Graph partitioning, or community detection, has been widely investigated in network science. Yet, the correct structure on a given is essentially data-driven. Thus, instead of formal definition, diverse measures have conceived to capture intuitive desirable properties shared by most structures. In this work, we propose preprocessing based doubly stochastic scaling adjacency matrices, highlight ...

In Ehrhart theory, the h∗-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal h∗-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, w...

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process [1] with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi cluster also support the consistency proof. This report is also a support do...

During the past few decades, multi-agent optimization problems have drawn increased attention from research community. When multiple objective functions are present among agents, many works optimize sum of these functions. However, this formulation implies a decision regarding relative importance each objective: optimizing is special case multi-objective problem in which all objectives prioriti...

This paper analyzes a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. The system manager’s o...

The main purpose of this paper is to study the existence of stationary solution for stochastic partial differential equations. We establish a new connection between backward doubly stochastic differential equations on infinite time horizon and the stationary solution of the SPDEs. For this we study the existence of the solution of the associated BDSDEs on infinite time horizon and prove it is a...