Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.

Adjusting the accelerating field distribution of a superconducting CH cavity

In a superconducting CH （cross bar H mode） cavity, the method of regulating the length of a drift tube is employed to adjust the distribution of the accelerating field. In this article, we simulate the electromagnetic field of a CH structure to illustrate the reason for adjusting the field distribution by varying drift tube length. Meanwhile, that the presence of the drift tube will cause a sharp rise in the maximum electric field is also shown. This phenomenon is contrary to superconducting cavity design principles in which the cavity geometry needs to be optimized to reduce the maximum electric field to avoid field emission. We propose a variable diameter superconducting CH cavity design to solve this conflict. The simulation of the variable diameter superconducting CH cavity shows that this method is feasible.

Distributed accelerated optimization algorithms:Insights from an ODE

In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.

New extreme value theory for maxima of maxima

Although advanced statistical models have been proposed to fit complex data better,the advances of science and technology have generated more complex data,e.g.,Big Data,in which existing probability theory and statistical models find their limitations.This work establishes probability foundations for studying extreme values of data generated from a mixture process with the mixture pattern depending on the sample length and data generating sources.In particular,we show that the limit distribution,termed as the accelerated max-stable distribution,of the maxima of maxima of sequences of random variables with the above mixture pattern is a product of three types of extreme value distributions.As a result,our theoretical results are more general than the classical extreme value theory and can be applicable to research problems related to Big Data.Examples are provided to give intuitions of the new distribution family.We also establish mixing conditions for a sequence of random variables to have the limit distributions.The results for the associated independent sequence and the maxima over arbitrary intervals are also developed.We use simulations to demonstrate the advantages of our newly established maxima of maxima extreme value theory.