Wyniki wyszukiwania - BazTech

1

A New Approach for Modeling with Discrete Fractional Equations

Atıcı F. M., Atıcı M., Belcher M., Marshall D.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

313--324

EN

In this paper, we introduce a new class of nonlinear discrete fractional equations to model tumor growth rates in mice. For the data fitting purpose, we develop a new method which can be considered as an improved version of the partial sum method for parameter estimations. We demonstrate the goodness of fit by comparing the models with three statistical measures.

2

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Marković D., Jukić D.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 1

145--155

EN

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the [...]. One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.

3

Monte Carlo fitting of data from muon catalyzed fusion experiments in solid hydrogen

Filipowicz M., Bystritsky V.M., Woźniak J.

Computer Science

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2008

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Vol. 9

11-20

EN

Applying the classical chi-square fitting procedure for multiparameter systems is in some cases extremely difficult due to the lack of an analytical expression for the theoretical functions describing the system. This paper presents an analysis procedure for experimental data using theoretical functions generated by Monte Carlo method, each corresponding to definite values of the minimization parameters. It was applied for the E742 experiment (TRIUMF, Vancouver, Canada) data analysis with the aim to analyze data from Muon Catalyzed Fusion experiments (extraction muonic atom scattering parameters and parameters of pd fusion in pdµ molecule).

PL

Zastosowanie klasycznej procedury fitowania przy użyciu estymatora chi-kwadrat jest w pewnych przypadkach bardzo trudne z powodu braku analitycznych wyrażeń na teoretyczne funkcje opisujące system. W pracy zaprezentowano procedurę analizy danych eksperymentalnych przy użyciu teoretycznych funkcji generowanych metodą Monte Carlo, odpowiadających zdefiniowanym wartościom szukanych parametrów. Analiza została zastosowana dla eksperymentu E742 (TRIUMF, Vancouver, Kanada) w celu opisu danych pochodzących z syntezy jądrowej katalizowanej mionami (uzyskanie parametrów opisujących rozpraszanie atomów mionowych i parametrów syntezy pd w molekule pdµ).

4

Ellipsoid Fourier Descriptor : hierarchical shape representation and deformable model

Dufrenois F.

Machine Graphics and Vision

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2000

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Vol. 9, No. 1/2

103-113

EN

This paper describes a new model-based segmentation and motion analysis technic combining Euler-Lagrange formalism and shape representation by Fourier decomposition. First, we propose to extend the concept of the 2D Fourier representation for closed curves to a new 3D hierarchical descriptor for closed surfaces. To study the shape deformation during motion, we establish also, the dynamic equations of motion of the Fourier parameters. Finally, some results on 2D data traking, 3D reconstructions and 3D data fitting are presented.