131,354 research outputs found
Evaluation of numerical integration schemes for a partial integro-differential equation
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
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
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
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
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
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
In this paper, the one-dimensional time-fractional diffusion-wave equation
with the fractional derivative of order 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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