strength interference model based on universal generating function

International Nuclear Information System (INIS)

An Zongwen; Huang Hongzhong; Liu Yu

2008-01-01

Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data

Silicon photonic transceiver circuit for high-speed polarization-based discrete variable quantum key distribution.

Science.gov (United States)

Cai, Hong; Long, Christopher M; DeRose, Christopher T; Boynton, Nicholas; Urayama, Junji; Camacho, Ryan; Pomerene, Andrew; Starbuck, Andrew L; Trotter, Douglas C; Davids, Paul S; Lentine, Anthony L

2017-05-29

We demonstrate a silicon photonic transceiver circuit for high-speed discrete variable quantum key distribution that employs a common structure for transmit and receive functions. The device is intended for use in polarization-based quantum cryptographic protocols, such as BB84. Our characterization indicates that the circuit can generate the four BB84 states (TE/TM/45°/135° linear polarizations) with >30 dB polarization extinction ratios and gigabit per second modulation speed, and is capable of decoding any polarization bases differing by 90° with high extinction ratios.

Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

Directory of Open Access Journals (Sweden)

Long Yuhua

2017-12-01

Full Text Available In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)

Variable speed wind turbine control by discrete-time sliding mode approach.

Science.gov (United States)

Torchani, Borhen; Sellami, Anis; Garcia, Germain

2016-05-01

The aim of this paper is to propose a new design variable speed wind turbine control by discrete-time sliding mode approach. This methodology is designed for linear saturated system. The saturation constraint is reported on inputs vector. To this end, the back stepping design procedure is followed to construct a suitable sliding manifold that guarantees the attainment of a stabilization control objective. It is well known that the mechanisms are investigated in term of the most proposed assumptions to deal with the damping, shaft stiffness and inertia effect of the gear. The objectives are to synthesize robust controllers that maximize the energy extracted from wind, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. Simulation results of the proposed scheme are presented. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Application of an efficient Bayesian discretization method to biomedical data

Directory of Open Access Journals (Sweden)

Gopalakrishnan Vanathi

2011-07-01

Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.

Improved Genetic Algorithm with Two-Level Approximation for Truss Optimization by Using Discrete Shape Variables

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Shen-yan Chen

2015-01-01

Full Text Available This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA to minimize truss weight by simultaneously optimizing size, shape, and topology variables. On the basis of a previously presented truss sizing/topology optimization method based on two-level approximation and genetic algorithm (GA, a new method for adding shape variables is presented, in which the nodal positions are corresponding to a set of coordinate lists. A uniform optimization model including size/shape/topology variables is established. First, a first-level approximate problem is constructed to transform the original implicit problem to an explicit problem. To solve this explicit problem which involves size/shape/topology variables, GA is used to optimize individuals which include discrete topology variables and shape variables. When calculating the fitness value of each member in the current generation, a second-level approximation method is used to optimize the continuous size variables. With the introduction of shape variables, the original optimization algorithm was improved in individual coding strategy as well as GA execution techniques. Meanwhile, the update strategy of the first-level approximation problem was also improved. The results of numerical examples show that the proposed method is effective in dealing with the three kinds of design variables simultaneously, and the required computational cost for structural analysis is quite small.

Discretization of 3d gravity in different polarizations

Science.gov (United States)

Dupuis, Maïté; Freidel, Laurent; Girelli, Florian

2017-10-01

We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

A three dimensional elastoplastic cyclic constitutive law with a semi discrete variable and a ratchetting stress

International Nuclear Information System (INIS)

Geyer, P.; Proix, J.M.; Jayet-Gendrot, S.; Schoenberger, P.; Taheri, S.

1995-01-01

The study of cyclic elastoplastic constitutive law is, at the moment, focused on non proportional loadings, but for uniaxial loadings some problems remain, as for example the ability for a law to describe simultaneously ratcheting (constant increment of strain) in non symmetrical ones. We propose a law with a discrete memory variable, the plastic strain at the last unloading, and a ratchetting stress which, in addition to previous phenomena, describes the other hand the choice of all macroscopic variables is justified by a microscopic analysis. The extension to 3D situations of this law is proposed. The discrete nature of the memory leads to discontinuity problems for some loading paths, a modification is then proposed which uses a differential evolution law. For large enough uniaxial cycles, the uniaxial law is nevertheless recovered. An incremental form of he implicit evolution problem is given, and we describe the implementation of this model in the Code Aster a thermomechanical structural software using the f.e.m. developed at Electricite de France. For a 316 stainless steel we present comparisons between experiments and numerical results in uniaxial and biaxial ratchetting and non proportional strain controlled test (circular, square, stair loading). (authors). 13 refs., 10 figs

Benford's law and continuous dependent random variables

Science.gov (United States)

Becker, Thealexa; Burt, David; Corcoran, Taylor C.; Greaves-Tunnell, Alec; Iafrate, Joseph R.; Jing, Joy; Miller, Steven J.; Porfilio, Jaclyn D.; Ronan, Ryan; Samranvedhya, Jirapat; Strauch, Frederick W.; Talbut, Blaine

2018-01-01

Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11% of the time, as one would expect if all digits were equally likely, but rather 30%. This phenomenon is known as Benford's Law. Analyzing which datasets adhere to Benford's Law and how quickly Benford behavior sets in are the two most important problems in the field. Most previous work studied systems of independent random variables, and relied on the independence in their analyses. Inspired by natural processes such as particle decay, we study the dependent random variables that emerge from models of decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow, and give several conjectures for other fragmentation processes. The main difficulty is that the resulting random variables are dependent. We handle this by using tools from Fourier analysis and irrationality exponents to obtain quantified convergence rates as well as introducing and developing techniques to measure and control the dependencies. The construction of these tools is one of the major motivations of this work, as our approach can be applied to many other dependent systems. As an example, we show that the n ! entries in the determinant expansions of n × n matrices with entries independently drawn from nice random variables converges to Benford's Law.

Synchronization Techniques in Parallel Discrete Event Simulation

OpenAIRE

Lindén, Jonatan

2018-01-01

Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

Discrete non-parametric kernel estimation for global sensitivity analysis

International Nuclear Information System (INIS)

Senga Kiessé, Tristan; Ventura, Anne

2016-01-01

This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.

Discrete-Time Systems

Indian Academy of Sciences (India)

We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

On Darboux-integrable semi-discrete chains

International Nuclear Information System (INIS)

Habibullin, Ismagil; Sakieva, Alfia; Zheltukhina, Natalya

2010-01-01

A differential-difference equation d/dx t (n+1,x) = f(x,t(n,x),t(n+1,x),d/dx t (n,x)) with unknown t(n, x) depending on the continuous and discrete variables x and n is studied. We call an equation of such kind Darboux integrable if there exist two functions (called integrals) F and I of a finite number of dynamical variables such that D x F = 0 and DI = I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp(n) = p(n + 1). It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for a general solution to Darboux-integrable chains is discussed and such solutions are found for a class of chains.

Analysis of transverse vibration and stability issues of discrete-continuous elastic systems with nonlinearly variable parameters

Directory of Open Access Journals (Sweden)

Jaroszewicz Jerzy

2018-01-01

Full Text Available The work is devoted to methods of analysis of vibrations and stability of discrete-continuous, multi-parameter models of beams, shafts, rotors, vanes, converting to homogeneous and one-dimensional. The properties of Cauchy's influence function and the characteristic series method were used to solve the boundary problem. It has been shown that the methods are an effective tool for solving boundary problems described by ordinary fourth-and second-order differential equations with variable parameters. Particular attention should be paid to the solution of the border problem of two-parameter elastic systems with variable distribution of parameters. Universal beam-specific equations with typical support conditions including vertical support, which do not depend on beam shape and axial load type, are recorded. The shape and type of load are considered in the form of an impact function that corresponds to any change in cross-section of the support and continuous axial load, so that the functions describing the stiffness, the mass and the continuous load are complete. As a result of the solution of the boundary vibration problem of freely bent support and any change in its cross-section, loaded with any longitudinal load, arranged on the resilient substrate, strict relations between the own frequency parameters and the load parameters were derived. Using the methods, simple calculations were made, easy to use in engineering practice and conditions of use were given. Experimental studies have confirmed the high accuracy of theoretical calculations using the proposed methods and formulas.

Comparison of small-footprint discrete return and full waveform airborne lidar data for estimating multiple forest variables

OpenAIRE

Sumnall, Matthew J.; Hill, Ross A.; Hinsley, Shelley A.

2016-01-01

The quantification of forest ecosystems is important for a variety of purposes, including the assessment of wildlife habitat, nutrient cycles, timber yield and fire propagation. This research assesses the estimation of forest structure, composition and deadwood variables from small-footprint airborne lidar data, both discrete return (DR) and full waveform (FW), acquired under leaf-on and leaf-off conditions. The field site, in the New Forest, UK, includes managed plantation and ancient, se...

Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

International Nuclear Information System (INIS)

Oliveira, J.V.P. de; Cardona, A.V.; Vilhena, M.T.M.B. de

2002-01-01

In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.

Science.gov (United States)

Cao, Hui; Zhou, Yicang; Ma, Zhien

2013-01-01

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

HIGHLY-ACCURATE MODEL ORDER REDUCTION TECHNIQUE ON A DISCRETE DOMAIN

Directory of Open Access Journals (Sweden)

L. D. Ribeiro

2015-09-01

Full Text Available AbstractIn this work, we present a highly-accurate technique of model order reduction applied to staged processes. The proposed method reduces the dimension of the original system based on null values of moment-weighted sums of heat and mass balance residuals on real stages. To compute these sums of weighted residuals, a discrete form of Gauss-Lobatto quadrature was developed, allowing a high degree of accuracy in these calculations. The locations where the residuals are cancelled vary with time and operating conditions, characterizing a desirable adaptive nature of this technique. Balances related to upstream and downstream devices (such as condenser, reboiler, and feed tray of a distillation column are considered as boundary conditions of the corresponding difference-differential equations system. The chosen number of moments is the dimension of the reduced model being much lower than the dimension of the complete model and does not depend on the size of the original model. Scaling of the discrete independent variable related with the stages was crucial for the computational implementation of the proposed method, avoiding accumulation of round-off errors present even in low-degree polynomial approximations in the original discrete variable. Dynamical simulations of distillation columns were carried out to check the performance of the proposed model order reduction technique. The obtained results show the superiority of the proposed procedure in comparison with the orthogonal collocation method.

Problems Identifying Independent and Dependent Variables

Science.gov (United States)

Leatham, Keith R.

2012-01-01

This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…

Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

Directory of Open Access Journals (Sweden)

O. M. Kwon

2012-01-01

Full Text Available The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Discretization of four types of Weyl group orbit functions

International Nuclear Information System (INIS)

Hrivnák, Jiří

2013-01-01

The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

Laplacians on discrete and quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2013-01-01

We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)

Interactions of Soliton Waves for a Generalized Discrete KdV Equation

International Nuclear Information System (INIS)

Zhou Tong; Zhu Zuo-Nong

2017-01-01

It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. (paper)

Performance on perceptual word identification is mediated by discrete states.

Science.gov (United States)

Swagman, April R; Province, Jordan M; Rouder, Jeffrey N

2015-02-01

We contrast predictions from discrete-state models of all-or-none information loss with signal-detection models of graded strength for the identification of briefly flashed English words. Previous assessments have focused on whether ROC curves are straight or not, which is a test of a discrete-state model where detection leads to the highest confidence response with certainty. We along with many others argue this certainty assumption is too constraining, and, consequently, the straight-line ROC test is too stringent. Instead, we assess a core property of discrete-state models, conditional independence, where the pattern of responses depends only on which state is entered. The conditional independence property implies that confidence ratings are a mixture of detect and guess state responses, and that stimulus strength factors, the duration of the flashed word in this report, affect only the probability of entering a state and not responses conditional on a state. To assess this mixture property, 50 participants saw words presented briefly on a computer screen at three variable flash durations followed by either a two-alternative confidence ratings task or a yes-no confidence ratings task. Comparable discrete-state and signal-detection models were fit to the data for each participant and task. The discrete-state models outperformed the signal detection models for 90 % of participants in the two-alternative task and for 68 % of participants in the yes-no task. We conclude discrete-state models are viable for predicting performance across stimulus conditions in a perceptual word identification task.

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

International Nuclear Information System (INIS)

Wu Zhengguang; Su Hongye; Chu Jian; Zhou Wuneng

2009-01-01

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

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

H∞ Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

Directory of Open Access Journals (Sweden)

Cheng Gong

2014-01-01

Full Text Available This paper investigates the H∞ filtering problem of discrete singular Markov jump systems (SMJSs with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on H∞-disturbance attenuation is presented, in which both stability and prescribed H∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependent H∞ filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI. Finally, an example is given to illustrate the effectiveness of the result.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

Science.gov (United States)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow

Geometric phases in discrete dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)

2016-10-14

In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.

Discretization-induced delays and their role in the dynamics

International Nuclear Information System (INIS)

Ramani, A; Grammaticos, B; Satsuma, J; Willox, R

2008-01-01

We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discrete one may lead to the appearance of a limit cycle. We explain that it is possible, thanks to the proper staggering of the discrete variables, to eliminate the hidden delay. However, in general, other instabilities may appear in the discrete system which can even lead to chaotic behaviour

Discrete simulation system based on artificial intelligence methods

Energy Technology Data Exchange (ETDEWEB)

Futo, I; Szeredi, J

1982-01-01

A discrete event simulation system based on the AI language Prolog is presented. The system called t-Prolog extends the traditional possibilities of simulation languages toward automatic problem solving by using backtrack in time and automatic model modification depending on logical deductions. As t-Prolog is an interactive tool, the user has the possibility to interrupt the simulation run to modify the model or to force it to return to a previous state for trying possible alternatives. It admits the construction of goal-oriented or goal-seeking models with variable structure. Models are defined in a restricted version of the first order predicate calculus using Horn clauses. 21 references.

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

Science.gov (United States)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Hoeffding’s Inequality for Sums of Dependent Random Variables

Czech Academy of Sciences Publication Activity Database

Pelekis, Christos; Ramon, J.

2017-01-01

Roč. 14, č. 6 (2017), č. článku 243. ISSN 1660-5446 Institutional support: RVO:67985807 Keywords : dependent random variables * Hoeffding’s inequality * k-wise independent random variables * martingale differences Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.868, year: 2016

Optimization of Operations Resources via Discrete Event Simulation Modeling

Science.gov (United States)

Joshi, B.; Morris, D.; White, N.; Unal, R.

1996-01-01

The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.

Coupled hydromechanical paleoclimate analyses of density-dependant groundwater flow in discretely fractured crystalline rock settings

Science.gov (United States)

Normani, S. D.; Sykes, J. F.; Jensen, M. R.

2009-04-01

A high resolution sub-regional scale (84 km2) density-dependent, fracture zone network groundwater flow model with hydromechanical coupling and pseudo-permafrost, was developed from a larger 5734 km2 regional scale groundwater flow model of a Canadian Shield setting in fractured crystalline rock. The objective of the work is to illustrate aspects of regional and sub-regional groundwater flow that are relevant to the long-term performance of a hypothetical nuclear fuel repository. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture zone network model delineated from surface features was superimposed onto an 789887 element flow domain mesh. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. The crystalline rock between these structural discontinuities was assigned properties characteristic of those reported for the Canadian Shield at the Underground Research Laboratory at Pinawa, Manitoba. Interconnectivity of permeable fracture features is an important pathway for the possibly relatively rapid migration of average water particles and subsequent reduction in residence times. The multiple 121000 year North American continental scale paleoclimate simulations are provided by W.R. Peltier using the University of Toronto Glacial Systems Model (UofT GSM). Values of ice sheet normal stress, and proglacial lake depth from the UofT GSM are applied to the sub-regional model as surface boundary conditions, using a freshwater head equivalent to the normal stress imposed by the ice sheet at its base. Permafrost depth is applied as a permeability reduction to both three-dimensional grid blocks and fractures that lie within the time varying permafrost zone. Two different paleoclimate simulations are applied to the sub-regional model to investigate the effect on the depth of glacial meltwater migration into the subsurface. In

Decomposing a Utility Function Based on Discrete Distribution Independence

DEFF Research Database (Denmark)

He, Ying; Dyer, James; Butler, John

2014-01-01

For two-attribute decision-making problems, the multilinear utility model cannot be applied when the risk aversion on one attribute depends on the level of the other attribute. We propose a family of general preference conditions called nth-degree discrete distribution independence that can...... accommodate a variety of dependence relationships between two attributes. The special case of second-degree discrete distribution independence is equivalent to the utility independence condition. We focus on third-degree discrete distribution independence that leads to a decomposition formula that contains...

On discrete stochastic processes with long-lasting time dependence in the variance

Science.gov (United States)

Queirós, S. M. D.

2008-11-01

In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of qm-exponencial, form (eqm=1 x=ex). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.

Statistical learning from nonrecurrent experience with discrete input variables and recursive-error-minimization equations

Science.gov (United States)

Carter, Jeffrey R.; Simon, Wayne E.

1990-08-01

Neural networks are trained using Recursive Error Minimization (REM) equations to perform statistical classification. Using REM equations with continuous input variables reduces the required number of training experiences by factors of one to two orders of magnitude over standard back propagation. Replacing the continuous input variables with discrete binary representations reduces the number of connections by a factor proportional to the number of variables reducing the required number of experiences by another order of magnitude. Undesirable effects of using recurrent experience to train neural networks for statistical classification problems are demonstrated and nonrecurrent experience used to avoid these undesirable effects. 1. THE 1-41 PROBLEM The statistical classification problem which we address is is that of assigning points in ddimensional space to one of two classes. The first class has a covariance matrix of I (the identity matrix) the covariance matrix of the second class is 41. For this reason the problem is known as the 1-41 problem. Both classes have equal probability of occurrence and samples from both classes may appear anywhere throughout the ddimensional space. Most samples near the origin of the coordinate system will be from the first class while most samples away from the origin will be from the second class. Since the two classes completely overlap it is impossible to have a classifier with zero error. The minimum possible error is known as the Bayes error and

Discrete Bose-Einstein spectra

International Nuclear Information System (INIS)

Vlad, Valentin I.; Ionescu-Pallas, Nicholas

2001-03-01

The Bose-Einstein energy spectrum of a quantum gas, confined in a rigid cubic box, is shown to become discrete and strongly dependent on the box geometry (size L), temperature, T and atomic mass number, A at , in the region of small γ=A at TV 1/3 . This behavior is the consequence of the random state degeneracy in the box. Furthermore, we demonstrate that the total energy does not obey the conventional law any longer, but a new law, which depends on γ and on the quantum gas fugacity. This energy law imposes a faster decrease to zero than it is classically expected, for γ→0. The lighter the gas atoms, the higher the temperatures or the box size, for the same effects in the discrete Bose-Einstein regime. (author)

Discrete Sparse Coding.

Science.gov (United States)

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

An integrable semi-discretization of the Boussinesq equation

International Nuclear Information System (INIS)

Zhang, Yingnan; Tian, Lixin

2016-01-01

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

International Nuclear Information System (INIS)

Zhu, Jiandao; Collette, Matthew

2015-01-01

The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events

On localization in the discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Bang, O.; Juul Rasmussen, J.; Christiansen, P.L.

