A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

Methodology and Computing in Applied Probability - Risk measures for tail risk have an important application in the dynamic portfolio insurance strategies. We propose a new risk measure called...     

Robust Group Synchronization via Cycle-Edge Message Passing

We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of group ratios and consequently solve the synchronization problem in our setting. We first explain why the group cycle consistency information is essential for effectively solving group synchronization problems. We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption. These guarantees hold as long as the ratio of corrupted cycles per edge is bounded by a reasonable constant. We also establish the stability of the proposed procedure to sub-Gaussian noise. We further establish exact recovery with high probability under a common uniform corruption model.

     

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration ✗ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.     

分块算子矩阵的加权EP

本文在加权广义Schur补的基础上, 引入并研究了Hilbert空间上分块算子矩阵的加权Moore-Penrose逆和加权EP. 进一步, 给出了加权EP算子在算子方程中的一个应用.     

Origin and manifestation of the anharmonic potential felt by an ion-cloud in an actual Paul trap

The anharmonic potential felt by a single-species ions confined in a rf quadrupole trap which results from a non-ideal trap configuration and the charge distribution of the ion cloud is studied. The rf resonance-absorption spectra are explained by a Duffing oscillator and a representation of the line-shape parameter is derived. For > 0.77, the electric signals will exhibit hysteresis. The relation with the anharmonic potential is discussed.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.