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Complex Gaussian integers for “Gaussian graphics”
ACM SIGPLAN Notices, 1993Some recent computer languages incorporate rational numbers, complex numbers, and rational complex numbers. We extend these numeric facilities to deal properly with Gaussian integers ---i.e., complex numbers whose real and imaginary parts are both ordinary (rational) integers.
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From almost Gaussian to Gaussian
AIP Conference Proceedings, 2015We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are “smoothed” by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian ...
Max H. M. Costa, Olivier Rioul
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Applied Mathematics and Computation, 1999
The paper studies (non-Gaussian) diffusions classified as either ``hypo-diffusion'' or ``hyper-diffusion'', where the \(\beta\) order moments are of the type \(t^{\beta/\alpha}\), with \(\beta\) and \(\alpha\) belonging to \(\mathbb{R}^*_+\). The authors introduce signed measures corresponding to non-Gaussian diffusions on \(\mathbb{R}\), inspired by ...
Michèle Mastrangelo +2 more
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The paper studies (non-Gaussian) diffusions classified as either ``hypo-diffusion'' or ``hyper-diffusion'', where the \(\beta\) order moments are of the type \(t^{\beta/\alpha}\), with \(\beta\) and \(\alpha\) belonging to \(\mathbb{R}^*_+\). The authors introduce signed measures corresponding to non-Gaussian diffusions on \(\mathbb{R}\), inspired by ...
Michèle Mastrangelo +2 more
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Gaussian–to–non-Gaussian transition in supercooled fluids
Physical Review A, 1991We devise a method based on an analysis of the non-Gaussian parameter in a finite time domain to determine the transition between Gaussian and non-Gaussian dynamics in a stochastic trapping model of a glass transition. We find evidence of the Gaussian--to--non-Gaussian transition in the supercooled region of soft-sphere fluids.
, Odagaki, , Hiwatari
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Gaussian and non-Gaussian statistics
Proceedings of International Symposium on Electromagnetic Compatibility ELMAGC-97, 1997The article presents a description of Gaussian statistical theory in relation to signal analysis. Special attention is placed on the correlation phenomena and the spectra. The main part of the paper deals with the higher-order statistics. The notions of the 3rd-moment and the cumulant function are introduced and their relation to the spectra and the ...
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Gaussian Variables and Gaussian Processes
2016Gaussian random processes play an important role both in theoretical probability and in various applied models. We start by recalling basic facts about Gaussian random variables and Gaussian vectors. We then discuss Gaussian spaces and Gaussian processes, and we establish the fundamental properties concerning independence and conditioning in the ...
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Gaussian filters for nonlinear filtering problems
IEEE Transactions on Automatic Control, 2000K Xiong
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Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
Journal of Chemical Physics, 2007Joost Vandevondele +2 more
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