1993-01-01

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits...

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

International Nuclear Information System (INIS)

Common, Alan K; Hone, Andrew N W

2008-01-01

The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

Fixed transaction costs and modelling limited dependent variables

NARCIS (Netherlands)

Hempenius, A.L.

1994-01-01

As an alternative to the Tobit model, for vectors of limited dependent variables, I suggest a model, which follows from explicitly using fixed costs, if appropriate of course, in the utility function of the decision-maker.

Quadratic time dependent Hamiltonians and separation of variables

International Nuclear Information System (INIS)

Anzaldo-Meneses, A.

2017-01-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing.

Science.gov (United States)

Scarani, Valerio; Renner, Renato

2008-05-23

We derive a bound for the security of quantum key distribution with finite resources under one-way postprocessing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols such as Bennett-Brassard 1984 and six-states protocol. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N approximately 10(5) signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Spatial discretizations for self-adjoint forms of the radiative transfer equations

International Nuclear Information System (INIS)

Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

2006-01-01

There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

An integrable semi-discretization of the Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)

2016-10-23

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Directory of Open Access Journals (Sweden)

Zhenhua Hu

2013-01-01

Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Discrete Quantum Gravity in the Regge Calculus Formalism

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2005-01-01

We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10 -33 cm, implying a discrete spacetime structure on these scales

Discrete quantum gravitation in formalism of Regge calculus

International Nuclear Information System (INIS)

Khatsimovskij, V.M.

2005-01-01

One deals with approach to the discrete quantum gravitation in terms of the Regge calculus formalism. The Regge calculus represents the general relativity theory for the Riemann varieties - the piecewise planar varieties. The Regge calculus makes use of the discrete set of variables, triangulation lengths, and contains the continuous general relativity theory serving as a limiting special case when lengths tend to zero. In terms of our approach the quantum mean values of the mentioned lengths differ from zero and 10 -33 cm Planck length and it implies the discrete structure of space-time at the mentioned scales [ru

Discrete Discriminant analysis based on tree-structured graphical models

DEFF Research Database (Denmark)

Perez de la Cruz, Gonzalo; Eslava, Guillermina

The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant a...... analysis based on tree{structured graphical models is a simple nonlinear method competitive with, and sometimes superior to, other well{known linear methods like those assuming mutual independence between variables and linear logistic regression.......The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant...

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

Science.gov (United States)

Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

2009-01-01

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Friction dependence of shallow granular flows from discrete particle simulations

NARCIS (Netherlands)

Thornton, Anthony Richard; Weinhart, Thomas; Luding, Stefan; Bokhove, Onno

2011-01-01

A shallow-layer model for granular flows is completed with a closure relation for the macroscopic bed friction or basal roughness obtained from micro-scale discrete particle simulations of steady flows. We systematically vary the bed friction by changing the contact friction coefficient between

The discrete hungry Lotka Volterra system and a new algorithm for computing matrix eigenvalues

Science.gov (United States)

Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa

2009-01-01

The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.

The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues

International Nuclear Information System (INIS)

Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa

2009-01-01

The discrete hungry Lotka–Volterra (dhLV) system is a generalization of the discrete Lotka–Volterra (dLV) system which stands for a prey–predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix

A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-01-01

In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N -soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N -soliton solutions in terms of pffafians are also provided. (paper)

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

Directory of Open Access Journals (Sweden)

Sung Soo Kim

2016-02-01

Full Text Available We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.

A response matrix method for slab-geometry discrete ordinates adjoint calculations in energy-dependent source-detector problems

Energy Technology Data Exchange (ETDEWEB)

Mansur, Ralph S.; Moura, Carlos A., E-mail: ralph@ime.uerj.br, E-mail: demoura@ime.uerj.br [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil). Departamento de Engenharia Mecanica; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional

2017-07-01

Presented here is an application of the Response Matrix (RM) method for adjoint discrete ordinates (S{sub N}) problems in slab geometry applied to energy-dependent source-detector problems. The adjoint RM method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint SN equations. Numerical results are given for two typical source-detector problems to illustrate the accuracy and the efficiency of the offered RM computer code. (author)

The constrained discrete-time state-dependent Riccati equation technique for uncertain nonlinear systems

Science.gov (United States)

Chang, Insu

The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

Science.gov (United States)

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Statistical Dependence of Pipe Breaks on Explanatory Variables

Directory of Open Access Journals (Sweden)

Patricia Gómez-Martínez

2017-02-01

Full Text Available Aging infrastructure is the main challenge currently faced by water suppliers. Estimation of assets lifetime requires reliable criteria to plan assets repair and renewal strategies. To do so, pipe break prediction is one of the most important inputs. This paper analyzes the statistical dependence of pipe breaks on explanatory variables, determining their optimal combination and quantifying their influence on failure prediction accuracy. A large set of registered data from Madrid water supply network, managed by Canal de Isabel II, has been filtered, classified and studied. Several statistical Bayesian models have been built and validated from the available information with a technique that combines reference periods of time as well as geographical location. Statistical models of increasing complexity are built from zero up to five explanatory variables following two approaches: a set of independent variables or a combination of two joint variables plus an additional number of independent variables. With the aim of finding the variable combination that provides the most accurate prediction, models are compared following an objective validation procedure based on the model skill to predict the number of pipe breaks in a large set of geographical locations. As expected, model performance improves as the number of explanatory variables increases. However, the rate of improvement is not constant. Performance metrics improve significantly up to three variables, but the tendency is softened for higher order models, especially in trunk mains where performance is reduced. Slight differences are found between trunk mains and distribution lines when selecting the most influent variables and models.

MINARET: Towards a time-dependent neutron transport parallel solver

International Nuclear Information System (INIS)

Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.

2013-01-01

We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)

Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

Directory of Open Access Journals (Sweden)

Valter J. S. Leite

2008-01-01

Full Text Available Sufficient linear matrix inequality (LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

Science.gov (United States)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Optical force on a discrete invisibility cloak in time-dependent fields

International Nuclear Information System (INIS)

Chaumet, Patrick C.; Zolla, Frederic; Nicolet, Andre; Belkebir, Kamal; Rahmani, Adel

2011-01-01

We study, in time domain, the exchange of momentum between an electromagnetic pulse and a three-dimensional, discrete, spherical invisibility cloak. We find that a discrete cloak, initially at rest, would experience an electromagnetic force due to the pulse but would acquire zero net momentum and net displacement. On the other hand, we find that while the cloak may manage to conceal an object and shroud it from the electromagnetic forces associated with the pulse, the cloak itself can experience optomechanical stress on a scale much larger than the object would in the absence of the cloak. We also consider the effects of material dispersion and losses on the electromagnetic forces experienced by the cloak and show that they lead to a transfer of momentum from the pulse to the cloak.

Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein–Gordon lattice

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein–Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom

[Correlation coefficient-based classification method of hydrological dependence variability: With auto-regression model as example].

Science.gov (United States)

Zhao, Yu Xi; Xie, Ping; Sang, Yan Fang; Wu, Zi Yi

2018-04-01

Hydrological process evaluation is temporal dependent. Hydrological time series including dependence components do not meet the data consistency assumption for hydrological computation. Both of those factors cause great difficulty for water researches. Given the existence of hydrological dependence variability, we proposed a correlationcoefficient-based method for significance evaluation of hydrological dependence based on auto-regression model. By calculating the correlation coefficient between the original series and its dependence component and selecting reasonable thresholds of correlation coefficient, this method divided significance degree of dependence into no variability, weak variability, mid variability, strong variability, and drastic variability. By deducing the relationship between correlation coefficient and auto-correlation coefficient in each order of series, we found that the correlation coefficient was mainly determined by the magnitude of auto-correlation coefficient from the 1 order to p order, which clarified the theoretical basis of this method. With the first-order and second-order auto-regression models as examples, the reasonability of the deduced formula was verified through Monte-Carlo experiments to classify the relationship between correlation coefficient and auto-correlation coefficient. This method was used to analyze three observed hydrological time series. The results indicated the coexistence of stochastic and dependence characteristics in hydrological process.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

Science.gov (United States)

Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.

2001-12-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.

Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

Science.gov (United States)

Žukovič, Milan; Hristopulos, Dionissios T.

2009-02-01

A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the Nc-state Potts model, each point is assigned to one of Nc classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of

Mapping of uncertainty relations between continuous and discrete time.

Science.gov (United States)

Chiuchiù, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Modeling discrete time-to-event data

CERN Document Server

Tutz, Gerhard

2016-01-01

This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...

New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

Directory of Open Access Journals (Sweden)

Hamid Reza Karimi

2009-01-01

Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

Spaces of fractional quotients, discrete operators, and their applications. II

International Nuclear Information System (INIS)

Lifanov, I K; Poltavskii, L N

1999-01-01

The theory of discrete operators in spaces of fractional quotients is developed. A theorem on the stability of discrete operators under smooth perturbations is proved. On this basis, using special quadrature formulae of rectangular kind, the convergence of approximate solutions of hypersingular integral equations to their exact solutions is demonstrated and a mathematical substantiation of the method of closed discrete vortex frameworks is obtained. The same line of argument is also applied to difference equations arising in the solution of the homogeneous Dirichlet problem for a general second-order elliptic equation with variable coefficients

Inferring network structure in non-normal and mixed discrete-continuous genomic data.

Science.gov (United States)

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2018-03-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

International Nuclear Information System (INIS)

Adesso, Gerardo; Ericsson, Marie; Illuminati, Fabrizio

2007-01-01

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N≥4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantum correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states

Graph-cut based discrete-valued image reconstruction.

Science.gov (United States)

Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim

2015-05-01

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

Quadratic Term Structure Models in Discrete Time

OpenAIRE

Marco Realdon

2006-01-01

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

Lattice fluid dynamics from perfect discretizations of continuum flows

International Nuclear Information System (INIS)

Katz, E.; Wiese, U.

1998-01-01

We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes and naturally exist on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e., grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with a square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation and is shown to represent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive flow equations that are approximately perfect. copyright 1998 The American Physical Society

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

String constraints on discrete symmetries in MSSM type II quivers

Energy Technology Data Exchange (ETDEWEB)

Anastasopoulos, Pascal [Technische Univ. Wien (Austria). Inst. fur Theor. Phys.; Cvetic, Mirjam [Univ. of Pennsylvania, Philadelphia PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics; Richter, Robert [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-11-15

We study the presence of discrete gauge symmetries in D-brane semirealistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

Science.gov (United States)

Ramachandran, Nirmal; Ganguli, Ranjan

2018-06-01

A discrete model is introduced to analyze transverse vibration of straight, clamped-free (CF) columns of variable cross-sectional geometry under the influence of gravity and a constant axial force at the tip. The discrete model is used to determine critical combinations of loading parameters - a gravity parameter and a tip force parameter - that cause onset of dynamic instability in the CF column. A methodology, based on matrix-factorization, is described to transform the discrete model into a family of models corresponding to weightless and unloaded clamped-free (WUCF) columns, each with a transverse vibration spectrum isospectral to the original model. Characteristics of models in this isospectral family are dependent on three transformation parameters. A procedure is discussed to convert the isospectral discrete model description into geometric description of realistic columns i.e. from the discrete model, we construct isospectral WUCF columns with rectangular cross-sections varying in width and depth. As part of numerical studies to demonstrate efficacy of techniques presented, frequency parameters of a uniform column and three types of tapered CF columns under different combinations of loading parameters are obtained from the discrete model. Critical combinations of these parameters for a typical tapered column are derived. These results match with published results. Example CF columns, under arbitrarily-chosen combinations of loading parameters are considered and for each combination, isospectral WUCF columns are constructed. Role of transformation parameters in determining characteristics of isospectral columns is discussed and optimum values are deduced. Natural frequencies of these WUCF columns computed using Finite Element Method (FEM) match well with those of the given gravity-loaded CF column with tip force, hence confirming isospectrality.

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks

International Nuclear Information System (INIS)

Brantley, P S

2001-01-01

An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems

Discrete Emotion Effects on Lexical Decision Response Times

Science.gov (United States)

Briesemeister, Benny B.; Kuchinke, Lars; Jacobs, Arthur M.

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account. PMID:21887307

Bayesian estimation of the discrete coefficient of determination.

Science.gov (United States)

Chen, Ting; Braga-Neto, Ulisses M

2016-12-01

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.

Discrete emotion effects on lexical decision response times.

Science.gov (United States)

Briesemeister, Benny B; Kuchinke, Lars; Jacobs, Arthur M

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account.

Discrete emotion effects on lexical decision response times.

Directory of Open Access Journals (Sweden)

Benny B Briesemeister

Full Text Available Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account.

Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

Directory of Open Access Journals (Sweden)

Jieqiong Wu

2015-09-01

Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.

Foundations of the probabilistic mechanics of discrete media

CERN Document Server

Axelrad, D R

1984-01-01

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of s

Commutative discrete filtering on unstructured grids based on least-squares techniques

International Nuclear Information System (INIS)

Haselbacher, Andreas; Vasilyev, Oleg V.

2003-01-01

The present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions. First, building on the work of Marsden et al. [J. Comp. Phys. 175 (2002) 584], a new commutative discrete filter based on least-squares techniques is constructed. Second, a new analysis of the discrete commutation error is carried out. The analysis indicates that the discrete commutation error is not only dependent on the number of vanishing moments of the filter weights, but also on the order of accuracy of the discrete gradient operator. The results of the analysis are confirmed by grid-refinement studies

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

Science.gov (United States)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

Science.gov (United States)

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

Quadratic time dependent Hamiltonians and separation of variables

Science.gov (United States)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

The time-dependent 3D discrete ordinates code TORT-TD with thermal-hydraulic feedback by ATHLET models

International Nuclear Information System (INIS)

Seubert, A.; Velkov, K.; Langenbuch, S.

2008-01-01

This paper describes the time-dependent 3D discrete ordinates transport code TORT-TD. Thermal-hydraulic feedback is considered by coupling TORT-TD with the thermal-hydraulics system code ATHLET. The coupled code TORT-TD/ATHLET allows 3D pin-by-pin analyses of transients in few energy groups and anisotropic scattering by solving the time-dependent transport equation using the unconditionally stable implicit method. The nuclear cross sections are interpolated between pre-calculated table values of fuel temperature, moderator density and boron concentration. For verification of the implementation, selected test cases have been calculated by TORT-TD/ATHLET. They include a control rod ejection transient in a small PWR fuel assembly arrangement and a local boron concentration change in a single PWR fuel assembly. In the latter, special attention has been paid to study the influence of the thermal-hydraulic feedback modelling in ATHLET. The results obtained for a control rod ejection accident in a PWR quarter core demonstrate the applicability of TORT-TD/ATHLET. (authors)

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads: Preprint

Energy Technology Data Exchange (ETDEWEB)

Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhou, Xinyang [University of Colorado; Liu, Zhiyuan [University of Colorado; Chen, Lijun [University of Colorado

2017-10-03

This paper considers distribution networks with distributed energy resources and discrete-rate loads, and designs an incentive-based algorithm that allows the network operator and the customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Four major challenges include: (1) the non-convexity from discrete decision variables, (2) the non-convexity due to a Stackelberg game structure, (3) unavailable private information from customers, and (4) different update frequency from two types of devices. In this paper, we first make convex relaxation for discrete variables, then reformulate the non-convex structure into a convex optimization problem together with pricing/reward signal design, and propose a distributed stochastic dual algorithm for solving the reformulated problem while restoring feasible power rates for discrete devices. By doing so, we are able to statistically achieve the solution of the reformulated problem without exposure of any private information from customers. Stability of the proposed schemes is analytically established and numerically corroborated.

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schroedinger equation on a semi-infinite strip

International Nuclear Information System (INIS)

Ducomet, Bernard; Zlotnik, Alexander; Zlotnik, Ilya

2014-01-01

We consider an initial-boundary value problem for a generalized 2D time-dependent Schroedinger equation (with variable coefficients) on a semi-infinite strip. For the Crank-Nicolson-type finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the unconditional uniform in time L2-stability is proved. Due to the splitting, an effective direct algorithm using FFT is developed now to implement the method with the discrete TBC for general potential. Numerical results on the tunnel effect for rectangular barriers are included together with the detailed practical error analysis confirming nice properties of the method. (authors)

How a dependent's variable non-randomness affects taper equation ...

African Journals Online (AJOL)

In order to apply the least squares method in regression analysis, the values of the dependent variable Y should be random. In an example of regression analysis linear and nonlinear taper equations, which estimate the diameter of the tree dhi at any height of the tree hi, were compared. For each tree the diameter at the ...

Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

DEFF Research Database (Denmark)

Román Marín, José Manuel; Rasmussen, Henrik K.

2009-01-01

equation is replaced with a temperature dependent pseudo time. The spatial coordinate system attached to the particles is discretized by 10-node quadratic tetrahedral elements using Cartesian coordinates. The temperature and the pressure are discretized by 10-node quadratic and linear interpolation...... utilizing an implicit variable step backwards differencing (BDF2) scheme, obtaining second order convergence of the temperature in time. A quadratic interpolation in time is applied to approximate the time integral in the K-BKZ equation. This type of scheme ensures third order accuracy with respect......, respectively, in the tetrahedral particle elements. The spatial discretization of the governing equations follows a mixed Galerkin finite element method. This type of scheme ensures third order accuracy with respect to the discretization of spatial dimension. The temperature equation is solved in time...

Calculated Low-Speed Steady and Time-Dependent Aerodynamic Derivatives for Some Airfoils Using a Discrete Vortex Method

Science.gov (United States)

Riley, Donald R.

2015-01-01

This paper contains a collection of some results of four individual studies presenting calculated numerical values for airfoil aerodynamic stability derivatives in unseparated inviscid incompressible flow due separately to angle-of-attack, pitch rate, flap deflection, and airfoil camber using a discrete vortex method. Both steady conditions and oscillatory motion were considered. Variables include the number of vortices representing the airfoil, the pitch axis / moment center chordwise location, flap chord to airfoil chord ratio, and circular or parabolic arc camber. Comparisons with some experimental and other theoretical information are included. The calculated aerodynamic numerical results obtained using a limited number of vortices provided in each study compared favorably with thin airfoil theory predictions. Of particular interest are those aerodynamic results calculated herein (such as induced drag) that are not readily available elsewhere.

Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

International Nuclear Information System (INIS)

Žukovič, Milan; Hristopulos, Dionissios T

2009-01-01

A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the N c -state Potts model, each point is assigned to one of N c classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of

Fractional equations of kicked systems and discrete maps

International Nuclear Information System (INIS)

Tarasov, Vasily E; Zaslavsky, George M

2008-01-01

Starting from kicked equations of motion with derivatives of non-integer orders, we obtain 'fractional' discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main property of the suggested fractional maps is a long-term memory. The memory effects in the fractional discrete maps mean that their present state evolution depends on all past states with special forms of weights. These forms are represented by combinations of power-law functions

A numerical model for density-and-viscosity-dependent flows in two-dimensional variably saturated porous media

Science.gov (United States)

Boufadel, Michel C.; Suidan, Makram T.; Venosa, Albert D.

