An algorithm for determining copositive matrices

In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of $\hat{T}^{-}=\{y\in \Delta_{m}| \beta^Ty\leq 0\}$ on the standard simplex $\Delta_m$, where each component of the vector $\beta$ is -1, 0 or 1.Comment: 15 page

Convergence rates in homogenization of higher order parabolic systems

This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp O(\va) convergence rate in the space L^2(0,T; H^{m-1}(\Om)) is obtained for both the initial-Dirichlet problem and the initial-Neumann problem. The duality argument inspired by \cite{suslinaD2013} is used here.Comment: 28 page

Proof of the deadlock-freeness of ALD routing algorithm

This is the appendix to the paper Load-Balanced Adaptive Routing for Torus Networks to provide a detailed, formal proof of the deadlock-freeness of the routing algorithm proposed in the paper. The paper is submitted to Electronics Letters, and the abstract of which is as follows: A new routing algorithm for torus interconnection networks to achieve high throughput on various traffic patterns, Adaptive Load-balanced routing with cycle Detection (ALD), is presented. Instead of the -channels scheme adopted in a few recently proposed algorithms of the same category, a cycle detection scheme is employed in ALD to handle deadlock, which leads to higher routing adaptability. Simulation results demonstrate that ALD achieves higher throughput than the recently proposed algorithms on both benign and adversarial traffic patterns