Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for 22-dimensional Calabi-Yau categories (with an appendix by Ben Davison)

We discuss semicanonical bases from the point of view of Cohomological Hall algebras via the "dimensional reduction" from 3-dimensional Calabi-Yau categories to 2-dimensional ones. Also, we discuss the notion of motivic Donaldson-Thomas invariants (as defined by M. Kontsevich and Y. Soibelman) in the framework of 2-dimensional Calabi-Yau categories. In particular we propose a conjecture which allows one to define Kac polynomials for a 2-dimensional Calabi-Yau category (this is a theorem of S. Mozgovoy in the case of preprojective algebras).Comment: The revised version contains the Appendix written by Ben Davison about the relationship of Kontsevich-Soibelman product with the one of Schiffmann-Vassero

Optimizing human-interpretable dialog management policy using Genetic Algorithm

Automatic optimization of spoken dialog management policies that are robust to environmental noise has long been the goal for both academia and industry. Approaches based on reinforcement learning have been proved to be effective. However, the numerical representation of dialog policy is human-incomprehensible and difficult for dialog system designers to verify or modify, which limits its practical application. In this paper we propose a novel framework for optimizing dialog policies specified in domain language using genetic algorithm. The human-interpretable representation of policy makes the method suitable for practical employment. We present learning algorithms using user simulation and real human-machine dialogs respectively.Empirical experimental results are given to show the effectiveness of the proposed approach.Comment: This technical report is an updated version of the conference paper: "H. Ren, W. Xu, and Y. Yan, Optimizing human-interpretable dialog management policy using genetic algorithm, in 2015 IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU), 2015, 791-797". Experiments on policy training via user simulator have been enriched and the reward function is update

The relativistic correction of the quarkonium melting temperature with a holographic potential

The relativistic correction of the AdS/CFT implied heavy quark potential is examined within the framework of the potential model. For the typical range of the coupling strength appropriate to heavy-ion collisions, we find the correction is significant in size and lowers the dissociation temperature of quarkonia.Comment: 11 pages, 2 tables in late

Central Limit Theorems for Super-OU Processes

In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases, our central limit theorems sharpen the corresponding results in the recent preprint of Milos in that the limit normal random variables in our central limit theorems are non-degenerate. Our central limit theorems in the large branching rate case are completely new. The main tool of the paper is the so called "backbone decomposition" of superprocesses