1999-04-01

We present a formulation for water flow and solute transport in two-dimensional variably saturated media that accounts for the effects of the solute on water density and viscosity. The governing equations are cast in a dimensionless form that depends on six dimensionless groups of parameters. These equations are discretized in space using the Galerkin finite element formulation and integrated in time using the backward Euler scheme with mass lumping. The modified Picard method is used to linearize the water flow equation. The resulting numerical model, the MARUN model, is verified by comparison to published numerical results. It is then used to investigate beach hydraulics at seawater concentration (about 30 g l -1) in the context of nutrients delivery for bioremediation of oil spills on beaches. Numerical simulations that we conducted in a rectangular section of a hypothetical beach revealed that buoyancy in the unsaturated zone is significant in soils that are fine textured, with low anisotropy ratio, and/or exhibiting low physical dispersion. In such situations, application of dissolved nutrients to a contaminated beach in a freshwater solution is superior to their application in a seawater solution. Concentration-engendered viscosity effects were negligible with respect to concentration-engendered density effects for the cases that we considered.

On the convergence of multigroup discrete-ordinates approximations

International Nuclear Information System (INIS)

Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

1987-01-01

Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

Duality for discrete integrable systems

International Nuclear Information System (INIS)

Quispel, G R W; Capel, H W; Roberts, J A G

2005-01-01

A new class of discrete dynamical systems is introduced via a duality relation for discrete dynamical systems with a number of explicitly known integrals. The dual equation can be defined via the difference of an arbitrary linear combination of integrals and its upshifted version. We give an example of an integrable mapping with two parameters and four integrals leading to a (four-dimensional) dual mapping with four parameters and two integrals. We also consider a more general class of higher-dimensional mappings arising via a travelling-wave reduction from the (integrable) MKdV partial-difference equation. By differencing the trace of the monodromy matrix we obtain a class of novel dual mappings which is shown to be integrable as level-set-dependent versions of the original ones

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

Switching dynamics in reaction networks induced by molecular discreteness

International Nuclear Information System (INIS)

Togashi, Yuichi; Kaneko, Kunihiko

2007-01-01

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states

A multidimensionally consistent version of Hirota’s discrete KdV equation

International Nuclear Information System (INIS)

Atkinson, James

2012-01-01

A multidimensionally consistent generalization of Hirota’s discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as superposition principle are given. It is discussed how an important property of the defining polynomial, a factorization of discriminants, appears also in the few other known discrete integrable multi-quadratic models. (fast track communication)

The discovery of timescale-dependent color variability of quasars

Energy Technology Data Exchange (ETDEWEB)

Sun, Yu-Han; Wang, Jun-Xian; Chen, Xiao-Yang [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026 (China); Zheng, Zhen-Ya, E-mail: sunyh92@mail.ustc.edu.cn, E-mail: jxw@ustc.edu.cn [School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287 (United States)

2014-09-01

Quasars are variable on timescales from days to years in UV/optical and generally appear bluer while they brighten. The physics behind the variations in fluxes and colors remains unclear. Using Sloan Digital Sky Survey g- and r-band photometric monitoring data for quasars in Stripe 82, we find that although the flux variation amplitude increases with timescale, the color variability exhibits the opposite behavior. The color variability of quasars is prominent at timescales as short as ∼10 days, but gradually reduces toward timescales up to years. In other words, the variable emission at shorter timescales is bluer than that at longer timescales. This timescale dependence is clearly and consistently detected at all redshifts from z = 0 to 3.5; thus, it cannot be due to contamination to broadband photometry from emission lines that do not respond to fast continuum variations. The discovery directly rules out the possibility that simply attributes the color variability to contamination from a non-variable redder component such as the host galaxy. It cannot be interpreted as changes in global accretion rate either. The thermal accretion disk fluctuation model is favored in the sense that fluctuations in the inner, hotter region of the disk are responsible for short-term variations, while longer-term and stronger variations are expected from the larger and cooler disk region. An interesting implication is that one can use quasar variations at different timescales to probe disk emission at different radii.

Cone-beam tomography with discrete data sets

International Nuclear Information System (INIS)

Barrett, H.H.

1994-01-01

Sufficiently conditions for cone-beam data are well known for the case of continuous data collection along a cone-vortex curve with continuous detectors. These continuous conditions are inadequate for real-world data where discrete vertex geometries and discrete detector arrays are used. In this paper we present a theoretical formulation of cone-beam tomography with arbitrary discrete arrays of detectors and vertices. The theory models the imaging system as a linear continuous-to-discrete mapping and represents the continuous object exactly as a Fourier series. The reconstruction problem is posed as the estimation of some subset of the Fourier coefficients. The main goal of the theory is to determine which Fourier coefficients can be reliably determined from the data delivered by a specific discrete design. A fourier component will be well determined by the data if it satisfies two conditions: it makes a strong contribution to the data, and this contribution is relatively independent of the contribution of other Fourier components. To make these considerations precise, we introduce a concept called the cross-talk matrix. A diagonal element of this matrix measures the strength of a Fourier component in the data, while an off-diagonal element quantifies the dependence or aliasing of two different components. (Author)

Model-based Quantile Regression for Discrete Data

KAUST Repository

Padellini, Tullia

2018-04-10

Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a model-based approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with R-INLA. We extend it also in the case of discrete responses, where there is no 1-to-1 relationship between quantiles and distribution\\'s parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting.

ABCB1 genetic variability and methadone dosage requirements in opioid-dependent individuals.

Science.gov (United States)

Coller, Janet K; Barratt, Daniel T; Dahlen, Karianne; Loennechen, Morten H; Somogyi, Andrew A

2006-12-01

The most common treatment for opioid dependence is substitution therapy with another opioid such as methadone. The methadone dosage is individualized but highly variable, and program retention rates are low due in part to nonoptimal dosing resulting in withdrawal symptoms and further heroin craving and use. Methadone is a substrate for the P-glycoprotein transporter, encoded by the ABCB1 gene, which regulates central nervous system exposure. This retrospective study aimed to investigate the influence of ABCB1 genetic variability on methadone dose requirements. Genomic deoxyribonucleic acid was isolated from opioid-dependent subjects (n = 60) and non-opioid-dependent control subjects (n = 60), and polymerase chain reaction-restriction fragment length polymorphism and allele-specific polymerase chain reaction were used to determine the presence of single nucleotide polymorphisms at positions 61, 1199, 1236, 2677, and 3435. ABCB1 haplotypes were inferred with PHASE software (version 2.1). There were no significant differences in the allele or genotype frequencies of the individual single nucleotide polymorphisms or haplotypes between the 2 populations. ABCB1 genetic variability influenced daily methadone dose requirements, such that subjects carrying 2 copies of the wild-type haplotype required higher doses compared with those with 1 copy and those with no copies (98.3 +/- 10.4, 58.6 +/- 20.9, and 55.4 +/- 26.1 mg/d, respectively; P = .029). In addition, carriers of the AGCTT haplotype required significantly lower doses than noncarriers (38.0 +/- 16.8 and 61.3 +/- 24.6 mg/d, respectively; P = .04). Although ABCB1 genetic variability is not related to the development of opioid dependence, identification of variant haplotypes may, after larger prospective studies have been performed, provide clinicians with a tool for methadone dosage individualization.

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Random discrete Morse theory and a new library of triangulations

DEFF Research Database (Denmark)

Benedetti, Bruno; Lutz, Frank Hagen

2014-01-01

We introduce random discrete Morse theory as a computational scheme to measure the complexity of a triangulation. The idea is to try to quantify the frequency of discrete Morse matchings with few critical cells. Our measure will depend on the topology of the space, but also on how nicely the space...... is triangulated. The scheme we propose looks for optimal discrete Morse functions with an elementary random heuristic. Despite its naiveté, this approach turns out to be very successful even in the case of huge inputs. In our view, the existing libraries of examples in computational topology are “too easy......” for testing algorithms based on discrete Morse theory. We propose a new library containing more complicated (and thus more meaningful) test examples....

Discrete time duration models with group-level heterogeneity

DEFF Research Database (Denmark)

Frederiksen, Anders; Honoré, Bo; Hu, Loujia

2007-01-01

Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration...

Calculated Low-Speed Steady and Time-Dependent Aerodynamic Derivatives for Several Different Wings Using a Discrete Vortex Method

Science.gov (United States)

Riley, Donald R.

2016-01-01

Calculated numerical values for some aerodynamic terms and stability Derivatives for several different wings in unseparated inviscid incompressible flow were made using a discrete vortex method involving a limited number of horseshoe vortices. Both longitudinal and lateral-directional derivatives were calculated for steady conditions as well as for sinusoidal oscillatory motions. Variables included the number of vortices used and the rotation axis/moment center chordwise location. Frequencies considered were limited to the range of interest to vehicle dynamic stability (kb <.24 ). Comparisons of some calculated numerical results with experimental wind-tunnel measurements were in reasonable agreement in the low angle-of-attack range considering the differences existing between the mathematical representation and experimental wind-tunnel models tested. Of particular interest was the presence of induced drag for the oscillatory condition.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks

DEFF Research Database (Denmark)

Iskhakov, Fedor; Jørgensen, Thomas H.; Rust, John

2017-01-01

We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid-point method (EGM) to discrete-continuous (DC) p...

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Leaping from Discrete to Continuous Independent Variables: Sixth Graders' Science Line Graph Interpretations

Science.gov (United States)

Boote, Stacy K.; Boote, David N.

2017-01-01

Students often struggle to interpret graphs correctly, despite emphasis on graphic literacy in U.S. education standards documents. The purpose of this study was to describe challenges sixth graders with varying levels of science and mathematics achievement encounter when transitioning from interpreting graphs having discrete independent variables…

Symmetries and discretizations of the O(3) nonlinear sigma model

Energy Technology Data Exchange (ETDEWEB)

Flore, Raphael [TPI, Universitaet Jena (Germany)

2011-07-01

Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.

Strong Decomposition of Random Variables

DEFF Research Database (Denmark)

Hoffmann-Jørgensen, Jørgen; Kagan, Abram M.; Pitt, Loren D.

2007-01-01

A random variable X is stongly decomposable if X=Y+Z where Y=Φ(X) and Z=X-Φ(X) are independent non-degenerated random variables (called the components). It is shown that at least one of the components is singular, and we derive a necessary and sufficient condition for strong decomposability...... of a discrete random variable....

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Discrete stochastic analogs of Erlang epidemic models.

Science.gov (United States)

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Attractors for discrete periodic dynamical systems

Science.gov (United States)

John E. Franke; James F. Selgrade

2003-01-01

A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...

A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations

Directory of Open Access Journals (Sweden)

Wenhua Zhang

2013-01-01

Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.

Discrete persistent-chain model for protein binding on DNA.

Science.gov (United States)

Lam, Pui-Man; Zhen, Yi

2011-04-01

We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra σ(i) at a site i of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost ɛ. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding. ©2011 American Physical Society

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

Science.gov (United States)

Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.

2017-07-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Energy Technology Data Exchange (ETDEWEB)

Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV

2008-01-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

Science.gov (United States)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Reduction of the Random Variables of the Turbulent Wind Field

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.

2012-01-01

.e. Importance Sampling (IS) or Subset Simulation (SS), will be deteriorated on problems with many random variables. The problem with PDEM is that a multidimensional integral has to be carried out over the space defined by the random variables of the system. The numerical procedure requires discretization......Applicability of the Probability Density Evolution Method (PDEM) for realizing evolution of the probability density for the wind turbines has rather strict bounds on the basic number of the random variables involved in the model. The efficiency of most of the Advanced Monte Carlo (AMC) methods, i...... of the integral domain; this becomes increasingly difficult as the dimensions of the integral domain increase. On the other hand efficiency of the AMC methods is closely dependent on the design points of the problem. Presence of many random variables may increase the number of the design points, hence affects...

Railway and road discrete choice model for foreign trade freight between Antioquia and the Port of Cartagena

Directory of Open Access Journals (Sweden)

J. D. Pineda-Jaramillo

2016-09-01

Full Text Available Most Colombian freight is transported on roads with barely acceptable conditions, and although there is a speculation about the need for a railway for freight transportation, there is not a study in Colombia showing the variables that influence the modal choice by the companies that generate freight transportation. This article presents the calculation of demand for a hypothetical railway through a discrete choice model. It begins with a qualitative research through focus group techniques to identify the variables that influence the choice of persons responsible for the transportation of large commercial companies in Antioquia (Colombia. The influential variables in the election were the cost and service frequency, and these variables were used to apply a Stated Preference (SP and Revealed Preference (RP survey, then to calibrate a Multinomial Logit Model (MNL, and to estimate the influence of each of them. We show that the probability of railway choice by the studied companies varies between 67% and 93%, depending on differences in these variables.

Long-time behaviour of discretizations of the simple pendulum equation

Energy Technology Data Exchange (ETDEWEB)

Cieslinski, Jan L [Uniwersytet w Bialymstoku, Wydzial Fizyki, ul. Lipowa 41, 15-424 Bialystok (Poland); Ratkiewicz, Boguslaw [Doctoral Studies, Wydzial Fizyki, Uniwersytet Adama Mickiewicza, Poznan (Poland)], E-mail: janek@alpha.uwb.edu.pl, E-mail: bograt@poczta.onet.pl

2009-03-13

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step.

Long-time behaviour of discretizations of the simple pendulum equation

International Nuclear Information System (INIS)

Cieslinski, Jan L; Ratkiewicz, Boguslaw

2009-01-01

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step

Data-Driven Process Discovery: A Discrete Time Algebra for Relational Signal Analysis

National Research Council Canada - National Science Library

Conrad, David

1996-01-01

.... Proposed is a time series transformation that encodes and compresses real-valued data into a well defined, discrete-space of 13 primitive elements where comparative evaluation between variables...

A Discrete Event Simulation Model for Evaluating the Performances of an M/G/C/C State Dependent Queuing System

Science.gov (United States)

Khalid, Ruzelan; M. Nawawi, Mohd Kamal; Kawsar, Luthful A.; Ghani, Noraida A.; Kamil, Anton A.; Mustafa, Adli

2013-01-01

M/G/C/C state dependent queuing networks consider service rates as a function of the number of residing entities (e.g., pedestrians, vehicles, and products). However, modeling such dynamic rates is not supported in modern Discrete Simulation System (DES) software. We designed an approach to cater this limitation and used it to construct the M/G/C/C state-dependent queuing model in Arena software. Using the model, we have evaluated and analyzed the impacts of various arrival rates to the throughput, the blocking probability, the expected service time and the expected number of entities in a complex network topology. Results indicated that there is a range of arrival rates for each network where the simulation results fluctuate drastically across replications and this causes the simulation results and analytical results exhibit discrepancies. Detail results that show how tally the simulation results and the analytical results in both abstract and graphical forms and some scientific justifications for these have been documented and discussed. PMID:23560037

Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

Directory of Open Access Journals (Sweden)

Kaibo Shi

2014-01-01

Full Text Available This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

Discrete choice models with multiplicative error terms

DEFF Research Database (Denmark)

Fosgerau, Mogens; Bierlaire, Michel

2009-01-01

The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term ε. In general, the universe of RUM consistent models is much larger, even fixing some specification of V due...

Solution of neutron transport equation using Daubechies' wavelet expansion in the angular discretization

International Nuclear Information System (INIS)

Cao Liangzhi; Wu Hongchun; Zheng Youqi

2008-01-01

Daubechies' wavelet expansion is introduced to discretize the angular variables of the neutron transport equation when the neutron angular flux varies very acutely with the angular directions. An improvement is made by coupling one-dimensional wavelet expansion and discrete ordinate method to make two-dimensional angular discretization efficient and stable. The angular domain is divided into several subdomains for treating the vacuum boundary condition exactly in the unstructured geometry. A set of wavelet equations coupled with each other is obtained in each subdomain. An iterative method is utilized to decouple the wavelet moments. The numerical results of several benchmark problems demonstrate that the wavelet expansion method can provide more accurate results by lower-order expansion than other angular discretization methods

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Directory of Open Access Journals (Sweden)

Baogui Xin

2015-04-01

Full Text Available A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

Angular dependence of the attosecond time delay in the H 2 + ion

Science.gov (United States)

Kheifets, Anatoli; Serov, Vladislav

2016-05-01

Angular dependence of attosecond time delay relative to polarization of light can now be measured using combination of RABBITT and COLTRIMS techniques. This dependence brings particularly useful information in molecules where it is sensitive to the orientation of the molecular axis. Here we extend the theoretical studies of and consider a molecular ion H2+in combination of an attosecond pulse train and a dressing IR field which is a characteristic set up of a RABBIT measurement. We solve the time-dependent Schrödinger equation using a fast spherical Bessel transformation (SBT) for the radial variable, a discrete variable representation for the angular variables and a split-step technique for the time evolution. The use of SBT ensures correct phase of the wave function for a long time evolution which is especially important in time delay calculations. To speed up computations, we implement an expanding coordinate (EC) system which allows us to reach space sizes and time periods unavailable by other techniques. Australian Research Council DP120101805.

Modelling discrete choice variables in assessment of teaching staff work satisfaction.

Science.gov (United States)

Mieilă, Mihai; Popescu, Constanţa; Tudorache, Ana-Maria; Toplicianu, Valerică

2015-01-01

Levels of self-reported job satisfaction and motivation were measured by survey in a sample of 286 teachers. Using the discrete choice framework, the paper tries to assess the relevance of the considered indicators (demographic, social, motivational) in overall teaching work satisfaction. The findings provide evidence that job satisfaction is correlated significantly with level of university degree held by the teacher, type of secondary school where the teacher is enrolled, revenues, and salary-tasks adequacy. This is important for the Romanian economy, since the education system is expected to provide future human resources with enhanced skills and abilities.

Modelling discrete choice variables in assessment of teaching staff work satisfaction.

Directory of Open Access Journals (Sweden)

Mihai Mieilă

Full Text Available Levels of self-reported job satisfaction and motivation were measured by survey in a sample of 286 teachers. Using the discrete choice framework, the paper tries to assess the relevance of the considered indicators (demographic, social, motivational in overall teaching work satisfaction. The findings provide evidence that job satisfaction is correlated significantly with level of university degree held by the teacher, type of secondary school where the teacher is enrolled, revenues, and salary-tasks adequacy. This is important for the Romanian economy, since the education system is expected to provide future human resources with enhanced skills and abilities.

A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

KAUST Repository

Zhu, Guangpu; Chen, Huangxin; Sun, Shuyu; Yao, Jun

2018-01-01

In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation

Finite Volumes Discretization of Topology Optimization Problems

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...

Discrete time analysis of a repairable machine

OpenAIRE

Alfa, Attahiru Sule; Castro, I. T.

2002-01-01

We consider, in discrete time, a single machine system that operates for a period of time represented by a general distribution. This machine is subject to failures during operations and the occurrence of these failures depends on how many times the machine has previously failed. Some failures are repairable and the repair times may or may not depend on the number of times the machine was previously repaired. Repair times also have a general distribution. The operating times...

