Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal ...

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...

Depth-first proof-number (df-pn) search is a powerful member of the family of algorithms based on proof and disproof numbers. While df-pn has succeeded in practice, its theoretical properties remain poorly understood. This paper resolves the question of completeness of df-pn: its ability to solve any finite boolean-valued game tree search problem in principle, given unlimited amounts of time an...

Sustainability issues involve complex interactions between social, economic, and environmental factors that are often viewed quite differently by disparate stakeholder groups. Issues of non-sustainability are wicked problems that have many, often obscure causes, and for which there is no single, straightforward solution. Furthermore, the concept of sustainability is itself contested. For exampl...

Hierarchical multimodal hub location problem is a cost-minimizing hub covering problem where two types of hubs and hub links, accounting for ground and air transportation, are to be established, while ensuring time-definite deliveries. We propose a mixed-integer programming formulation and perform a comprehensive sensitivity analysis on the Turkish network. We show that the locations of airport...

A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch (EED) problem. Furthermore, the polynomial functions of both objective functions are aggregated into ...

In this manuscript we will present a new fast technique for solving the generalized eigenvalue problem T x = λSx, in which both matrices T and S are symmetric tridiagonal matrices and the matrix S is assumed to be positive definite.1 A method for computing the eigenvalues is translating it to a standard eigenvalue problem of the following form: L−1T L−T (LT x) = λ(LT x), where S = LLT is the Ch...

Open loop dynamic stability is a major feature of operability. An optimization approach for open loop stable process design is presented. It is based on Lyapunov’s stability theory and formulated as an eigenvalue optimization problem. The resultant non-linear semi-definite programming problem is reformulated into an interior-point / logarithmic-barriertransformation programming problem. The pro...

We present a self-contained and comprehensive study of the Fisher-Rao space matrix-valued non-commutative probability measures, related Hellinger space. Our is natural generalization classical commutative measures Bures-Wasserstein Hermitian positive-definite matrices. introduce justify canonical entropy on space, which differs from von Neumann entropy. consequently derive analogues heat flow, ...