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252 results on '"Provost, Serge B."'

1. Une initiation au concept de l'infini

Author

Ades, Michel, Guillemette, David, and Provost, Serge B.

Subjects
Mathematics - History and Overview, 11-xx:Number theory, 11-01, 11-02, 11-03
Abstract

In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to demonstrate the countability of rationals. Cantor's diagonal procedure is explored, demonstrating that the infinity of real numbers is greater than that of integers. There is therefore a hierarchy of infinities, enabling us to elaborate on the continuum hypothesis, which remains an unsolved problem in mathematics., Comment: 14 pages, in French language, 4 figures,5 Pictures

Published
2024

2. Effects of Transceiver Jitter on the Performance of Optical Scattering Communication Systems

Author

Shen, Zanqiu, Ma, Jianshe, Provost, Serge B., and Su, Ping

Subjects
Electrical Engineering and Systems Science - Signal Processing, Physics - Optics
Abstract

In ultraviolet communications, the transceiver jitter effects have been ignored in previous studies, which can result in non-negligible performance degradation especially in vibration states or in mobile scenes. To address this issue, we model the relationship between the received power and transceiver jitter by making use of a moment-based density function approximation method. Based on this relationship, we incorporate the transceiver jitter effects in combination with Poisson distribution. The error rate results are obtained assuming on-off key modulation with optimal threshold based detection. We validate the error rate expressions by comparing the analytical results with Monte-Carlo simulation results. The results show that the transceiver jitter effects cause performance degradation especially in smaller transceiver elevation angles or in shorter distances, which are often adopted in short-range ultraviolet communications. The results also show that larger elevation angle cases have a better performance with respect to anti-jitter and may perform better compared to smaller elevation angle situations in the case of larger standard deviation of jitter. This work studies for the first time the transceiver jitter effects in ultraviolet communications and provides guidelines for experimental system design., Comment: 5 pages, 2 figures, comments are welcome!

Published
2024
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4. Multivariate Statistical Analysis in the Real and Complex Domains

Author

Mathai, Arak M., Provost, Serge B., and Haubold, Hans J.

Subjects
multivariate statistical analysis, mathematical statistics, complex domain, matrix-variate, Gaussian distributions, Wishart distribution, type-1 distributions, type-2 distributions, factor analysis, classifications, cluster, profile analyses, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBT Probability & statistics, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics, bic Book Industry Communication::P Mathematics & science::PH Physics::PHS Statistical physics
Abstract

This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout.

Published
2022
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5. A class of copulae associated with Brownian motion processes and their maxima

Author

Adès, Michel, Dufour, Matthieu, Provost, Serge B., and Vachon, Marie-Claude

Subjects
Mathematics - Statistics Theory
Abstract

The main objective of this paper consists in creating a new class of copulae from various joint distributions occurring in connection with certain Brownian motion processes. We focus our attention on the distributions of univariate Brownian motions having a drift parameter and their maxima and on correlated bivariate Brownian motions by considering the maximum value of one of them. The copulae generated therefrom and their associated density functions are explicitly given as well as graphically represented., Comment: 25 pages, 3 figures

Published
2020

19. Factor Analysis

Author

Mathai, Arak M., Provost, Serge B., Haubold, Hans J., Mathai, Arak M., Provost, Serge B., and Haubold, Hans J.

Published
2022
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26. Nonparametric Copula Density Estimation Methodologies.

Author

Provost, Serge B. and Zang, Yishan

Subjects
*PROBABILITY density function, *DENSITY, *DISTRIBUTION (Probability theory), *POLYNOMIAL approximation, *BIVARIATE analysis
Abstract

This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels' empirical copulas, by making use of Bernstein's approximating polynomials of appropriately selected orders; by differentiating linearized distribution functions evaluated at optimally spaced grid points; and by implementing the kernel density estimation technique in conjunction with a repositioning of the pseudo-observations and a certain criterion for determining suitable bandwidths. Smoother representations of such density estimates can further be secured by approximating them by means of moment-based bivariate polynomials. The various copula density estimation techniques being advocated herein are successfully applied to an actual dataset as well as a random sample generated from a known distribution. [ABSTRACT FROM AUTHOR]

Published
2024
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36. Generalized Quadratic Forms

Author

Mathai, A. M., Provost, Serge B., Hayakawa, Takesi, Diggle, P., editor, Fienberg, S., editor, Krickeberg, K., editor, Olkin, I., editor, Wermuth, N., editor, Mathai, A. M., Provost, Serge B., and Hayakawa, Takesi

Published
1995
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37. Zonal Polynomials

Author

Mathai, A. M., Provost, Serge B., Hayakawa, Takesi, Diggle, P., editor, Fienberg, S., editor, Krickeberg, K., editor, Olkin, I., editor, Wermuth, N., editor, Mathai, A. M., Provost, Serge B., and Hayakawa, Takesi

Published
1995
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38. Preliminaries

Author

Mathai, A. M., Provost, Serge B., Hayakawa, Takesi, Diggle, P., editor, Fienberg, S., editor, Krickeberg, K., editor, Olkin, I., editor, Wermuth, N., editor, Mathai, A. M., Provost, Serge B., and Hayakawa, Takesi

Published
1995
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39. Quadratic and Bilinear Forms In Normal Vectors

Author

Mathai, A. M., Provost, Serge B., Hayakawa, Takesi, Diggle, P., editor, Fienberg, S., editor, Krickeberg, K., editor, Olkin, I., editor, Wermuth, N., editor, Mathai, A. M., Provost, Serge B., and Hayakawa, Takesi

Published
1995
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45. The generalized Pearson family of distributions and explicit representation of the associated density functions.

Author

Provost, Serge B., Zareamoghaddam, Hossein, Ahmed, S. Ejaz, and Ha, Hyung-Tae

Subjects
*DISTRIBUTION (Probability theory), *DENSITY, *CONTINUOUS functions, *LINEAR systems, *DATA modeling
Abstract

A moment-based density approximation technique that is based on a generalization of Pearson's system of frequency curves is introduced in this paper. More specifically, the derivative of the logarithm of a continuous density function is expressed as a ratio of polynomials whose coefficients are determined by solving a linear system, and a simple representation of the resulting density function is provided. Additionally, a result relating a sample to its moments is stated and derived. It is then explained that, when used in conjunction with sample moments, the methodology being herein advocated can be utilized for the purpose of modeling data sets, irrespective of their size. Several illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Published
2022
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