Interaction of discrete and continuous boundary layer modes to cause transition

International Nuclear Information System (INIS)

Durbin, Paul A.; Zaki, Tamer A.; Liu Yang

2009-01-01

The interaction of discrete and continuous Orr-Sommerfeld modes in a boundary layer is studied by computer simulation. The discrete mode is an unstable Tollmien-Schlichting wave. The continuous modes generate jet-like disturbances inside the boundary layer. Either mode alone does not cause transition to turbulence; however, the interaction between them does. The continuous mode jets distort the discrete modes, producing Λ shaped vortices. Breakdown to turbulence is subsequent. The lateral spacing of the Λ's is sometimes the same as the wavelength of the continuous mode, sometimes it differs, depending on the ratio of wavelength to boundary layer thickness.

Discrete event simulation tool for analysis of qualitative models of continuous processing systems

Science.gov (United States)

Malin, Jane T. (Inventor); Basham, Bryan D. (Inventor); Harris, Richard A. (Inventor)

1990-01-01

An artificial intelligence design and qualitative modeling tool is disclosed for creating computer models and simulating continuous activities, functions, and/or behavior using developed discrete event techniques. Conveniently, the tool is organized in four modules: library design module, model construction module, simulation module, and experimentation and analysis. The library design module supports the building of library knowledge including component classes and elements pertinent to a particular domain of continuous activities, functions, and behavior being modeled. The continuous behavior is defined discretely with respect to invocation statements, effect statements, and time delays. The functionality of the components is defined in terms of variable cluster instances, independent processes, and modes, further defined in terms of mode transition processes and mode dependent processes. Model construction utilizes the hierarchy of libraries and connects them with appropriate relations. The simulation executes a specialized initialization routine and executes events in a manner that includes selective inherency of characteristics through a time and event schema until the event queue in the simulator is emptied. The experimentation and analysis module supports analysis through the generation of appropriate log files and graphics developments and includes the ability of log file comparisons.

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

International Nuclear Information System (INIS)

Penney, Mark D; Koh, Dax Enshan; Spekkens, Robert W

2017-01-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits. (paper)

Punishment induced behavioural and neurophysiological variability reveals dopamine-dependent selection of kinematic movement parameters

Science.gov (United States)

Galea, Joseph M.; Ruge, Diane; Buijink, Arthur; Bestmann, Sven; Rothwell, John C.

2013-01-01

Action selection describes the high-level process which selects between competing movements. In animals, behavioural variability is critical for the motor exploration required to select the action which optimizes reward and minimizes cost/punishment, and is guided by dopamine (DA). The aim of this study was to test in humans whether low-level movement parameters are affected by punishment and reward in ways similar to high-level action selection. Moreover, we addressed the proposed dependence of behavioural and neurophysiological variability on DA, and whether this may underpin the exploration of kinematic parameters. Participants performed an out-and-back index finger movement and were instructed that monetary reward and punishment were based on its maximal acceleration (MA). In fact, the feedback was not contingent on the participant’s behaviour but pre-determined. Blocks highly-biased towards punishment were associated with increased MA variability relative to blocks with either reward or without feedback. This increase in behavioural variability was positively correlated with neurophysiological variability, as measured by changes in cortico-spinal excitability with transcranial magnetic stimulation over the primary motor cortex. Following the administration of a DA-antagonist, the variability associated with punishment diminished and the correlation between behavioural and neurophysiological variability no longer existed. Similar changes in variability were not observed when participants executed a pre-determined MA, nor did DA influence resting neurophysiological variability. Thus, under conditions of punishment, DA-dependent processes influence the selection of low-level movement parameters. We propose that the enhanced behavioural variability reflects the exploration of kinematic parameters for less punishing, or conversely more rewarding, outcomes. PMID:23447607

The discrete adjoint method for parameter identification in multibody system dynamics.

Science.gov (United States)

Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

2018-01-01

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

Truss topology optimization with discrete design variables — Guaranteed global optimality and benchmark examples

DEFF Research Database (Denmark)

Achtziger, Wolfgang; Stolpe, Mathias

2007-01-01

this problem is well-studied for continuous bar areas, we consider in this study the case of discrete areas. This problem is of major practical relevance if the truss must be built from pre-produced bars with given areas. As a special case, we consider the design problem for a single available bar area, i.......e., a 0/1 problem. In contrast to the heuristic methods considered in many other approaches, our goal is to compute guaranteed globally optimal structures. This is done by a branch-and-bound method for which convergence can be proven. In this branch-and-bound framework, lower bounds of the optimal......-integer problems. The main intention of this paper is to provide optimal solutions for single and multiple load benchmark examples, which can be used for testing and validating other methods or heuristics for the treatment of this discrete topology design problem....

Affective norms of 875 Spanish words for five discrete emotional categories and two emotional dimensions.

Science.gov (United States)

Hinojosa, J A; Martínez-García, N; Villalba-García, C; Fernández-Folgueiras, U; Sánchez-Carmona, A; Pozo, M A; Montoro, P R

2016-03-01

In the present study, we introduce affective norms for a new set of Spanish words, the Madrid Affective Database for Spanish (MADS), that were scored on two emotional dimensions (valence and arousal) and on five discrete emotional categories (happiness, anger, sadness, fear, and disgust), as well as on concreteness, by 660 Spanish native speakers. Measures of several objective psycholinguistic variables--grammatical class, word frequency, number of letters, and number of syllables--for the words are also included. We observed high split-half reliabilities for every emotional variable and a strong quadratic relationship between valence and arousal. Additional analyses revealed several associations between the affective dimensions and discrete emotions, as well as with some psycholinguistic variables. This new corpus complements and extends prior databases in Spanish and allows for designing new experiments investigating the influence of affective content in language processing under both dimensional and discrete theoretical conceptions of emotion. These norms can be downloaded as supplemental materials for this article from www.dropbox.com/s/o6dpw3irk6utfhy/Hinojosa%20et%20al_Supplementary%20materials.xlsx?dl=0 .

Central limit theorem for the Banach-valued weakly dependent random variables

International Nuclear Information System (INIS)

Dmitrovskij, V.A.; Ermakov, S.V.; Ostrovskij, E.I.

1983-01-01

The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

Discrete kink dynamics in hydrogen-bonded chains: The one-component model

DEFF Research Database (Denmark)

Karpan, V. M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth

2002-01-01

"parabola-constant" approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete traveling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity...

A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

International Nuclear Information System (INIS)

Vargas, L.

1988-01-01

The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

Equivalent conditions of complete moment convergence for extended negatively dependent random variables

Directory of Open Access Journals (Sweden)

Qunying Wu

2017-05-01

Full Text Available Abstract In this paper, we study the equivalent conditions of complete moment convergence for sequences of identically distributed extended negatively dependent random variables. As a result, we extend and generalize some results of complete moment convergence obtained by Chow (Bull. Inst. Math. Acad. Sin. 16:177-201, 1988 and Li and Spătaru (J. Theor. Probab. 18:933-947, 2005 from the i.i.d. case to extended negatively dependent sequences.

Discrete-time sliding mode control for MR vehicle suspension system

Energy Technology Data Exchange (ETDEWEB)

Sohn, J W; Choi, S B [Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha University, Incheon 402-751 (Korea, Republic of); Wereley, N M [Smart Structures Laboratory, Department of Aerospace Engineering, University of Maryland, College Park, MD 20742 (United States)], E-mail: seungbok@inha.ac.kr

2009-02-01

This paper presents control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers via a discrete-time sliding mode control algorithm (DSMC). A cylindrical MR damper is designed by incorporating Bingham model of the MR fluid and the field-dependent damping characteristics of the MR damper are evaluated. A full-vehicle suspension model installed with independent four MR dampers is constructed and the governing equations which include vertical, pitch and roll motion are derived. A discrete-time control model is established with considering system uncertainties and a discrete-time sliding mode controller which has inherent robustness to model uncertainty and external disturbance is formulated. Vibration control performances under bump excitation are evaluated and presented.

Discrete-time sliding mode control for MR vehicle suspension system

International Nuclear Information System (INIS)

Sohn, J W; Choi, S B; Wereley, N M

2009-01-01

This paper presents control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers via a discrete-time sliding mode control algorithm (DSMC). A cylindrical MR damper is designed by incorporating Bingham model of the MR fluid and the field-dependent damping characteristics of the MR damper are evaluated. A full-vehicle suspension model installed with independent four MR dampers is constructed and the governing equations which include vertical, pitch and roll motion are derived. A discrete-time control model is established with considering system uncertainties and a discrete-time sliding mode controller which has inherent robustness to model uncertainty and external disturbance is formulated. Vibration control performances under bump excitation are evaluated and presented.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

International Nuclear Information System (INIS)

Fernandez, P.; Wang, Q.

2017-01-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

Science.gov (United States)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

Modeling of brittle-viscous flow using discrete particles

Science.gov (United States)

Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.

2017-04-01

Many geological processes involve both viscous flow and brittle fractures, e.g. boudinage, folding and magmatic intrusions. Numerical modeling of such viscous-brittle materials poses challenges: one has to account for the discrete fracturing, the continuous viscous flow, the coupling between them, and potential pressure dependence of the flow. The Discrete Element Method (DEM) is a numerical technique, widely used for studying fracture of geomaterials. However, the implementation of viscous fluid flow in discrete element models is not trivial. In this study, we model quasi-viscous fluid flow behavior using Esys-Particle software (Abe et al., 2004). We build on the methodology of Abe and Urai (2012) where a combination of elastic repulsion and dashpot interactions between the discrete particles is implemented. Several benchmarks are presented to illustrate the material properties. Here, we present extensive, systematic material tests to characterize the rheology of quasi-viscous DEM particle packing. We present two tests: a simple shear test and a channel flow test, both in 2D and 3D. In the simple shear tests, simulations were performed in a box, where the upper wall is moved with a constant velocity in the x-direction, causing shear deformation of the particle assemblage. Here, the boundary conditions are periodic on the sides, with constant forces on the upper and lower walls. In the channel flow tests, a piston pushes a sample through a channel by Poisseuille flow. For both setups, we present the resulting stress-strain relationships over a range of material parameters, confining stress and strain rate. Results show power-law dependence between stress and strain rate, with a non-linear dependence on confining force. The material is strain softening under some conditions (which). Additionally, volumetric strain can be dilatant or compactant, depending on porosity, confining pressure and strain rate. Constitutive relations are implemented in a way that limits the

Vertical discretizations for compressible Euler equation atmospheric models giving optimal representation of normal modes

International Nuclear Information System (INIS)

Thuburn, J.; Woollings, T.J.

2005-01-01

Accurate representation of different kinds of wave motion is essential for numerical models of the atmosphere, but is sensitive to details of the discretization. In this paper, numerical dispersion relations are computed for different vertical discretizations of the compressible Euler equations and compared with the analytical dispersion relation. A height coordinate, an isentropic coordinate, and a terrain-following mass-based coordinate are considered, and, for each of these, different choices of prognostic variables and grid staggerings are considered. The discretizations are categorized according to whether their dispersion relations are optimal, are near optimal, have a single zero-frequency computational mode, or are problematic in other ways. Some general understanding of the factors that affect the numerical dispersion properties is obtained: heuristic arguments concerning the normal mode structures, and the amount of averaging and coarse differencing in the finite difference scheme, are shown to be useful guides to which configurations will be optimal; the number of degrees of freedom in the discretization is shown to be an accurate guide to the existence of computational modes; there is only minor sensitivity to whether the equations for thermodynamic variables are discretized in advective form or flux form; and an accurate representation of acoustic modes is found to be a prerequisite for accurate representation of inertia-gravity modes, which, in turn, is found to be a prerequisite for accurate representation of Rossby modes

Construction of adjoint operators for coupled equations depending on different variables

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1986-01-01

A procedure is described for the construction of the adjoint operator matrix in case of coupled equations defining quantities that depend on different sets of variables. This case is not properly treated in the literature. From this procedure a simple rule can be deduced for the construction of such adjoint operator matrices

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Application of discrete function and software control flow to dependability assessment of embedded digital system

International Nuclear Information System (INIS)

Choi, Jong Gyun; Seong, Poong Hyun

2001-01-01

This article describes a combinatorial model for estimating the reliability of the embedded digital system by means of discrete function theory and software control flow. This model includes a coverage model for fault processing mechanisms implemented in digital system. Furthermore, the model considers the interaction between hardware and software. The fault processing mechanisms make it difficult for many types of components in digital system to be treated as binary state, good or bad. The discrete function theory provides a complete analysis of multi-state system as which the digital system can be regarded Through adaptation software control flow to discrete function theory, the HW/SW interaction is considered for estimation of the reliability of digital system. Using this model, we predict the reliability of one board controller in a digital system, Interposing Logic System(ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is general combinatinal model, the simplification of this model becomes a conservative model that treats the system as binary state. Moreover, if information for coverage factor of fault tolerance mechanisms implemented in system through fault injection experiment is obtained, this model can consider detailed interaction of system components

Discrete-time Calogero-Moser system and Lagrangian 1-form structure

International Nuclear Information System (INIS)

Yoo-Kong, Sikarin; Lobb, Sarah; Nijhoff, Frank

2011-01-01

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time and continuous time, as a first example of a Lagrangian 1-form structure in the sense of the recent paper (Lobb and Nijhoff 2009 J. Phys. A: Math. Theor.42 454013). The discrete-time model of the CM system was established some time ago arising as a pole reduction of a semi-discrete version of the Kadomtsev-Petviashvili (KP) equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper, we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation and the level of the CM system, we establish the proper Lagrangian 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in Lobb and Nijhoff (2009), for the simpler case of Lagrangian 1-forms. (paper)

Sensitivity analysis of a coupled hydro-mechanical paleo-climate model of density-dependent groundwater flow in discretely fractured crystalline rock

International Nuclear Information System (INIS)

Normani, S.D.; Sykes, J.F.

2011-01-01

A high resolution three-dimensional sub-regional scale (104 km 2 ) density-dependent, discretely fractured groundwater flow model with hydro-mechanical coupling and pseudo-permafrost was developed from a larger 5734 km 2 regional-scale groundwater flow model of a Canadian Shield setting. The objective of the work is to determine the sensitivity of modelled groundwater system evolution to the hydro-mechanical parameters. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture network model delineated from surface features was superimposed onto an approximate 790 000 element domain mesh with approximately 850 000 nodes. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. Interconnectivity of the permeable fracture zones is an important pathway for the possible migration and subsequent reduction in groundwater and contaminant residence times. The crystalline rock matrix between these structural discontinuities was assigned mechanical and flow properties characteristic of those reported for the Canadian Shield. The variation of total dissolved solids with depth was assigned using literature data for the Canadian Shield. Performance measures for the sensitivity analysis include equivalent freshwater heads, environmental heads, linear velocities, and depth of penetration by conservative non-decaying tracers released at the surface. A 121 000 year North American continental scale paleo-climate simulation was applied to the domain with ice-sheet histories estimated by the University of Toronto Glacial Systems Model (UofT GSM). Hydro-mechanical coupling between the rock matrix and the pore fluid, due to the ice sheet normal stress, was included in the simulations. The flow model included the influence of vertical strain and assumed that areal loads were homogeneous. Permafrost depth was applied as a permeability reduction

Discrete Ordinates Method-Like Computation with Group Condensation and Angle Collapsing in Transport Theory

International Nuclear Information System (INIS)

Won, Jong Hyuck; Cho, Nam Zin

2010-01-01

In group condensation for transport method, it is well-known that angle-dependent total cross section is generated. To remove this difficulty on angledependent total cross section, we normally perform the group condensation on total cross section by using scalar flux weight as used in neutron diffusion method. In this study, angle-dependent total cross section is directly applied to the discrete ordinates method. In addition, angle collapsing concept is introduced based on equivalence to reduce calculational burden of transport computation. We also show numerical results for a heterogeneous 1-D slab problem with local/global iteration, in which fine-group discrete ordinates calculation is used in local problem while few-group angle collapsed discrete ordinates calculation is used in global problem iteratively

Discrete modelling of the electrochemical performance of SOFC electrodes

International Nuclear Information System (INIS)

Schneider, L.C.R.; Martin, C.L.; Bultel, Y.; Bouvard, D.; Siebert, E.

2006-01-01

The composite anode and cathode of solid oxide fuel cells (SOFC) are modelled as sintered mixtures of electrolyte and electrocatalyst particles. A particle packing is first created numerically by the discrete element method (DEM) from a loose packing of 40 000 spherical, monosized, homogeneously mixed, and randomly positioned particles. Once the microstructure is sintered numerically, the effective electrode conductivity is determined by discretization of the particle packing into a resistance network. Each particle contact is characteristic of a bond resistance that depends on contact geometry and particle properties. The network, which typically consists of 120 000 bond resistances in total, is solved using Kirchhoff's current law. Distributions of local current densities and particle potentials are then performed. We investigate how electrode performance depends on parameters such as electrode composition, thickness, density and intrinsic material conductivities that are temperature dependent. The simulations show that the best electrode performance is obtained for compositions close to the percolation threshold of the electronic conductor. Depending on particle conductivities, the electrode performance is a function of its thickness. Additionally, DEM simulations generate useful microstructural information such as: coordination numbers, triple phase boundary length and percolation thresholds

Value of Construction Company and its Dependence on Significant Variables

Science.gov (United States)

Vítková, E.; Hromádka, V.; Ondrušková, E.

2017-10-01

The paper deals with the value of the construction company assessment respecting usable approaches and determinable variables. The reasons of the value of the construction company assessment are different, but the most important reasons are the sale or the purchase of the company, the liquidation of the company, the fusion of the company with another subject or the others. According the reason of the value assessment it is possible to determine theoretically different approaches for valuation, mainly it concerns about the yield method of valuation and the proprietary method of valuation. Both approaches are dependant of detailed input variables, which quality will influence the final assessment of the company´s value. The main objective of the paper is to suggest, according to the analysis, possible ways of input variables, mainly in the form of expected cash-flows or the profit, determination. The paper is focused mainly on methods of time series analysis, regression analysis and mathematical simulation utilization. As the output, the results of the analysis on the case study will be demonstrated.

Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach.

Science.gov (United States)

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng

2016-03-01

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

Discrete element modeling of deformable particles in YADE

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Martin Haustein

2017-01-01

Full Text Available In this paper we describe the open-source discrete element framework YADE and the implementation of a new deformation engine. YADE is a highly expandable software package that allows the simulation of current industrial problems in the field of granular materials using particle-based numerical methods. The description of the compaction of powders and granular material like metal pellets is now possible with a pure and simple discrete element approach in a modern DEM-framework. The deformation is realized by expanding the radius of the spherical particles, depending on their overlap, so that the volume of the material is kept constant.

Meshes optimized for discrete exterior calculus (DEC).

