Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Multi chiral-doublets in one single nucleus

Adiabatic and configuration-fixed constraint triaxial relativistic mean field (RMF) approaches are developed for the first time and a new phenomenon, the existence of multi chiral-doublets (M$\chi$D), i.e., more than one pairs of chiral doublets bands in one single nucleus, is suggested for nuclei in A~100 region, typically for $^{106}$Rh, based on the triaxial deformations together with their corresponding proton and neutron configurations.Comment: 10 pages, 4 figure

Horizon Entropy in Modified Gravity

We present an observation about the proposal that four-dimensional modification of general relativity may explain the observed cosmic acceleration today. Assuming that the thermodynamical nature of gravity theory continues to hold in modified gravity theories, we derive the modified horizon entropy formula from the modified Friedmann equation. We argue that our results imply that there are conceptual problems in some models of four-dimensional modification of general relativity.Comment: 8 pages. v2: references adde

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

Multi-GPU Acceleration of the iPIC3D Implicit Particle-in-Cell Code

iPIC3D is a widely used massively parallel Particle-in-Cell code for the simulation of space plasmas. However, its current implementation does not support execution on multiple GPUs. In this paper, we describe the porting of iPIC3D particle mover to GPUs and the optimization steps to increase the performance and parallel scaling on multiple GPUs. We analyze the strong scaling of the mover on two GPU clusters and evaluate its performance and acceleration. The optimized GPU version which uses pinned memory and asynchronous data prefetching outperform their corresponding CPU versions by 5-10x on two different systems equipped with NVIDIA K80 and V100 GPUs.Comment: Accepted for publication in ICCS 201