Self-consistent Force Scheme in the Discrete Boltzmann Equation

In the work of N. Martys et al. [Nicos S. Martys, Xiaowen Shan, Hudong Chen, Phys. Rev. E, Vol. 58, Num.5, 1998 ], a self-consistent force term to any order in the Boltzmann-BKG equation is derived by the Hermite basis with raw velocity. As an extension, in the present work, the force term is expanded by the Hermite basis with the relative velocity in the comoving coordinate and the Hermite basis with the relative velocity scaled by the local temperature. It is found that the force scheme proposed by He et al. [Xiaoyi He, Xiaowen Shan, Gary D. Doolen, Phys. Rev. E, Vol. 57, Num.1,1998] can be derived by the Hermite basis with the relative velocity. Furthermore, another new force scheme in which the velocity is scaled by the local temperature is obtained.Comment: this is a pure theoretical work associated with the force scheme for the discrete Boltzmann equation. It has 7 pages, 0 figure. This work is prepared to be submited to Physical Review serie

Local times for spectrally negative L\'evy processes

For spectrally negative L\'evy processes, adapting an approach from \cite{BoLi:sub1} we identify joint Laplace transforms involving local times evaluated at either the first passage times, or independent exponential times, or inverse local times. The Laplace transforms are expressed in terms of the associated scale functions. Connections are made with the permanental process and the Markovian loop soup measure.Comment: 23 page

Integral functionals for spectrally positive Levy processes

We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L\'evy processes. Via Lamperti type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes

An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure

This paper concerns the almost sure time dependent local extinction behavior for super-coalescing Brownian motion $X$ with $(1+\beta)$-stable branching and Lebesgue initial measure on \bR. We first give a representation of $X$ using excursions of a continuous state branching process and Arratia's coalescing Brownian flow. For any nonnegative, nondecreasing and right continuous function $g$, put \tau:=\sup \{t\geq 0: X_t([-g(t),g(t)])>0 \}. We prove that \bP\{\tau=\infty\}=0 or 1 according as the integral $\int_1^\infty g(t)t^{-1-1/\beta} dt$ is finite or infinite.Comment: 14 page

A Chaotic Cipher Mmohocc and Its Randomness Evaluation

After a brief introduction to a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics of mixing, unpredictability, and sensitivity to initial conditions, we conducted the randomness statistical tests against the keystreams generated by the cipher. Two batteries of most stringent randomness tests, namely the NIST Suite and the Diehard Suite, were performed. The results showed that the keystreams have successfully passed all the statistical tests. We conclude that Mmohocc can generate high-quality pseudorandom numbers from a statistical point of view.Comment: 8 pages, 4 figures, and 3 tables, submitted to ICCS0

A Chaotic Cipher Mmohocc and Its Security Analysis

In this paper we introduce a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics. The designs of the major components of the cipher are given. Its cryptographic properties of period, auto- and cross-correlations, and the mixture of Markov processes and spatiotemporal effects are investigated. The cipher is resistant to the related-key-IV attacks, Time/Memory/Data tradeoff attacks, algebraic attacks, and chosen-text attacks. The keystreams successfully passed two batteries of statistical tests and the encryption speed is comparable with RC4.Comment: 14 pages, 4 figures, 4 table

A distribution-function-valued SPDE and its applications

In this paper we further study the stochastic partial differential equation first proposed by Xiong (2013). Under localized conditions on the coefficients we show that the solution is in fact distribution-function-valued and we establish the pathwise uniqueness of the solution. As applications we obtain the well-posedness of the martingale problems for two classes of measure-valued diffusions: interacting super-Brownian motions and interacting Fleming-Viot processes. Properties of the two superprocesses such as the existence of density fields and the extinction behaviors are also studied

MG-WFBP: Efficient Data Communication for Distributed Synchronous SGD Algorithms

Distributed synchronous stochastic gradient descent has been widely used to train deep neural networks on computer clusters. With the increase of computational power, network communications have become one limiting factor on system scalability. In this paper, we observe that many deep neural networks have a large number of layers with only a small amount of data to be communicated. Based on the fact that merging some short communication tasks into a single one may reduce the overall communication time, we formulate an optimization problem to minimize the training iteration time. We develop an optimal solution named merged-gradient WFBP (MG-WFBP) and implement it in our open-source deep learning platform B-Caffe. Our experimental results on an 8-node GPU cluster with 10GbE interconnect and trace-based simulation results on a 64-node cluster both show that the MG-WFBP algorithm can achieve much better scaling efficiency than existing methods WFBP and SyncEASGD.Comment: 9 pages, INFOCOM 201

How long does the surplus stay close to its historical high?

In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions.Comment: 19page

Branching Particle Systems in Spectrally One-sided Levy Processes

We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump-Mode-Jagers branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure-valued processes can be studied via the excursions for the corresponding Levy processes.Comment: 23pages, 2 figure