Energy Technology Data Exchange (ETDEWEB)

Mousley, Sarah C. [Univ. of Illinois, Urbana-Champaign, IL (United States); Deakin, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knupp, Patrick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-12-01

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

On discrete 2D integrable equations of higher order

International Nuclear Information System (INIS)

Adler, V E; Postnikov, V V

2014-01-01

We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)

Discrete control systems

CERN Document Server

Okuyama, Yoshifumi

2014-01-01

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability.

Science.gov (United States)

Lu, Zeqin; Jhoja, Jaspreet; Klein, Jackson; Wang, Xu; Liu, Amy; Flueckiger, Jonas; Pond, James; Chrostowski, Lukas

2017-05-01

This work develops an enhanced Monte Carlo (MC) simulation methodology to predict the impacts of layout-dependent correlated manufacturing variations on the performance of photonics integrated circuits (PICs). First, to enable such performance prediction, we demonstrate a simple method with sub-nanometer accuracy to characterize photonics manufacturing variations, where the width and height for a fabricated waveguide can be extracted from the spectral response of a racetrack resonator. By measuring the spectral responses for a large number of identical resonators spread over a wafer, statistical results for the variations of waveguide width and height can be obtained. Second, we develop models for the layout-dependent enhanced MC simulation. Our models use netlist extraction to transfer physical layouts into circuit simulators. Spatially correlated physical variations across the PICs are simulated on a discrete grid and are mapped to each circuit component, so that the performance for each component can be updated according to its obtained variations, and therefore, circuit simulations take the correlated variations between components into account. The simulation flow and theoretical models for our layout-dependent enhanced MC simulation are detailed in this paper. As examples, several ring-resonator filter circuits are studied using the developed enhanced MC simulation, and statistical results from the simulations can predict both common-mode and differential-mode variations of the circuit performance.

A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

KAUST Repository

Duru, Kenneth

2014-01-01

A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.

Population and prehistory III: food-dependent demography in variable environments.

Science.gov (United States)

Lee, Charlotte T; Puleston, Cedric O; Tuljapurkar, Shripad

2009-11-01

The population dynamics of preindustrial societies depend intimately on their surroundings, and food is a primary means through which environment influences population size and individual well-being. Food production requires labor; thus, dependence of survival and fertility on food involves dependence of a population's future on its current state. We use a perturbation approach to analyze the effects of random environmental variation on this nonlinear, age-structured system. We show that in expanding populations, direct environmental effects dominate induced population fluctuations, so environmental variability has little effect on mean hunger levels, although it does decrease population growth. The growth rate determines the time until population is limited by space. This limitation introduces a tradeoff between population density and well-being, so population effects become more important than the direct effects of the environment: environmental fluctuation increases mortality, releasing density dependence and raising average well-being for survivors. We discuss the social implications of these findings for the long-term fate of populations as they transition from expansion into limitation, given that conditions leading to high well-being during growth depress well-being during limitation.

Discrete Element Modeling

Energy Technology Data Exchange (ETDEWEB)

Morris, J; Johnson, S

2007-12-03

The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

DBKGrad: An R Package for Mortality Rates Graduation by Discrete Beta Kernel Techniques

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Angelo Mazza

2014-04-01

Full Text Available We introduce the R package DBKGrad, conceived to facilitate the use of kernel smoothing in graduating mortality rates. The package implements univariate and bivariate adaptive discrete beta kernel estimators. Discrete kernels have been preferred because, in this context, variables such as age, calendar year and duration, are pragmatically considered as discrete and the use of beta kernels is motivated since it reduces boundary bias. Furthermore, when data on exposures to the risk of death are available, the use of adaptive bandwidth, that may be selected by cross-validation, can provide additional benefits. To exemplify the use of the package, an application to Italian mortality rates, for different ages and calendar years, is presented.

Discrete PID Tuning Using Artificial Intelligence Techniques

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Petr DOLEŽEL

2009-06-01

Full Text Available PID controllers are widely used in industry these days due to their useful properties such as simple tuning or robustness. While they are applicable to many control problems, they can perform poorly in some applications. Highly nonlinear system control with constrained manipulated variable can be mentioned as an example. The point of the paper is to string together convenient qualities of conventional PID control and progressive techniques based on Artificial Intelligence. Proposed control method should deal with even highly nonlinear systems. To be more specific, there is described new method of discrete PID controller tuning in this paper. This method tunes discrete PID controller parameters online through the use of genetic algorithm and neural model of controlled system in order to control successfully even highly nonlinear systems. After method description and some discussion, there is performed control simulation and comparison to one chosen conventional control method.

A fast iterative model for discrete velocity calculations on triangular grids

International Nuclear Information System (INIS)

Szalmas, Lajos; Valougeorgis, Dimitris

2010-01-01

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.

A new DOI detector design using discrete crystal array with depth-dependent reflector patterns and single-ended readout

Energy Technology Data Exchange (ETDEWEB)

Lee, Seung-Jae; Lee, Chaeyeong [Department of Radiological Science, Yonsei University, Wonju 26493 (Korea, Republic of); Kang, Jihoon, E-mail: ray.jihoon.kang@gmail.com [Department of Biomedical Engineering, Chonnam National University, 50 Daehak-ro, Yeosu, Jeonnam 59626 (Korea, Republic of); Chung, Yong Hyun, E-mail: ychung@yonsei.ac.kr [Department of Radiological Science, Yonsei University, Wonju 26493 (Korea, Republic of)

2017-01-21

We developed a depth of interaction (DOI) positron emission tomography (PET) detector using depth-dependent reflector patterns in a discrete crystal array. Due to the different reflector patterns at depth, light distribution was changed relative to depth. As a preliminary experiment, we measured DOI detector module crystal identification performance. The crystal consisted of a 9×9 array of 2 mmx2 mmx20 mm lutetium-yttrium oxyorthosilicate (LYSO) crystals. The crystal array was optically coupled to a 64-channel position-sensitive photomultiplier tube with a 2 mmx2 mm anode size and an 18.1 mmx18.1 mm effective area. We obtained the flood image with an Anger-type calculation. DOI layers and 9×9 pixels were well distinguished in the obtained images. Preclinical PET scanners based on this detector design offer the prospect of high and uniform spatial resolution.

A new DOI detector design using discrete crystal array with depth-dependent reflector patterns and single-ended readout

International Nuclear Information System (INIS)

Lee, Seung-Jae; Lee, Chaeyeong; Kang, Jihoon; Chung, Yong Hyun

2017-01-01

We developed a depth of interaction (DOI) positron emission tomography (PET) detector using depth-dependent reflector patterns in a discrete crystal array. Due to the different reflector patterns at depth, light distribution was changed relative to depth. As a preliminary experiment, we measured DOI detector module crystal identification performance. The crystal consisted of a 9×9 array of 2 mmx2 mmx20 mm lutetium-yttrium oxyorthosilicate (LYSO) crystals. The crystal array was optically coupled to a 64-channel position-sensitive photomultiplier tube with a 2 mmx2 mm anode size and an 18.1 mmx18.1 mm effective area. We obtained the flood image with an Anger-type calculation. DOI layers and 9×9 pixels were well distinguished in the obtained images. Preclinical PET scanners based on this detector design offer the prospect of high and uniform spatial resolution.

Using k-dependence causal forest to mine the most significant dependency relationships among clinical variables for thyroid disease diagnosis.

Directory of Open Access Journals (Sweden)

LiMin Wang

Full Text Available Numerous data mining models have been proposed to construct computer-aided medical expert systems. Bayesian network classifiers (BNCs are more distinct and understandable than other models. To graphically describe the dependency relationships among clinical variables for thyroid disease diagnosis and ensure the rationality of the diagnosis results, the proposed k-dependence causal forest (KCF model generates a series of submodels in the framework of maximum spanning tree (MST and demonstrates stronger dependence representation. Friedman test on 12 UCI datasets shows that KCF has classification accuracy advantage over the other state-of-the-art BNCs, such as Naive Bayes, tree augmented Naive Bayes, and k-dependence Bayesian classifier. Our extensive experimental comparison on 4 medical datasets also proves the feasibility and effectiveness of KCF in terms of sensitivity and specificity.

Control approach development for variable recruitment artificial muscles

Science.gov (United States)

Jenkins, Tyler E.; Chapman, Edward M.; Bryant, Matthew

2016-04-01

This study characterizes hybrid control approaches for the variable recruitment of fluidic artificial muscles with double acting (antagonistic) actuation. Fluidic artificial muscle actuators have been explored by researchers due to their natural compliance, high force-to-weight ratio, and low cost of fabrication. Previous studies have attempted to improve system efficiency of the actuators through variable recruitment, i.e. using discrete changes in the number of active actuators. While current variable recruitment research utilizes manual valve switching, this paper details the current development of an online variable recruitment control scheme. By continuously controlling applied pressure and discretely controlling the number of active actuators, operation in the lowest possible recruitment state is ensured and working fluid consumption is minimized. Results provide insight into switching control scheme effects on working fluids, fabrication material choices, actuator modeling, and controller development decisions.

Exercise training improves heart rate variability after methamphetamine dependency.

Science.gov (United States)

Dolezal, Brett Andrew; Chudzynski, Joy; Dickerson, Daniel; Mooney, Larissa; Rawson, Richard A; Garfinkel, Alan; Cooper, Christopher B

2014-06-01

Heart rate variability (HRV) reflects a healthy autonomic nervous system and is increased with physical training. Methamphetamine dependence (MD) causes autonomic dysfunction and diminished HRV. We compared recently abstinent methamphetamine-dependent participants with age-matched, drug-free controls (DF) and also investigated whether HRV can be improved with exercise training in the methamphetamine-dependent participants. In 50 participants (MD = 28; DF = 22), resting heart rate (HR; R-R intervals) was recorded over 5 min while seated using a monitor affixed to a chest strap. Previously reported time domain (SDNN, RMSSD, pNN50) and frequency domain (LFnu, HFnu, LF/HF) parameters of HRV were calculated with customized software. MD were randomized to thrice-weekly exercise training (ME = 14) or equal attention without training (MC = 14) over 8 wk. Groups were compared using paired and unpaired t-tests. Statistical significance was set at P ≤ 0.05. Participant characteristics were matched between groups (mean ± SD): age = 33 ± 6 yr; body mass = 82.7 ± 12 kg, body mass index = 26.8 ± 4.1 kg·min. Compared with DF, the MD group had significantly higher resting HR (P HRV indices were similar between ME and MC groups. However, after training, the ME group significantly (all P HRV, based on several conventional indices, was diminished in recently abstinent, methamphetamine-dependent individuals. Moreover, physical training yielded a marked increase in HRV, representing increased vagal modulation or improved autonomic balance.

The Fourier U(2 Group and Separation of Discrete Variables

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Kurt Bernardo Wolf

2011-06-01

Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.

Energy-pointwise discrete ordinates transport methods

International Nuclear Information System (INIS)

Williams, M.L.; Asgari, M.; Tashakorri, R.

1997-01-01

A very brief description is given of a one-dimensional code, CENTRM, which computes a detailed, space-dependent flux spectrum in a pointwise-energy representation within the resolved resonance range. The code will become a component in the SCALE system to improve computation of self-shielded cross sections, thereby enhancing the accuracy of codes such as KENO. CENTRM uses discrete-ordinates transport theory with an arbitrary angular quadrature order and a Legendre expansion of scattering anisotropy for moderator materials and heavy nuclides. The CENTRM program provides capability to deterministically compute full energy range, space-dependent angular flux spectra, rigorously accounting for resonance fine-structure and scattering anisotropy effects

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

International Nuclear Information System (INIS)

Xu Xixiang; Cao Weili

2007-01-01

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.

Anyons in discrete gauge theories with Chern-Simons terms

International Nuclear Information System (INIS)

Bais, F.A.; Driel, P. van; Wild Propitius, M. de

1993-01-01

A gauge theory with a discrete group H in (2+1)-dimensional space-time is known to describe (non-abelian) anyons. We study the effect of adding a Chern-Simons term to such a theory. As in a previous paper, we emphasize the algebraic structure underlying a discrete H gauge theory, namely the Hopf algebra D(H). For H≅Z N , we argue on physical grounds that a Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H). Accordingly, the physically inequivalent models are labeled by the elements of the cohomology group H 3 (H, U(1)). It depends periodically on the coefficient of the Chern-Simons term which model is realized. This establishes a relation with the discrete topological field theories of Dijkgraaf and Witten. We extrapolate these results to non-abelian H, and work out the representative example H≅anti D 2 . (orig.)

Assessment of bidirectional influences between family relationships and adolescent problem behavior: Discrete versus continuous time analysis

NARCIS (Netherlands)

Delsing, M.J.M.H.; Oud, J.H.L.; Bruyn, E.E.J. De

2005-01-01

In family research, bidirectional influences between the family and the individual are usually analyzed in discrete time. Results from discrete time analysis, however, have been shown to be highly dependent on the length of the observation interval. Continuous time analysis using stochastic

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

OpenAIRE

Agafonov, S. I.

2005-01-01

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces

International Nuclear Information System (INIS)

Höhn, Philipp A.

2014-01-01

A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R N , a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed

Lung ventilation injures areas with discrete alveolar flooding, in a surface tension-dependent fashion.

Science.gov (United States)

Wu, You; Kharge, Angana Banerjee; Perlman, Carrie E

2014-10-01

With proteinaceous-liquid flooding of discrete alveoli, a model of the edema pattern in the acute respiratory distress syndrome, lung inflation over expands aerated alveoli adjacent to flooded alveoli. Theoretical considerations suggest that the overexpansion may be proportional to surface tension, T. Yet recent evidence indicates proteinaceous edema liquid may not elevate T. Thus whether the overexpansion is injurious is not known. Here, working in the isolated, perfused rat lung, we quantify fluorescence movement from the vasculature to the alveolar liquid phase as a measure of overdistension injury to the alveolar-capillary barrier. We label the perfusate with fluorescence; micropuncture a surface alveolus and instill a controlled volume of nonfluorescent liquid to obtain a micropunctured-but-aerated region (control group) or a region with discrete alveolar flooding; image the region at a constant transpulmonary pressure of 5 cmH2O; apply five ventilation cycles with a positive end-expiratory pressure of 0-20 cmH2O and tidal volume of 6 or 12 ml/kg; return the lung to a constant transpulmonary pressure of 5 cmH2O; and image for an additional 10 min. In aerated areas, ventilation is not injurious. With discrete alveolar flooding, all ventilation protocols cause sustained injury. Greater positive end-expiratory pressure or tidal volume increases injury. Furthermore, we determine T and find injury increases with T. Inclusion of either plasma proteins or Survanta in the flooding liquid does not alter T or injury. Inclusion of 2.7-10% albumin and 1% Survanta together, however, lowers T and injury. Contrary to expectation, albumin inclusion in our model facilitates exogenous surfactant activity. Copyright © 2014 the American Physiological Society.

A note on the optimal pricing strategy in the discrete-time Geo/Geo/1 queuing system with sojourn time-dependent reward

Directory of Open Access Journals (Sweden)

Doo Ho Lee

Full Text Available This work studies the optimal pricing strategy in a discrete-time Geo/Geo/1 queuing system under the sojourn time-dependent reward. We consider two types of pricing schemes. The first one is called the ex-post payment scheme where the server charges a price that is proportional to the time a customer spends in the system, and the second one is called ex-ante payment scheme where the server charges a flat price for all services. In each pricing scheme, a departing customer receives the reward that is inversely proportional to his/her sojourn time. The server should make the optimal pricing decisions in order to maximize its expected profits per time unit in each pricing scheme. This work also investigates customer's equilibrium joining or balking behavior under server's optimal pricing strategy. Numerical experiments are also conducted to validate our analysis. Keywords: Optimal pricing, Equilibrium behavior, Geo/Geo/1 queue, Sojourn time-dependent reward

Distance and Azimuthal Dependence of Ground‐Motion Variability for Unilateral Strike‐Slip Ruptures

KAUST Repository

Vyas, Jagdish Chandra

2016-06-21

We investigate near‐field ground‐motion variability by computing the seismic wavefield for five kinematic unilateral‐rupture models of the 1992 Mw 7.3 Landers earthquake, eight simplified unilateral‐rupture models based on the Landers event, and a large Mw 7.8 ShakeOut scenario. We include the geometrical fault complexity and consider different 1D velocity–density profiles for the Landers simulations and a 3D heterogeneous Earth structure for the ShakeOut scenario. For the Landers earthquake, the computed waveforms are validated using strong‐motion recordings. We analyze the simulated ground‐motion data set in terms of distance and azimuth dependence of peak ground velocity (PGV). Our simulations reveal that intraevent ground‐motion variability Graphic is higher in close distances to the fault (<20  km) and decreases with increasing distance following a power law. This finding is in stark contrast to constant sigma‐values used in empirical ground‐motion prediction equations. The physical explanation of a large near‐field Graphic is the presence of strong directivity and rupture complexity. High values of Graphic occur in the rupture‐propagation direction, but small values occur in the direction perpendicular to it. We observe that the power‐law decay of Graphic is primarily controlled by slip heterogeneity. In addition, Graphic, as function of azimuth, is sensitive to variations in both rupture speed and slip heterogeneity. The azimuth dependence of the ground‐motion mean μln(PGV) is well described by a Cauchy–Lorentz function that provides a novel empirical quantification to model the spatial dependency of ground motion. Online Material: Figures of slip distributions, residuals to ground‐motion prediction equations (GMPEs), distance and azimuthal dependence, and directivity predictor of ground‐motion variability for different source models.

Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays.

Science.gov (United States)

Liu, Hongjian; Wang, Zidong; Shen, Bo; Huang, Tingwen; Alsaadi, Fuad E

2018-06-01

This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion. Copyright © 2018 Elsevier Ltd. All rights reserved.

Learning dynamic Bayesian networks with mixed variables

DEFF Research Database (Denmark)

Bøttcher, Susanne Gammelgaard

This paper considers dynamic Bayesian networks for discrete and continuous variables. We only treat the case, where the distribution of the variables is conditional Gaussian. We show how to learn the parameters and structure of a dynamic Bayesian network and also how the Markov order can be learned...

High-order solution methods for grey discrete ordinates thermal radiative transfer

Energy Technology Data Exchange (ETDEWEB)

Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

2016-12-15

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

Modeling discrete and rhythmic movements through motor primitives: a review.

Science.gov (United States)

Degallier, Sarah; Ijspeert, Auke

2010-10-01

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

Are Health State Valuations from the General Public Biased? A Test of Health State Reference Dependency Using Self-assessed Health and an Efficient Discrete Choice Experiment.

