131,354 research outputs found

    Evaluation of numerical integration schemes for a partial integro-differential equation

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    Numerical methods are important in computational neuroscience where complex nonlinear systems are studied. This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integro-differential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficiency determined. Various ODE solvers in Matlab are used with the Fourier series method to solve the neural model, with an evaluation of the accuracy of the approximation versus the efficiency of the method. The two methodologies are then compared

    A novel code generation methodology for block diagram modeler and simulators Scicos and VSS

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    Block operations during simulation in Scicos and VSS environments can naturally be described as Nsp functions. But the direct use of Nsp functions for simulation leads to poor performance since the Nsp language is interpreted, not compiled. The methodology presented in this paper is used to develop a tool for generating efficient compilable code, such as C and ADA, for Scicos and VSS models from these block Nsp functions. Operator overloading and partial evaluation are the key elements of this novel approach. This methodology may be used in other simulation environments such as Matlab/Simulink

    Automatization of TDS data evaluation

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    Tato práce se zabývá automatizací vyhodnocování dat termální desorpční spektroskopie (TDS). Teoretická část pojednává o procesích adsorpce a desorpce atomů a molekul a teplotní závislosti desorpce. Součástí práce je také kvantitativní analýza signálu měřícího přístroje. Hlavním cílem praktické části bylo vytvoření počítačového programu na automatizaci vyhodnocování dat TDS. Popis programu a uživatelská příručka jsou také součástí práce. Proběhlo testování programu na předchozích měření a kinetické parametry desorpce byly zjištěny u několika vzorků.This bachelor thesis is focused on automatization of post-processing and evaluation of thermal desorption spectroscopy (TDS) data. The theoretical part discusses the processes of adsorption and desorption of atoms and molecules on surfaces and the thermal dependence of the latter. This work also provides a quantitative analysis of the measured signal from the instrument. The main objective of the practical part is to create a computer tool for automatization of TDS data evaluation. Description of the program, as well as a user guide, is included in the work. Comprehensive tests of the created program were concluded on previously measured TDS spectra and the kinetic parameters of several samples were determined.

    A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

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    We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as a infinite system of ordinary differential equations, and by truncation it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers Eq. in dimension 1.Comment: 28 pages, 10 figure

    Automatic Frechet differentiation for the numerical solution of boundary-value problems

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    A new solver for nonlinear boundary-value problems (BVPs) in Matlab is presented, based on the Chebfun software system for representing functions and operators automatically as numerical objects. The solver implements Newton's method in function space, where instead of the usual Jacobian matrices, the derivatives involved are Frechet derivatives. A major novelty of this approach is the application of automatic differentiation (AD) techniques to compute the operator-valued Frechet derivatives in the continuous context. Other novelties include the use of anonymous functions and numbering of each variable to enable a recursive, delayed evaluation of derivatives with forward mode AD. The AD techniques are applied within a new Chebfun class called chebop which allows users to set up and solve nonlinear BVPs in a few lines of code, using the "nonlinear backslash" operator (\). This framework enables one to study the behaviour of Newton's method in function space

    A Fast Learning Algorithm for Image Segmentation with Max-Pooling Convolutional Networks

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    We present a fast algorithm for training MaxPooling Convolutional Networks to segment images. This type of network yields record-breaking performance in a variety of tasks, but is normally trained on a computationally expensive patch-by-patch basis. Our new method processes each training image in a single pass, which is vastly more efficient. We validate the approach in different scenarios and report a 1500-fold speed-up. In an application to automated steel defect detection and segmentation, we obtain excellent performance with short training times

    Propagation Speed of the Maximum of the Fundamental Solution to the Fractional Diffusion-Wave Equation

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    In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order 1α21 \le \alpha \le 2 is revisited. This equation interpolates between the diffusion and the wave equations that behave quite differently regarding their response to a localized disturbance: whereas the diffusion equation describes a process, where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. For the time fractional diffusion-wave equation, the propagation speed of a disturbance is infinite, but its fundamental solution possesses a maximum that disperses with a finite speed. In this paper, the fundamental solution of the Cauchy problem for the time-fractional diffusion-wave equation, its maximum location, maximum value, and other important characteristics are investigated in detail. To illustrate analytical formulas, results of numerical calculations and plots are presented. Numerical algorithms and programs used to produce plots are discussed.Comment: 22 pages 6 figures. This paper has been presented by F. Mainardi at the International Workshop: Fractional Differentiation and its Applications (FDA12) Hohai University, Nanjing, China, 14-17 May 201
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