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On Lipschitz Bounds of General Convolutional Neural Networks [article]

Dongmian Zou, Radu Balan, Maneesh Singh
2018 arXiv   pre-print
In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed.  ...  Several CNNs, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically and compared to the theoretical bounds.  ...  Note that they are all C ∞ smooth functions.Table Ilists the Bessel bounds for all the layers.  ... 
arXiv:1808.01415v1 fatcat:f5fkbyaiobhe3jfgcfuw4sunom

Estimation and Simulation of the Riesz-Bessel Distribution

V. V. Anh, R. McVinish, C. Pesee
2005 Communications in Statistics - Theory and Methods  
Estimation is addressed by nonlinear generalized least squares regression on the empirical characteristic function. The estimator is seen to approximate the maximum likelihood estimator.  ...  In this paper, further properties of the Riesz-Bessel distribution are provided. These properties allow for the simulation of random variables from the Riesz-Bessel distribution.  ...  For the stable and Linnik distributions estimates based on the empirical characteristic function have proven useful.  ... 
doi:10.1080/03610920500200295 fatcat:suqrlti6cbgmtnwbrv75kz72hq

Bessel regression model: Robustness to analyze bounded data [article]

Wagner Barreto-Souza, Vinícius D. Mayrink, Alexandre B. Simas
2020 arXiv   pre-print
Finally, three empirical illustrations are explored to confront results from bessel and beta regressions.  ...  In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is a robust alternative to the beta model.  ...  Fernando Quintana (Pontificia Universidad Católica de Chile -Santiago, Chile) for detailed discussions and suggestions on an earlier version of this paper.  ... 
arXiv:2003.05157v1 fatcat:loec2jqxfvacnlt3pwa2b4i43a

Strong approximation of Bessel processes [article]

Madalina Deaconu, Samuel Herrmann
2021 arXiv   pre-print
Based on this procedure, we emphasize an algorithm which is easy to implement. Moreover, we can develop the method for any dimension.  ...  We consider the path approximation of Bessel processes and develop a new and efficient algorithm.  ...  In Figure 6 (right), one generation of the upper and lower bounds is represented for any t ∈ {ρ −1 (s n )} n≥1 ∩ [0, 2].  ... 
arXiv:2106.00397v1 fatcat:6qu3jmmdxngrvoudweeizcst4u

Bessel-like birth-death process [article]

Vygintas Gontis, Aleksejus Kononovicius
2019 arXiv   pre-print
We propose and generalize Bessel-like birth-death process having clear representation by SDEs.  ...  The new process helps to integrate alternatives of description and to derive equations for the probability density function (PDF) of burst and inter-burst duration of the proposed continuous time birth-death  ...  Transition rates in general case depend on x and N .  ... 
arXiv:1904.13064v1 fatcat:iauljwkjwjfhvg2mzvxgbyf2qq

On the Computation of Modified Bessel Function Ratios

Walter Gautschi, Josef Slavik
1978 Mathematics of Computation  
A detailed comparison is made between a continued fraction of Gauss, and one of Perron, for the evaluation of ratios of modified Bessel functions Iv(x)/lv_x(x), x > 0, v > 0.  ...  generating sequences of Bessel functions by downward recursion.  ...  The case of large v is of some interest in connection with the computation of starting values for subsequent generation of sequences of Bessel functions by downward recursion (cf. [1] ).  ... 
doi:10.2307/2006491 fatcat:yofoodqfyrf4lkvmkkdnpensg4

On the computation of modified Bessel function ratios

Walter Gautschi, Josef Slavik
1978 Mathematics of Computation  
A detailed comparison is made between a continued fraction of Gauss, and one of Perron, for the evaluation of ratios of modified Bessel functions Iv(x)/lv_x(x), x > 0, v > 0.  ...  generating sequences of Bessel functions by downward recursion.  ...  The case of large v is of some interest in connection with the computation of starting values for subsequent generation of sequences of Bessel functions by downward recursion (cf. [1] ).  ... 
doi:10.1090/s0025-5718-1978-0470267-9 fatcat:pp5eykajhjdpdpseshkfcks5fa

Page 189 of American Society of Civil Engineers. Collected Journals Vol. 4, Issue 3 [page]

1999 American Society of Civil Engineers. Collected Journals  
Because of the political sit uation in Europe at that time, Halphen did not publish his work on these distributions himself, except for a short note (Halphen 1941) in which he gave the density functions  ...  Because of their complex form involving Bessel functions and exponential factorial functions, Halphen’s distributions have remained for several years in oblivion.  ... 