Science.gov (United States)

Jonker, Marcel F; Attema, Arthur E; Donkers, Bas; Stolk, Elly A; Versteegh, Matthijs M

2017-12-01

Health state valuations of patients and non-patients are not the same, whereas health state values obtained from general population samples are a weighted average of both. The latter constitutes an often-overlooked source of bias. This study investigates the resulting bias and tests for the impact of reference dependency on health state valuations using an efficient discrete choice experiment administered to a Dutch nationally representative sample of 788 respondents. A Bayesian discrete choice experiment design consisting of eight sets of 24 (matched pairwise) choice tasks was developed, with each set providing full identification of the included parameters. Mixed logit models were used to estimate health state preferences with respondents' own health included as an additional predictor. Our results indicate that respondents with impaired health worse than or equal to the health state levels under evaluation have approximately 30% smaller health state decrements. This confirms that reference dependency can be observed in general population samples and affirms the relevance of prospect theory in health state valuations. At the same time, the limited number of respondents with severe health impairments does not appear to bias social tariffs as obtained from general population samples. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Discrete port-Hamiltonian systems

NARCIS (Netherlands)

Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

2006-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

Applied discrete-time queues

CERN Document Server

Alfa, Attahiru S

2016-01-01

This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

Time Discretization Techniques

KAUST Repository

Gottlieb, S.; Ketcheson, David I.

2016-01-01

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

Reactive scattering theory for molecular transitions in time-dependent fields

International Nuclear Information System (INIS)

Peskin, U.; Miller, W.H.

1995-01-01

A new approach is introduced for computing probabilities of molecular transitions in time-dependent fields. The method is based on the stationary (t,t') representation of the Schroedinger equation and is shown to be equivalent to infinite order time-dependent perturbation theory. Bound-to-bound (i.e., photoexcitation) and bound-to-continuum (i.e., photoreaction) transitions are regarded as reactive collisions with the ''time coordinate'' as the reaction coordinate in an extended Hilbert space. A numerical method based on imposing absorbing boundary conditions for the time coordinate in a discrete variable representation framework is introduced. A single operation of the Green's operator provides all the state-specific transition probabilities as well as partial state-resolved (inclusive) reaction probabilities. Illustrative numerical applications are given for model systems

Human Performance Technology (HPT): An Examination of Definitions through Dependent and Independent Variables.

Science.gov (United States)

Irlbeck, Sonja A.

2002-01-01

Provides a chronological perspective of human performance technology (HPT) definitions and an evaluation of them in terms of independent and dependent variables. Discusses human competence and performance technology and compares the definitions with the goals that have been articulated for HPT. (Author/LRW)

Discrete repulsive oscillator wavefunctions

International Nuclear Information System (INIS)

Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

2009-01-01

For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi—Pasta—Ulam lattice

International Nuclear Information System (INIS)

Xu Quan; Tian Qiang

2013-01-01

Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi—Pasta—Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too. (condensed matter: structural, mechanical, and thermal properties)

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Time Evolution Of The Wigner Function In Discrete Quantum Phase Space For A Soluble Quasi-spin Model

CERN Document Server

Galetti, D

2000-01-01

Summary: The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with an $SU(2)$-based semiclassical continuous approach to the Lipkin model is also presented.

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

Discrete Planck spectra

International Nuclear Information System (INIS)

Vlad, Valentin I.; Ionescu-Pallas, Nicholas

2000-10-01

The Planck radiation spectrum of ideal cubic and spherical cavities, in the region of small adiabatic invariance, γ = TV 1/3 , is shown to be discrete and strongly dependent on the cavity geometry and temperature. This behavior is the consequence of the random distribution of the state weights in the cubic cavity and of the random overlapping of the successive multiplet components, for the spherical cavity. The total energy (obtained by summing up the exact contributions of the eigenvalues and their weights, for low values of the adiabatic invariance) does not obey any longer Stefan-Boltzmann law. The new law includes a corrective factor depending on γ and imposes a faster decrease of the total energy to zero, for γ → 0. We have defined the double quantized regime both for cubic and spherical cavities by the superior and inferior limits put on the principal quantum numbers or the adiabatic invariance. The total energy of the double quantized cavities shows large differences from the classical calculations over unexpected large intervals, which are measurable and put in evidence important macroscopic quantum effects. (author)

Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion

KAUST Repository

Cañ izo, J.A.; Desvillettes, L.; Fellner, K.

2010-01-01

We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori

An edgeworth expansion for a sum of M-Dependent random variables

Directory of Open Access Journals (Sweden)

Wan Soo Rhee

1985-01-01

Full Text Available Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1, we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2 under the assumption that E[exp(it Sσ1] is small away from the origin. The result is of the best possible order.

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

2011-01-01

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

Motivation as an independent and a dependent variable in medical education: a review of the literature.

Science.gov (United States)

Kusurkar, R A; Ten Cate, Th J; van Asperen, M; Croiset, G

2011-01-01

Motivation in learning behaviour and education is well-researched in general education, but less in medical education. To answer two research questions, 'How has the literature studied motivation as either an independent or dependent variable? How is motivation useful in predicting and understanding processes and outcomes in medical education?' in the light of the Self-determination Theory (SDT) of motivation. A literature search performed using the PubMed, PsycINFO and ERIC databases resulted in 460 articles. The inclusion criteria were empirical research, specific measurement of motivation and qualitative research studies which had well-designed methodology. Only studies related to medical students/school were included. Findings of 56 articles were included in the review. Motivation as an independent variable appears to affect learning and study behaviour, academic performance, choice of medicine and specialty within medicine and intention to continue medical study. Motivation as a dependent variable appears to be affected by age, gender, ethnicity, socioeconomic status, personality, year of medical curriculum and teacher and peer support, all of which cannot be manipulated by medical educators. Motivation is also affected by factors that can be influenced, among which are, autonomy, competence and relatedness, which have been described as the basic psychological needs important for intrinsic motivation according to SDT. Motivation is an independent variable in medical education influencing important outcomes and is also a dependent variable influenced by autonomy, competence and relatedness. This review finds some evidence in support of the validity of SDT in medical education.

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

International Nuclear Information System (INIS)

Coelho, Pedro J.

2014-01-01

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan

2011-01-01

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate

Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

International Nuclear Information System (INIS)

Zhang Yufeng; Fan Engui; Zhang Yongqing

2006-01-01

With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

The Effect of Haptic Guidance on Learning a Hybrid Rhythmic-Discrete Motor Task.

Science.gov (United States)

Marchal-Crespo, Laura; Bannwart, Mathias; Riener, Robert; Vallery, Heike

2015-01-01

Bouncing a ball with a racket is a hybrid rhythmic-discrete motor task, combining continuous rhythmic racket movements with discrete impact events. Rhythmicity is exceptionally important in motor learning, because it underlies fundamental movements such as walking. Studies suggested that rhythmic and discrete movements are governed by different control mechanisms at different levels of the Central Nervous System. The aim of this study is to evaluate the effect of fixed/fading haptic guidance on learning to bounce a ball to a desired apex in virtual reality with varying gravity. Changing gravity changes dominance of rhythmic versus discrete control: The higher the value of gravity, the more rhythmic the task; lower values reduce the bouncing frequency and increase dwell times, eventually leading to a repetitive discrete task that requires initiation and termination, resembling target-oriented reaching. Although motor learning in the ball-bouncing task with varying gravity has been studied, the effect of haptic guidance on learning such a hybrid rhythmic-discrete motor task has not been addressed. We performed an experiment with thirty healthy subjects and found that the most effective training condition depended on the degree of rhythmicity: Haptic guidance seems to hamper learning of continuous rhythmic tasks, but it seems to promote learning for repetitive tasks that resemble discrete movements.

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

Science.gov (United States)

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

2017-10-01

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

Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate

Phase dependence of transport-aperture coordination variability reveals control strategy of reach-to-grasp movements.

Science.gov (United States)

Rand, Miya K; Shimansky, Y P; Hossain, Abul B M I; Stelmach, George E

2010-11-01

Based on an assumption of movement control optimality in reach-to-grasp movements, we have recently developed a mathematical model of transport-aperture coordination (TAC), according to which the hand-target distance is a function of hand velocity and acceleration, aperture magnitude, and aperture velocity and acceleration (Rand et al. in Exp Brain Res 188:263-274, 2008). Reach-to-grasp movements were performed by young adults under four different reaching speeds and two different transport distances. The residual error magnitude of fitting the above model to data across different trials and subjects was minimal for the aperture-closure phase, but relatively much greater for the aperture-opening phase, indicating considerable difference in TAC variability between those phases. This study's goal is to identify the main reasons for that difference and obtain insights into the control strategy of reach-to-grasp movements. TAC variability within the aperture-opening phase of a single trial was found minimal, indicating that TAC variability between trials was not due to execution noise, but rather a result of inter-trial and inter-subject variability of motor plan. At the same time, the dependence of the extent of trial-to-trial variability of TAC in that phase on the speed of hand transport was sharply inconsistent with the concept of speed-accuracy trade-off: the lower the speed, the larger the variability. Conversely, the dependence of the extent of TAC variability in the aperture-closure phase on hand transport speed was consistent with that concept. Taking into account recent evidence that the cost of neural information processing is substantial for movement planning, the dependence of TAC variability in the aperture-opening phase on task performance conditions suggests that it is not the movement time that the CNS saves in that phase, but the cost of neuro-computational resources and metabolic energy required for TAC regulation in that phase. Thus, the CNS

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

International Nuclear Information System (INIS)

Song, Qiankun; Wang, Zidong

2007-01-01

In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov-Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

International Nuclear Information System (INIS)

Gerstl, S.A.W.; Zardecki, A.

1985-01-01

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

Effects of environmental variables on invasive amphibian activity: Using model selection on quantiles for counts

Science.gov (United States)

Muller, Benjamin J.; Cade, Brian S.; Schwarzkoph, Lin

2018-01-01

Many different factors influence animal activity. Often, the value of an environmental variable may influence significantly the upper or lower tails of the activity distribution. For describing relationships with heterogeneous boundaries, quantile regressions predict a quantile of the conditional distribution of the dependent variable. A quantile count model extends linear quantile regression methods to discrete response variables, and is useful if activity is quantified by trapping, where there may be many tied (equal) values in the activity distribution, over a small range of discrete values. Additionally, different environmental variables in combination may have synergistic or antagonistic effects on activity, so examining their effects together, in a modeling framework, is a useful approach. Thus, model selection on quantile counts can be used to determine the relative importance of different variables in determining activity, across the entire distribution of capture results. We conducted model selection on quantile count models to describe the factors affecting activity (numbers of captures) of cane toads (Rhinella marina) in response to several environmental variables (humidity, temperature, rainfall, wind speed, and moon luminosity) over eleven months of trapping. Environmental effects on activity are understudied in this pest animal. In the dry season, model selection on quantile count models suggested that rainfall positively affected activity, especially near the lower tails of the activity distribution. In the wet season, wind speed limited activity near the maximum of the distribution, while minimum activity increased with minimum temperature. This statistical methodology allowed us to explore, in depth, how environmental factors influenced activity across the entire distribution, and is applicable to any survey or trapping regime, in which environmental variables affect activity.

On the Two-Moment Approximation of the Discrete-Time GI/G/1 Queue with a Single Vacation

Directory of Open Access Journals (Sweden)

Doo Ho Lee

2016-01-01

Full Text Available We consider a discrete-time GI/G/1 queue in which the server takes exactly one vacation each time the system becomes empty. The interarrival times of arriving customers, the service times, and the vacation times are all generic discrete random variables. Under our study, we derive an exact transform-free expression for the stationary system size distribution through the modified supplementary variable technique. Utilizing obtained results, we introduce a simple two-moment approximation for the system size distribution. From this, approximations for the mean system size along with the system size distribution could be obtained. Finally, some numerical examples are given to validate the proposed approximation method.

TWO MEASURES OF THE DEPENDENCE OF PREFERENTIAL RANKINGS ON CATEGORICAL VARIABLES

Directory of Open Access Journals (Sweden)

Lissowski Grzegorz

2017-06-01

Full Text Available The aim of this paper is to apply a general methodology for constructing statistical methods, which is based on decision theory, to give a statistical description of preferential rankings, with a focus on the rankings’ dependence on categorical variables. In the paper, I use functions of description errors that are based on the Kemeny and Hamming distances between preferential orderings, but the proposed methodology can also be applied to other methods of estimating description errors.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

Science.gov (United States)

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea

2013-01-01

Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.

A generalized endogenous grid method for discrete-continuous choice

OpenAIRE

John Rust; Bertel Schjerning; Fedor Iskhakov

2012-01-01

This paper extends Carroll's endogenous grid method (2006 "The method of endogenous gridpoints for solving dynamic stochastic optimization problems", Economic Letters) for models with sequential discrete and continuous choice. Unlike existing generalizations, we propose solution algorithm that inherits both advantages of the original method, namely it avoids all root finding operations, and also efficiently deals with restrictions on the continuous decision variable. To further speed up the s...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

Two new discrete integrable systems

International Nuclear Information System (INIS)

Chen Xiao-Hong; Zhang Hong-Qing

2013-01-01

In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra à 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity

Space-Time Discrete KPZ Equation

Science.gov (United States)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Analysis of Tourism Resource Dependency on Collaboration among Local Governments in the Multi-Regional Tourism Development

Directory of Open Access Journals (Sweden)

Ha Dong-Won

2014-01-01

Full Text Available The purpose of this study was to derive the multidimensional attributes of resource dependency of local governments in multi-regional tourism development. The questionnaire was designed based on resource dependence theory and related literature, and five factors of resource dependency were derived by analysis of the questionnaire for the civil servants who participated in the Jirisan area tourism development project which is a representative multi-regional tourism development project of Korea. The measured values of the derived possession, importance, discretion, alternative, and connection were found in various ways according to the project characteristics such as project scale and visitors in the Jirisan area tourism development project. This shows that a variety of variables have an effect on resource dependency.

Discrete density of states

International Nuclear Information System (INIS)

Aydin, Alhun; Sisman, Altug

2016-01-01

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Discussion of discrete D shape toroidal coil

International Nuclear Information System (INIS)

Kaiho, Katsuyuki; Ohara, Takeshi; Agatsuma, Ko; Onishi, Toshitada

1988-01-01

A novel design for a toroidal coil, called the D shape coil, was reported by J. File. The coil conductors are in pure tension and then subject to no bending moment. This leads to a smaller number of emf supports in a simpler configuration than that with the conventional toroidal coil of circular cross-section. The contours of the D shape are given as solutions of a differential equation. This equation includes the function of the magnetic field distribution in the conductor region which is inversely proportional to the winding radius. It is therefore important to use the exact magnetic field distribution. However the magnetic field distribution becomes complicated when the D shape toroidal coil is comprised of discrete coils and also depends on the D shape configuration. A theory and a computer program for designing the practical pure-tension toroidal coil are developed. Using this computer code, D shape conductors are calculated for various numbers of discrete coils and the results are compared. Electromagnetic forces in the coils are also calculated. It is shown that the hoop stress in the conductors depends only on the total ampere-turns of the coil when the contours of the D shape are similar. (author)

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

The spectral transform as a tool for solving nonlinear discrete evolution equations

International Nuclear Information System (INIS)

Levi, D.

1979-01-01

In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

3-D Discrete Analytical Ridgelet Transform

OpenAIRE

Helbert , David; Carré , Philippe; Andrès , Éric

2006-01-01

International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...

Critical bifurcation surfaces of 3D discrete dynamics

Directory of Open Access Journals (Sweden)

Michael Sonis

2000-01-01

Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.

Does attentional selectivity in the flanker task improve discretely or gradually?

Directory of Open Access Journals (Sweden)

Ronald eHübner

2012-10-01

Full Text Available An important question is whether attentional selectivity improves discretely or continuously during stimulus processing. In a recent study, Hübner, et al. (2010 found that the discrete DSTP model accounted better for flanker-task data than various continuous improvement models. However, in a subsequent study, White, et al. (2011 introduced the continuous SSP model and showed that it was superior to the DSTP model. From this result they concluded that attentional selectivity improves continuously rather than discretely. Because different stimuli and procedures were used in these two studies, though, we questioned that the superiority of the SSP model holds generally. Therefore, we fit the SSP model to Hübner et al.’s data and found that the DSTP model was again superior. A series of four experiments revealed that model superiority depends on the response-stimulus interval (RSI. Together, our results demonstrate that methodological details can be crucial for model selection, and that further comparisons between the models are needed before it can be decided whether attentional selectivity improves continuously or discretely.

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Latent variables and route choice behavior

DEFF Research Database (Denmark)

Prato, Carlo Giacomo; Bekhor, Shlomo; Pronello, Cristina

2012-01-01

In the last decade, a broad array of disciplines has shown a general interest in enhancing discrete choice models by considering the incorporation of psychological factors affecting decision making. This paper provides insight into the comprehension of the determinants of route choice behavior...... and bound algorithm. A hybrid model consists of measurement equations, which relate latent variables to measurement indicators and utilities to choice indicators, and structural equations, which link travelers’ observable characteristics to latent variables and explanatory variables to utilities. Estimation...

Continuous-variable quantum homomorphic signature

Science.gov (United States)

Li, Ke; Shang, Tao; Liu, Jian-wei

2017-10-01

Quantum cryptography is believed to be unconditionally secure because its security is ensured by physical laws rather than computational complexity. According to spectrum characteristic, quantum information can be classified into two categories, namely discrete variables and continuous variables. Continuous-variable quantum protocols have gained much attention for their ability to transmit more information with lower cost. To verify the identities of different data sources in a quantum network, we propose a continuous-variable quantum homomorphic signature scheme. It is based on continuous-variable entanglement swapping and provides additive and subtractive homomorphism. Security analysis shows the proposed scheme is secure against replay, forgery and repudiation. Even under nonideal conditions, it supports effective verification within a certain verification threshold.

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

CGBayesNets: conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data.

Science.gov (United States)

McGeachie, Michael J; Chang, Hsun-Hsien; Weiss, Scott T

2014-06-01

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

ADAM: analysis of discrete models of biological systems using computer algebra.

Science.gov (United States)

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web

A dynamic approach to dependability studies

International Nuclear Information System (INIS)

Labeau, P.E.

2008-01-01

Dependability studies have now become an important part of the performance management of industrial plants. These last decades, several methods have been proposed and widely used for the analysis of systems of components subject to degradation and failure. These methods are based either on Boolean representations (for example, event trees/fault trees), or on discrete-state models (Markovian reliability, Petri nets, Bayesian networks...). However, the underlying, inherently continuous, physical processes have scarcely been accounted for, at least in an integrated fashion, in dependability studies. This paper first describes, through simple cases, the limitations of discrete approaches and the need of hybrid, discrete-continuous methods. It then summarizes the main concepts of dynamic reliability. Finally, some possible application domains are presented, as well as challenges that still need to be tackled to favour the diffusion of this approach among industrial circles. (author)

Discrete density of states

Energy Technology Data Exchange (ETDEWEB)

Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

2016-03-22

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Homogenization of discrete media

International Nuclear Information System (INIS)

Pradel, F.; Sab, K.

1998-01-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)

Homogenization of discrete media

Energy Technology Data Exchange (ETDEWEB)

Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)

1998-11-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.

A non-linear discrete transform for pattern recognition of discrete chaotic systems

International Nuclear Information System (INIS)

Karanikas, C.; Proios, G.

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter

A non-linear discrete transform for pattern recognition of discrete chaotic systems

CERN Document Server

Karanikas, C

2003-01-01

It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.

A study of renal blood flow regulation using the discrete wavelet transform

Science.gov (United States)

Pavlov, Alexey N.; Pavlova, Olga N.; Mosekilde, Erik; Sosnovtseva, Olga V.

