Positional Order and Diffusion Processes in Particle Systems

Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and the mean square displacement $M$ to be $\Psi \sim \exp(- {\bf K}^2 M /2d)$ with a reciprocal vector ${\bf K}$ and the dimension of the system $d$. On the basis of the relation, the behavior of positional order is predicted to be $\Psi \sim \exp(-{\bf K}^2Dt)$ when the system involves normal diffusion with a diffusion constant $D$. We also find that a diffusion process with swapping positions of particles contributes to higher orders of the cumulants. The swapping diffusion allows particle to diffuse without destroying the positional order while the normal diffusion destroys it.Comment: 4 pages, 4 figures. Submitted to Phys. Rev.

BiSeg: Simultaneous Instance Segmentation and Semantic Segmentation with Fully Convolutional Networks

We present a simple and effective framework for simultaneous semantic segmentation and instance segmentation with Fully Convolutional Networks (FCNs). The method, called BiSeg, predicts instance segmentation as a posterior in Bayesian inference, where semantic segmentation is used as a prior. We extend the idea of position-sensitive score maps used in recent methods to a fusion of multiple score maps at different scales and partition modes, and adopt it as a robust likelihood for instance segmentation inference. As both Bayesian inference and map fusion are performed per pixel, BiSeg is a fully convolutional end-to-end solution that inherits all the advantages of FCNs. We demonstrate state-of-the-art instance segmentation accuracy on PASCAL VOC.Comment: BMVC201

Approximate Methods for Solving Chance Constrained Linear Programs in Probability Measure Space

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to solve this problem. This paper presents numerical methods to solve chance-constrained linear programs in probability measure space for the first time. We propose two solvable optimization problems as approximate problems of the original problem. We prove the uniform convergence of each approximate problem. Moreover, numerical experiments have been implemented to validate the proposed methods

最適化の数理と応用

Open House, ISM in Tachikawa, 2013.6.14統計数理研究所オープンハウス（立川）、H25.6.14ポスター発

関数空間上の線形計画問題に対する主双対内点法 (統計数理研究所 研究活動 (平成５年度 研究報告会要旨))

創立５０周年記念号(2