Page 5971 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
In general the function n,(t; y) is not known (though one can usually compute its Laplace transform), so this does not always yield an explicit expression.  ...  Let Z be a one-dimensional diffusion with generator $4 4, and X a one-dimensional diffusion with generator $44, where v = —1/s and dn = s*dm.  ... 

Conditions for generation of stable and accurate hybrid TD-FD MoM solutions

Mengtao Yuan, A. De, T.K. Sarkar, Jinhwan Koh, Baek Ho Jung
2006 IEEE transactions on microwave theory and techniques  
Three different types of functions, namely, Hermite, Bessel-Chebyshev, and Laguerre, have been used for extrapolation.  ...  In this hybrid TD-FD approach, one generates the early time response using a TD code at a spatial location and uses a FD code to generate the low-frequency response at the same place.  ...  The Bessel-Chebyshev basis functions have the narrowest range of . From the bounds on , we can easily obtain the lower bounds on (except for Hermite functions), which are also shown in Table I .  ... 
doi:10.1109/tmtt.2006.875823 fatcat:o2kcygwrcba7xmqxety2oepopm

Radial and Directional Posteriors for Bayesian Neural Networks [article]

Changyong Oh, Kamil Adamczewski, Mijung Park
2019 arXiv   pre-print
We propose a new variational family for Bayesian neural networks.  ...  Bound on the ratio of modified Bessel function of the first kind I ν (z) Directly evaluating Bessel functions and calculating their ratio is expensive and unstable operation for large ν.  ...  With Thm. 2 and Thm. 3, the gap between lower bound and upper bound is negligible uniformly on z and ν. For ν ≥ 500, scipy.special.ive cannot even generate a non-nan finite number.  ... 
arXiv:1902.02603v2 fatcat:v4a34bdmvvbhrawjlhjgdejqma

Page 5388 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
The authors present a general unified upper bound for the total variation distance between any nonnegative integer-valued random variable with finite variance and a Poisson random variable.  ...  The Bessel process (R,"') is a diffusion on (0,00) with infinitesi- mal operator f”(x)/2 + (2v + 1)f"(x)/2x, C;") = fp (Ry) ~7ds, S,'' = C,"'/logt.  ... 

Efficient Continuous HRTF Model Using Data Independent Basis Functions: Experimentally Guided Approach

Wen Zhang, Rodney A. Kennedy, Thushara D. Abhayapala
2009 IEEE Transactions on Audio, Speech, and Language Processing  
Index Terms-Continuous model, Fourier-Bessel series, headrelated transfer function (HRTF).  ...  This paper introduces a continuous functional model for head-related transfer functions (HRTFs) in the horizontal auditory scene.  ...  between Bessel functions of the first kind for a specific order on the interval to expand a general function [21] .  ... 
doi:10.1109/tasl.2009.2014265 fatcat:kdo33auxjngdbeyo5nr5e4ykxe

Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions

Ronald R. Coifman, Stéphane Lafon
2006 Applied and Computational Harmonic Analysis  
We describe a simple scheme, based on the Nyström method, for extending empirical functions f defined on a set X to a larger setX.  ...  This approach allows us to present a novel multiscale extension scheme for empirical functions.  ...  We also express our thanks to the reviewers for their useful suggestions.  ... 
doi:10.1016/j.acha.2005.07.005 fatcat:vccz4zruybglxge7quzprx2vsu

Page 70 of Physical Review Vol. 86, Issue 1 [page]

1952 Physical Review  
}}. (3.6) The order of the Bessel function is in general not ra- tional, and hence it is too complicated for numerical computation.  ...  The solution of the Schrédinger equation for r>R is then found to be approximately r>R, r<R, (1/r)J ng (2), (3.4) where J n¢,y(z), is a Bessel function of the first kind and =[(3RW*)'(apR)}expl[—au(r—R  ... 
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