2010-02-01

In this paper we provide a way to distinguish features of renal blood flow autoregulation mechanisms in normotensive and hypertensive rats based on the discrete wavelet transform. Using the variability of the wavelet coefficients we show distinctions that occur between the normal and pathological states. A reduction of this variability in hypertension is observed on the microscopic level of the blood flow in efferent arteriole of single nephrons. This reduction is probably associated with higher flexibility of healthy cardiovascular system.

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

New Discrete Fibonacci Charge Pump Design, Evaluation and Measurement

Science.gov (United States)

Matoušek, David; Hospodka, Jiří; Šubrt, Ondřej

2017-06-01

This paper focuses on the practical aspects of the realisation of Dickson and Fibonacci charge pumps. Standard Dickson charge pump circuit solution and new Fibonacci charge pump implementation are compared. Both charge pumps were designed and then evaluated by LTspice XVII simulations and realised in a discrete form on printed circuit board (PCB). Finally, the key parameters as the output voltage, efficiency, rise time, variable power supply and clock frequency effects were measured.

Discrete elements method of neutron transport

International Nuclear Information System (INIS)

Mathews, K.A.

1988-01-01

In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks

International Nuclear Information System (INIS)

Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S.

2012-01-01

This Letter addresses the stability analysis problem for a class of uncertain discrete-time stochastic fuzzy neural networks (DSFNNs) with time-varying delays. By constructing a new Lyapunov–Krasovskii functional combined with the free weighting matrix technique, a new set of delay-dependent sufficient conditions for the robust exponential stability of the considered DSFNNs is established in terms of Linear Matrix Inequalities (LMIs). Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained theory. -- Highlights: ► Applications of neural networks require the knowledge of dynamic behaviors. ► Exponential stability of discrete-time stochastic fuzzy neural networks is studied. ► Linear matrix inequality optimization approach is used to obtain the result. ► Delay-dependent stability criterion is established in terms of LMIs. ► Examples with simulation are provided to show the effectiveness of the result.

Statistical methodology for discrete fracture model - including fracture size, orientation uncertainty together with intensity uncertainty and variability

Energy Technology Data Exchange (ETDEWEB)

Darcel, C. (Itasca Consultants SAS (France)); Davy, P.; Le Goc, R.; Dreuzy, J.R. de; Bour, O. (Geosciences Rennes, UMR 6118 CNRS, Univ. def Rennes, Rennes (France))

2009-11-15

the lineament scale (k{sub t} = 2) on the other, addresses the issue of the nature of the transition. We develop a new 'mechanistic' model that could help in modeling why and where this transition can occur. The transition between both regimes would occur for a fracture length of 1-10 m and even at a smaller scale for the few outcrops that follow the self-similar density model. A consequence for the disposal issue is that the model that is likely to apply in the 'blind' scale window between 10-100 m is the self-similar model as it is defined for large-scale lineaments. The self-similar model, as it is measured for some outcrops and most lineament maps, is definitely worth being investigated as a reference for scales above 1-10 m. In the rest of the report, we develop a methodology for incorporating uncertainty and variability into the DFN modeling. Fracturing properties arise from complex processes which produce an intrinsic variability; characterizing this variability as an admissible variation of model parameter or as the division of the site into subdomains with distinct DFN models is a critical point of the modeling effort. Moreover, the DFN model encompasses a part of uncertainty, due to data inherent uncertainties and sampling limits. Both effects must be quantified and incorporated into the DFN site model definition process. In that context, all available borehole data including recording of fracture intercept positions, pole orientation and relative uncertainties are used as the basis for the methodological development and further site model assessment. An elementary dataset contains a set of discrete fracture intercepts from which a parent orientation/density distribution can be computed. The elementary bricks of the site, from which these initial parent density distributions are computed, rely on the former Single Hole Interpretation division of the boreholes into sections whose local boundaries are expected to reflect - locally - geology

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

Science.gov (United States)

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms

Science.gov (United States)

Egan, Raphael; Gibou, Frédéric

2017-10-01

We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

A paradigm for discrete physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.

1987-01-01

An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity

The TORT three-dimensional discrete ordinates neutron/photon transport code (TORT version 3)

Energy Technology Data Exchange (ETDEWEB)

Rhoades, W.A.; Simpson, D.B.

1997-10-01

TORT calculates the flux or fluence of neutrons and/or photons throughout three-dimensional systems due to particles incident upon the system`s external boundaries, due to fixed internal sources, or due to sources generated by interaction with the system materials. The transport process is represented by the Boltzman transport equation. The method of discrete ordinates is used to treat the directional variable, and a multigroup formulation treats the energy dependence. Anisotropic scattering is treated using a Legendre expansion. Various methods are used to treat spatial dependence, including nodal and characteristic procedures that have been especially adapted to resist numerical distortion. A method of body overlay assists in material zone specification, or the specification can be generated by an external code supplied by the user. Several special features are designed to concentrate machine resources where they are most needed. The directional quadrature and Legendre expansion can vary with energy group. A discontinuous mesh capability has been shown to reduce the size of large problems by a factor of roughly three in some cases. The emphasis in this code is a robust, adaptable application of time-tested methods, together with a few well-tested extensions.

Panel data models extended to spatial error autocorrelation or a spatially lagged dependent variable

NARCIS (Netherlands)

Elhorst, J. Paul

2001-01-01

This paper surveys panel data models extended to spatial error autocorrelation or a spatially lagged dependent variable. In particular, it focuses on the specification and estimation of four panel data models commonly used in applied research: the fixed effects model, the random effects model, the

Continuous- and Discrete-Time Stimulus Sequences for High Stimulus Rate Paradigm in Evoked Potential Studies

Directory of Open Access Journals (Sweden)

Tao Wang

2013-01-01

Full Text Available To obtain reliable transient auditory evoked potentials (AEPs from EEGs recorded using high stimulus rate (HSR paradigm, it is critical to design the stimulus sequences of appropriate frequency properties. Traditionally, the individual stimulus events in a stimulus sequence occur only at discrete time points dependent on the sampling frequency of the recording system and the duration of stimulus sequence. This dependency likely causes the implementation of suboptimal stimulus sequences, sacrificing the reliability of resulting AEPs. In this paper, we explicate the use of continuous-time stimulus sequence for HSR paradigm, which is independent of the discrete electroencephalogram (EEG recording system. We employ simulation studies to examine the applicability of the continuous-time stimulus sequences and the impacts of sampling frequency on AEPs in traditional studies using discrete-time design. Results from these studies show that the continuous-time sequences can offer better frequency properties and improve the reliability of recovered AEPs. Furthermore, we find that the errors in the recovered AEPs depend critically on the sampling frequencies of experimental systems, and their relationship can be fitted using a reciprocal function. As such, our study contributes to the literature by demonstrating the applicability and advantages of continuous-time stimulus sequences for HSR paradigm and by revealing the relationship between the reliability of AEPs and sampling frequencies of the experimental systems when discrete-time stimulus sequences are used in traditional manner for the HSR paradigm.

Discrete-Event Simulation

Directory of Open Access Journals (Sweden)

Prateek Sharma

2015-04-01

Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.

Relating zeta functions of discrete and quantum graphs

Science.gov (United States)

Harrison, Jonathan; Weyand, Tracy

2018-02-01

We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

Science.gov (United States)

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Less Conservative ℋ∞ Fuzzy Control for Discrete-Time Takagi-Sugeno Systems

Directory of Open Access Journals (Sweden)

Leonardo Amaral Mozelli

2011-01-01

Full Text Available New analysis and control design conditions of discrete-time fuzzy systems are proposed. Using fuzzy Lyapunov's functions and introducing slack variables, less conservative conditions are obtained. The controller guarantees system stabilization and ℋ∞ performance. Numerical tests and a practical experiment in Chua's circuit are presented to show the effectiveness.

Construction of Discrete Time Shadow Price

International Nuclear Information System (INIS)

Rogala, Tomasz; Stettner, Lukasz

2015-01-01

In the paper expected utility from consumption over finite time horizon for discrete time markets with bid and ask prices and strictly concave utility function is considered. The notion of weak shadow price, i.e. an illiquid price, depending on the portfolio, under which the model without bid and ask price is equivalent to the model with bid and ask price is introduced. Existence and the form of weak shadow price is shown. Using weak shadow price usual (called in the paper strong) shadow price is then constructed

Numerical computation of discrete differential scattering cross sections for Monte Carlo charged particle transport

International Nuclear Information System (INIS)

Walsh, Jonathan A.; Palmer, Todd S.; Urbatsch, Todd J.

2015-01-01

Highlights: • Generation of discrete differential scattering angle and energy loss cross sections. • Gauss–Radau quadrature utilizing numerically computed cross section moments. • Development of a charged particle transport capability in the Milagro IMC code. • Integration of cross section generation and charged particle transport capabilities. - Abstract: We investigate a method for numerically generating discrete scattering cross sections for use in charged particle transport simulations. We describe the cross section generation procedure and compare it to existing methods used to obtain discrete cross sections. The numerical approach presented here is generalized to allow greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data computed with this method compare favorably with discrete data generated with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code, Milagro. We verify the implementation of charged particle transport in Milagro with analytic test problems and we compare calculated electron depth–dose profiles with another particle transport code that has a validated electron transport capability. Finally, we investigate the integration of the new discrete cross section generation method with the charged particle transport capability in Milagro.

Discrete dynamics versus analytic dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2014-01-01

For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

3-D discrete analytical ridgelet transform.

Science.gov (United States)

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Analysis of Discrete Mittag - Leffler Functions

Directory of Open Access Journals (Sweden)

N. Shobanadevi

2015-03-01

Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.

Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

2002-01-01

In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Stepwise latent class models for explaining group-level putcomes using discrete individual-level predictors

NARCIS (Netherlands)

Bennink, Margot; Croon, M.A.; Vermunt, J.K.

2015-01-01

Explaining group-level outcomes from individual-level predictors requires aggregating the individual-level scores to the group level and correcting the group-level estimates for measurement errors in the aggregated scores. However, for discrete variables it is not clear how to perform the

Size dependence of energy storage and dissipation in a discrete dislocation plasticity analysis of static friction

NARCIS (Netherlands)

Deshpande, VS; Needleman, A; Van der Giessen, E; Deshpande, V.S.

2005-01-01

The initiation of frictional sliding between a flat-bottomed indenter and a planar single crystal substrate is analyzed using discrete dislocation plasticity. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion,

Discrete mechanics

CERN Document Server

Caltagirone, Jean-Paul

2014-01-01

This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling.  The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H

Discrete mechanics

International Nuclear Information System (INIS)

Lee, T.D.

1985-01-01

This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

BAYESIAN TECHNIQUES FOR COMPARING TIME-DEPENDENT GRMHD SIMULATIONS TO VARIABLE EVENT HORIZON TELESCOPE OBSERVATIONS

Energy Technology Data Exchange (ETDEWEB)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios, E-mail: junhankim@email.arizona.edu [Department of Astronomy and Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721 (United States)

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

Discrete series representations for sl(2|1), Meixner polynomials and oscillator models

International Nuclear Information System (INIS)

Jafarov, E I; Van der Jeugt, J

2012-01-01

We explore a model for a one-dimensional quantum oscillator based on the Lie superalgebra sl(2|1). For this purpose, a class of discrete series representations of sl(2|1) is constructed, each representation characterized by a real number β > 0. In this model, the position and momentum operators of the oscillator are odd elements of sl(2|1) and their expressions involve an arbitrary parameter γ. In each representation, the spectrum of the Hamiltonian is the same as that of a canonical oscillator. The spectrum of a position operator can be continuous or infinite discrete, depending on the value of γ. We determine the position wavefunctions both in the continuous and the discrete case and discuss their properties. In the discrete case, these wavefunctions are given in terms of Meixner polynomials. From the embedding osp(1|2) subset of sl(2|1), it can be seen why the case γ = 1 corresponds to a paraboson oscillator. Consequently, taking the values (β, γ) = (1/2, 1) in the sl(2|1) model yields a canonical oscillator. (paper)

Cycles of a discrete time bipolar artificial neural network

International Nuclear Information System (INIS)

Cheng Suisun; Chen, J.-S.; Yueh, W.-C.

2009-01-01

A discrete time bipolar neural network depending on two parameters is studied. It is observed that its dynamical behaviors can be classified into six cases. For each case, the long time behaviors can be summarized in terms of fixed points, periodic points, basin of attractions, and related initial distributions. Mathematical reasons are supplied for these observations and applications in cellular automata are illustrated.

New Discrete Fibonacci Charge Pump Design, Evaluation and Measurement

Directory of Open Access Journals (Sweden)

Matoušek David

2017-06-01

Full Text Available This paper focuses on the practical aspects of the realisation of Dickson and Fibonacci charge pumps. Standard Dickson charge pump circuit solution and new Fibonacci charge pump implementation are compared. Both charge pumps were designed and then evaluated by LTspice XVII simulations and realised in a discrete form on printed circuit board (PCB. Finally, the key parameters as the output voltage, efficiency, rise time, variable power supply and clock frequency effects were measured.

Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model

International Nuclear Information System (INIS)

Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang

2016-01-01

A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.

Discrete gauge symmetries in discrete MSSM-like orientifolds

International Nuclear Information System (INIS)

Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.

2012-01-01

Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

A Decision Tool that Combines Discrete Event Software Process Models with System Dynamics Pieces for Software Development Cost Estimation and Analysis

Science.gov (United States)

Mizell, Carolyn Barrett; Malone, Linda

2007-01-01

The development process for a large software development project is very complex and dependent on many variables that are dynamic and interrelated. Factors such as size, productivity and defect injection rates will have substantial impact on the project in terms of cost and schedule. These factors can be affected by the intricacies of the process itself as well as human behavior because the process is very labor intensive. The complex nature of the development process can be investigated with software development process models that utilize discrete event simulation to analyze the effects of process changes. The organizational environment and its effects on the workforce can be analyzed with system dynamics that utilizes continuous simulation. Each has unique strengths and the benefits of both types can be exploited by combining a system dynamics model and a discrete event process model. This paper will demonstrate how the two types of models can be combined to investigate the impacts of human resource interactions on productivity and ultimately on cost and schedule.

Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

International Nuclear Information System (INIS)

Marchiolli, M.A.; Ruzzi, M.

2012-01-01

We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics. - Highlights: ► We construct a discrete version of the Weyl–Wigner–Moyal formalism. ► Coherent states for finite-dimensional discrete phase spaces are established. ► Discrete coordinate and momentum operators are properly defined. ► Uncertainty principles depend on the topology of finite physical systems. ► Corrections for the discrete Heisenberg uncertainty relation are also obtained.

A novel discrete PSO algorithm for solving job shop scheduling problem to minimize makespan

Science.gov (United States)

Rameshkumar, K.; Rajendran, C.

2018-02-01

In this work, a discrete version of PSO algorithm is proposed to minimize the makespan of a job-shop. A novel schedule builder has been utilized to generate active schedules. The discrete PSO is tested using well known benchmark problems available in the literature. The solution produced by the proposed algorithms is compared with best known solution published in the literature and also compared with hybrid particle swarm algorithm and variable neighborhood search PSO algorithm. The solution construction methodology adopted in this study is found to be effective in producing good quality solutions for the various benchmark job-shop scheduling problems.

Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Directory of Open Access Journals (Sweden)

Petr Stehlík

2015-01-01

Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′  (or  Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Adaptive Discrete Hypergraph Matching.

Science.gov (United States)

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

Principles of discrete time mechanics

CERN Document Server

Jaroszkiewicz, George

2014-01-01

Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro

2011-01-01

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Modern approaches to discrete curvature

CERN Document Server

Romon, Pascal

2017-01-01

 This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids

Energy Technology Data Exchange (ETDEWEB)

Rieben, R N; White, D A; Wallin, B K; Solberg, J M

2006-06-12

We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.

Noether symmetries of discrete mechanico–electrical systems

International Nuclear Information System (INIS)

Fu Jingli; Xie Fengping; Chen Benyong

2008-01-01

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

Science.gov (United States)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

DEFF Research Database (Denmark)

Stolpe, Mathias; Bendsøe, Martin P.

2007-01-01

This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)

2016-12-15

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

International Nuclear Information System (INIS)

Pham, Huyên; Wei, Xiaoli

2016-01-01

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Elementary exact calculations of degree growth and entropy for discrete equations.

Science.gov (United States)

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

1996-01-01

Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

Topology and layout optimization of discrete and continuum structures

Science.gov (United States)

Bendsoe, Martin P.; Kikuchi, Noboru

1993-01-01

The basic features of the ground structure method for truss structure an continuum problems are described. Problems with a large number of potential structural elements are considered using the compliance of the structure as the objective function. The design problem is the minimization of compliance for a given structural weight, and the design variables for truss problems are the cross-sectional areas of the individual truss members, while for continuum problems they are the variable densities of material in each of the elements of the FEM discretization. It is shown how homogenization theory can be applied to provide a relation between material density and the effective material properties of a periodic medium with a known microstructure of material and voids.

Current in heavy-current planar diode with discrete emission surface

International Nuclear Information System (INIS)

Belomyttsev, S.Ya.; Korovin, S.D.; Pegel', I.V

1999-01-01

Dependence of current in a high-current planar diode on the size of emission centres was studied. Essential effect of emission surface microstructure on the current value in the planar diode was demonstrated. It was determined that if the distance between the emitter essentially exceeded their size then current dependence on the ratio of size to the value of the diode gap was an exponential function with 3/2 index. Current dependence on voltage obeyed the exponential law with 3/2 index up to higher voltage values in the planar diode with discrete emission surface in contrast to the case of a planar diode with homogeneous emission surface [ru

Observability of discretized partial differential equations

Science.gov (United States)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Bifacial DNA origami-directed discrete, three-dimensional, anisotropic plasmonic nanoarchitectures with tailored optical chirality.

Science.gov (United States)

Lan, Xiang; Chen, Zhong; Dai, Gaole; Lu, Xuxing; Ni, Weihai; Wang, Qiangbin

2013-08-07

Discrete three-dimensional (3D) plasmonic nanoarchitectures with well-defined spatial configuration and geometry have aroused increasing interest, as new optical properties may originate from plasmon resonance coupling within the nanoarchitectures. Although spherical building blocks have been successfully employed in constructing 3D plasmonic nanoarchitectures because their isotropic nature facilitates unoriented localization, it still remains challenging to assemble anisotropic building blocks into discrete and rationally tailored 3D plasmonic nanoarchitectures. Here we report the first example of discrete 3D anisotropic gold nanorod (AuNR) dimer nanoarchitectures formed using bifacial DNA origami as a template, in which the 3D spatial configuration is precisely tuned by rationally shifting the location of AuNRs on the origami template. A distinct plasmonic chiral response was experimentally observed from the discrete 3D AuNR dimer nanoarchitectures and appeared in a spatial-configuration-dependent manner. This study represents great progress in the fabrication of 3D plasmonic nanoarchitectures with tailored optical chirality.

Investigations on the discrete Gi(G)1 queue with and without loss

International Nuclear Information System (INIS)

Gergely, T.; Toeroek, T.L.

1975-12-01

A comprehensive discussion of the method for investigating queuing systems characterized by random variables of integer values is given. Specially the discrete GI(G)1 queuing systems are considered. The first part of the paper takes a short summary on the theory of discrete stochastic processes. In the second part the properties of the fundamental characteristics of the queuing system as the busy period, the waiting time and the output processes are discussed. In the last section some remarks are added to show the direction of further investigations. To demonstrated the simplicity of the relations verified in the paper some computed examples are presented in the appendix. The computations were performed with a mini-computer of 8K words memory. (Sz.Z.)

Discrete Mathematics Re "Tooled."

Science.gov (United States)

Grassl, Richard M.; Mingus, Tabitha T. Y.

1999-01-01

Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre

2017-04-19

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression.

Science.gov (United States)

Vitense, Kelsey; Hanson, Mark A; Herwig, Brian R; Zimmer, Kyle D; Fieberg, John

2018-03-01

Ecosystems sometimes undergo dramatic shifts between contrasting regimes. Shallow lakes, for instance, can transition between two alternative stable states: a clear state dominated by submerged aquatic vegetation and a turbid state dominated by phytoplankton. Theoretical models suggest that critical nutrient thresholds differentiate three lake types: highly resilient clear lakes, lakes that may switch between clear and turbid states following perturbations, and highly resilient turbid lakes. For effective and efficient management of shallow lakes and other systems, managers need tools to identify critical thresholds and state-dependent relationships between driving variables and key system features. Using shallow lakes as a model system for which alternative stable states have been demonstrated, we developed an integrated framework using Bayesian latent variable regression (BLR) to classify lake states, identify critical total phosphorus (TP) thresholds, and estimate steady state relationships between TP and chlorophyll a (chl a) using cross-sectional data. We evaluated the method using data simulated from a stochastic differential equation model and compared its performance to k-means clustering with regression (KMR). We also applied the framework to data comprising 130 shallow lakes. For simulated data sets, BLR had high state classification rates (median/mean accuracy >97%) and accurately estimated TP thresholds and state-dependent TP-chl a relationships. Classification and estimation improved with increasing sample size and decreasing noise levels. Compared to KMR, BLR had higher classification rates and better approximated the TP-chl a steady state relationships and TP thresholds. We fit the BLR model to three different years of empirical shallow lake data, and managers can use the estimated bifurcation diagrams to prioritize lakes for management according to their proximity to thresholds and chance of successful rehabilitation. Our model improves upon

Violation of Bell's Inequality Using Continuous Variable Measurements

Science.gov (United States)

Thearle, Oliver; Janousek, Jiri; Armstrong, Seiji; Hosseini, Sara; Schünemann Mraz, Melanie; Assad, Syed; Symul, Thomas; James, Matthew R.; Huntington, Elanor; Ralph, Timothy C.; Lam, Ping Koy

2018-01-01

A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B =2.31 ±0.02 . This opens new possibilities for using continuous variable states for device independent quantum protocols.

Integrable discretizations of the short pulse equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

1982-01-01

The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

Discrete computational structures

CERN Document Server

Korfhage, Robert R

1974-01-01

Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize

A discrete single server queue with Markovian arrivals and phase type group services

Directory of Open Access Journals (Sweden)

Attahiru Sule Alfa

1995-01-01

Full Text Available We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified matrix-geometric type. Efficient algorithmic procedures for the computation of the rate matrix, steady-state probability vector, and some important system performance measures are developed. The steady-state waiting time distribution is derived explicitly. Some numerical examples are presented.

Encoding dependence in Bayesian causal networks

Science.gov (United States)

Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

Discrete integrable systems and deformations of associative algebras

International Nuclear Information System (INIS)

Konopelchenko, B G

2009-01-01

Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

International Nuclear Information System (INIS)

Aquilanti, V; Marinelli, D; Marzuoli, A

2014-01-01

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed

A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

DEFF Research Database (Denmark)

Stolpe, Mathias; Bendsøe, Martin P.

2007-01-01

This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities......) and cuts....

Robust Moving Horizon H∞ Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

Directory of Open Access Journals (Sweden)

F. Yıldız Tascikaraoglu

2014-01-01

Full Text Available In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

Discrete hierarchical organization of social group sizes.

Science.gov (United States)

Zhou, W-X; Sornette, D; Hill, R A; Dunbar, R I M

2005-02-22

The 'social brain hypothesis' for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non-human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3-5, 9-15, 30-45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.

Geometry and Hamiltonian mechanics on discrete spaces

International Nuclear Information System (INIS)

Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

Leader-Following Consensus Stability of Discrete-Time Linear Multiagent Systems with Observer-Based Protocols

Directory of Open Access Journals (Sweden)

Bingbing Xu

2013-01-01

Full Text Available We consider the leader-following consensus problem of discrete-time multiagent systems on a directed communication topology. Two types of distributed observer-based consensus protocols are considered to solve such a problem. The observers involved in the proposed protocols include full-order observer and reduced-order observer, which are used to reconstruct the state variables. Two algorithms are provided to construct the consensus protocols, which are based on the modified discrete-time algebraic Riccati equation and Sylvester equation. In light of graph and matrix theory, some consensus conditions are established. Finally, a numerical example is provided to illustrate the obtained result.

Norms for 10,491 Spanish words for five discrete emotions: Happiness, disgust, anger, fear, and sadness.

Science.gov (United States)

Stadthagen-González, Hans; Ferré, Pilar; Pérez-Sánchez, Miguel A; Imbault, Constance; Hinojosa, José Antonio

2017-09-18

The discrete emotion theory proposes that affective experiences can be reduced to a limited set of universal "basic" emotions, most commonly identified as happiness, sadness, anger, fear, and disgust. Here we present norms for 10,491 Spanish words for those five discrete emotions collected from a total of 2,010 native speakers, making it the largest set of norms for discrete emotions in any language to date. When used in conjunction with the norms from Hinojosa, Martínez-García et al. (Behavior Research Methods, 48, 272-284, 2016) and Ferré, Guasch, Martínez-García, Fraga, & Hinojosa (Behavior Research Methods, 49, 1082-1094, 2017), researchers now have access to ratings of discrete emotions for 13,633 Spanish words. Our norms show a high degree of inter-rater reliability and correlate highly with those from Ferré et al. (2017). Our exploration of the relationship between the five discrete emotions and relevant lexical and emotional variables confirmed findings of previous studies conducted with smaller datasets. The availability of such large set of norms will greatly facilitate the study of emotion, language and related fields. The norms are available as supplementary materials to this article.

Displacement in the parameter space versus spurious solution of discretization with large time step

International Nuclear Information System (INIS)

Mendes, Eduardo; Letellier, Christophe

2004-01-01

In order to investigate a possible correspondence between differential and difference equations, it is important to possess discretization of ordinary differential equations. It is well known that when differential equations are discretized, the solution thus obtained depends on the time step used. In the majority of cases, such a solution is considered spurious when it does not resemble the expected solution of the differential equation. This often happens when the time step taken into consideration is too large. In this work, we show that, even for quite large time steps, some solutions which do not correspond to the expected ones are still topologically equivalent to solutions of the original continuous system if a displacement in the parameter space is considered. To reduce such a displacement, a judicious choice of the discretization scheme should be made. To this end, a recent discretization scheme, based on the Lie expansion of the original differential equations, proposed by Monaco and Normand-Cyrot will be analysed. Such a scheme will be shown to be sufficient for providing an adequate discretization for quite large time steps compared to the pseudo-period of the underlying dynamics

Classical solutions for discrete potential boundary value problems with generalized Leray-Lions type operator and variable exponent

Directory of Open Access Journals (Sweden)

Bila Adolphe Kyelem

2017-04-01

Full Text Available In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin's critical point theory, which ensures the existence of solutions by ground state and mountain pass methods.

Discrete fracture modelling of the Finnsjoen rock mass. Phase 1: Feasibility study

International Nuclear Information System (INIS)

Geier, J.E.; Axelsson, C.L.

1991-03-01

The geometry and properties of discrete fractures are expected to control local heterogeneity in flow and solute transport within crystalline rock in the Finnsjoen area. The present report describes the first phase of a discrete-fracture modelling study, the goal of which is to develop stochastic-continuum and hydrologic properties. In the first phase of this study, the FracMan discrete fracture modelling package was used to analyse discrete fracture geometrical and hyrological data. Constant-pressure packer tests were analysed using fractional dimensional methods to estimate effective transmissivities and flow dimension for the packer test intervals. Discrete fracture data on orientation, size, shape, and location were combined with hydrologic data to develop a preliminary conceptual model for the conductive fractures at the site. The variability of fracture properties was expressed in the model by probability distributions. The preliminary conceptual model was used to simulate three-dimensional populations of conductive fractures in 25 m and 50 m cubes of rock. Transient packer tests were simulated in these fracture populations, and the simulated results were used to validate the preliminary conceptual model. The calibrated model was used to estimate the components of effective conductivity tensors for the rock by simulating steady-state groundwater flow through the cubes in three orthogonal directions. Monte Carlo stochastic simulations were performed for alternative realizations of the conceptual model. The number of simulations was insufficient to give a quantitative prediction of the effective conductivity heterogeneity and anisotropy on the scales of the cubes. However, the results give preliminary, rough estimates of these properties, and provide a demonstration of how the discrete-fracture network concept can be applied to derive data that is necessary for stochastic continuum and channel network modelling. (authors)

Integrable structure in discrete shell membrane theory.

Science.gov (United States)

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

A discrete-ordinates solution for a radiation therapy problem

International Nuclear Information System (INIS)

Goldschmidt, Gustavo Brun; Reichert, Janice Teresinha; Barichello, Liliane Basso

2008-01-01

A concise and accurate procedure for evaluating dose distribution, in a radiation therapy planning, is presented. The analytical discrete-ordinates method (ADO method) is used to develop a complete solution for a spectral dependent radiative transfer equation, in a one-dimensional medium, according to a multigroup scheme. Numerical results are presented for test problems, where the Klein-Nishina scattering kernel was used to describe the interaction processes. (author)

Discrete port-Hamiltonian systems : mixed interconnections

NARCIS (Netherlands)

Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der

2005-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

Variability of interconnected wind plants: correlation length and its dependence on variability time scale

Science.gov (United States)

St. Martin, Clara M.; Lundquist, Julie K.; Handschy, Mark A.

2015-04-01

The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. But how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer ‘how far is far enough,’ we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of five-minute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25-2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high

Local and global dynamics of Ramsey model: From continuous to discrete time.

Science.gov (United States)

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Method of nuclear reactor control using a variable temperature load dependent set point

International Nuclear Information System (INIS)

Kelly, J.J.; Rambo, G.E.

1982-01-01

A method and apparatus for controlling a nuclear reactor in response to a variable average reactor coolant temperature set point is disclosed. The set point is dependent upon percent of full power load demand. A manually-actuated ''droop mode'' of control is provided whereby the reactor coolant temperature is allowed to drop below the set point temperature a predetermined amount wherein the control is switched from reactor control rods exclusively to feedwater flow

State Dependence in Unemployment

DEFF Research Database (Denmark)

Ahmad, Nisar

2014-01-01

This study examines the extent state dependence among unemployed immigrants in a dynamic discrete choice framework. Three alternative methodologies are employed to control for the problem of the initial condition. The empirical findings show that there is a considerable correlation between the un...

Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

Directory of Open Access Journals (Sweden)

Walter H. Aschbacher

2009-01-01

Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

Natural variability of biochemical biomarkers in the macro-zoobenthos: Dependence on life stage and environmental factors.

Science.gov (United States)

Scarduelli, Lucia; Giacchini, Roberto; Parenti, Paolo; Migliorati, Sonia; Di Brisco, Agnese Maria; Vighi, Marco

2017-11-01

Biomarkers are widely used in ecotoxicology as indicators of exposure to toxicants. However, their ability to provide ecologically relevant information remains controversial. One of the major problems is understanding whether the measured responses are determined by stress factors or lie within the natural variability range. In a previous work, the natural variability of enzymatic levels in invertebrates sampled in pristine rivers was proven to be relevant across both space and time. In the present study, the experimental design was improved by considering different life stages of the selected taxa and by measuring more environmental parameters. The experimental design considered sampling sites in 2 different rivers, 8 sampling dates covering the whole seasonal cycle, 4 species from 3 different taxonomic groups (Plecoptera, Perla grandis; Ephemeroptera, Baetis alpinus and Epeorus alpicula; Tricoptera, Hydropsyche pellucidula), different life stages for each species, and 4 enzymes (acetylcholinesterase, glutathione S-transferase, alkaline phosphatase, and catalase). Biomarker levels were related to environmental (physicochemical) parameters to verify any kind of dependence. Data were statistically elaborated using hierarchical multilevel Bayesian models. Natural variability was found to be relevant across both space and time. The results of the present study proved that care should be paid when interpreting biomarker results. Further research is needed to better understand the dependence of the natural variability on environmental parameters. Environ Toxicol Chem 2017;36:3158-3167. © 2017 SETAC. © 2017 SETAC.

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES

Directory of Open Access Journals (Sweden)

Decio Levi

2016-06-01

Full Text Available In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.

Path integral measure and triangulation independence in discrete gravity

Science.gov (United States)

Dittrich, Bianca; Steinhaus, Sebastian

2012-02-01

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

On the effects of the degree of discretion in reporting managerial performance

NARCIS (Netherlands)

De Waegenaere, A.M.B.; Wielhouwer, J.L.

2011-01-01

We consider a principal-agent setting in which a manager’s compensation depends on a noisy performance signal, and the manager is granted the right to choose an (accounting) method to determine the value of the performance signal. We study the effect of the degree of such reporting discretion,

A latent class multiple constraint multiple discrete-continuous extreme value model of time use and goods consumption.

Science.gov (United States)

2016-06-01

This paper develops a microeconomic theory-based multiple discrete continuous choice model that considers: (a) that both goods consumption and time allocations (to work and non-work activities) enter separately as decision variables in the utility fu...

Persistence of non-Markovian Gaussian stationary processes in discrete time

Science.gov (United States)

Nyberg, Markus; Lizana, Ludvig

2018-04-01

The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n . Few results are known for the persistence P0(n ) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n ) ˜θn . Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n ) analytically in z -transform space in terms of the autocorrelation function A (n ) . If A (n )→0 as n →∞ , we extract θ numerically, while if A (n )=0 , for finite n >N , we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A (n )=0 for n >1 , the double exponential-correlated "second order autoregressive process", where A (n ) =c1λ1n+c2λ2n , and power-law-correlated variables, where A (n ) ˜n-μ . Apart from the power-law case when μ <5 , we find excellent agreement with simulations.

Maximal Inequalities for Dependent Random Variables

DEFF Research Database (Denmark)

Hoffmann-Jorgensen, Jorgen

2016-01-01

Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X-1, X-2,... be random variables with partial sums S-k = X-1 + ... + X-k. Then a......Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X-1, X-2,... be random variables with partial sums S-k = X-1 + ... + X......-k. Then a maximal inequality gives conditions ensuring that the maximal partial sum M-n = max(1) (...

Performance comparisons of enhanced tubes with discrete and wavy disruption shapes

Energy Technology Data Exchange (ETDEWEB)

Arman, B.; Rabas, T.J.

1993-08-01

This paper presents comparisons of the friction factors and heat-transfer coefficients obtained with enhanced tubes with transverse discrete and almost transverse wavy two-dimensional disruptions. Both experimental data and numerical predictions were used for the comparisons. For the latter a two-layer turbulence model incorporated in a body-fitted, finite-volume method was used. The disruption shape, discrete or wavy, depends on the manufacturing process. If an extrusion process is used, discrete disruptions (ribs) of various profiles are obtained that are separated from each other by a flat or unaltered inside diameter. If a spirally indenting process is used, a wavy proflie is obtained with a continuously varying inside diameter between two adjacent disruption peaks. These disruptions are transverse or almost transverse to the tube axis and separated by a distance that exceeds the reattachment length. Based on these comparisons, the following conclusions are obtained: (1) the disruption shape is not an important correlating parameter for discrete disruptions, (2) only the friction factor is influenced by the shape for wavy disruptions, and (3) there are major differences between both the friction-factor and heat-transfer performance of discrete and wavy disruptions with the same maximum disruption height and spacing. However, the most important finding is that the groove radius of spirally indented tubes should be increased because of the substantial reduction of the friction factor but only a small decrease in the thermal performance. Additional comparisons of predicted results were made to obtain a fundamental understanding of the influence of these different shapes.

On conservation laws for models in discrete, noncommutative and fractional differential calculus

International Nuclear Information System (INIS)

Klimek, M.

2001-01-01

We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied

Cuspidal discrete series for projective hyperbolic spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens

2013-01-01

Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

Assessment of variability in the hydrological cycle of the Loess Plateau, China: examining dependence structures of hydrological processes

Science.gov (United States)

Guo, A.; Wang, Y.

2017-12-01

Investigating variability in dependence structures of hydrological processes is of critical importance for developing an understanding of mechanisms of hydrological cycles in changing environments. In focusing on this topic, present work involves the following: (1) identifying and eliminating serial correlation and conditional heteroscedasticity in monthly streamflow (Q), precipitation (P) and potential evapotranspiration (PE) series using the ARMA-GARCH model (ARMA: autoregressive moving average; GARCH: generalized autoregressive conditional heteroscedasticity); (2) describing dependence structures of hydrological processes using partial copula coupled with the ARMA-GARCH model and identifying their variability via copula-based likelihood-ratio test method; and (3) determining conditional probability of annual Q under different climate scenarios on account of above results. This framework enables us to depict hydrological variables in the presence of conditional heteroscedasticity and to examine dependence structures of hydrological processes while excluding the influence of covariates by using partial copula-based ARMA-GARCH model. Eight major catchments across the Loess Plateau (LP) are used as study regions. Results indicate that (1) The occurrence of change points in dependence structures of Q and P (PE) varies across the LP. Change points of P-PE dependence structures in all regions almost fully correspond to the initiation of global warming, i.e., the early 1980s. (3) Conditional probabilities of annual Q under various P and PE scenarios are estimated from the 3-dimensional joint distribution of (Q, P and PE) based on the above change points. These findings shed light on mechanisms of the hydrological cycle and can guide water supply planning and management, particularly in changing environments.

Railway capacity and expansion analysis using time discretized paths

DEFF Research Database (Denmark)

Reinhardt, Line Blander; Pisinger, David; Lusby, Richard Martin

2017-01-01

of railway freight transportation on a long term strategic level. The model uses an hourly time discretization and analyses the impact of railway network expansions based on future demand forecasts. It provides an optimal macroscopic freight train schedule and can indicate the time and place of any...... variable penalties for the different passenger busy time slots. As part of a European Union project, all models are applied to a realistic case study that focuses on analyzing the capacity of railway network, in Denmark and Southern Sweden using demand forecasts for 2030. Results suggest that informative...

Discrete-Event Simulation

OpenAIRE

Prateek Sharma

2015-01-01

Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...