MAD-Bayes (MAP-based Asymptotic Derivations) has been recently proposed as a general technique to derive scalable algorithm for Bayesian Nonparametric models. However, the combinatorial nature of objective functions derived from MAD-Bayes results in hard optimization problem, for which current practice employs heuristic algorithms analogous to k-means to find local minimum. In this paper, we co...

Generalized Hamilton system is defined by generalized Poisson bracket, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion,. In the paper, Combinatorial operator η in 1-form space ( ) P Λ on Poisson manifold P is constructed and sufficient and necessary conditions that the vector field which induced by 1-form is...

A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is equivalent to computing the discrete homotopy group of the 1-skeleton of the permutahedron. To compute this group we introduce combinatorial techniques that we belie...

An infinite matrix is called totally positive if its minors of all orders are nonnegative. A nonnegative sequence (an)n≥0 is called log-convex (logconcave, resp.) if aiaj+1 ≥ ai+1aj ( aiaj+1 ≤ ai+1aj , resp.) for 0 ≤ i < j . The object of this talk is to study various positivity properties of Riordan arrays, including the total positivity of such a matrix, the log-convexity of the 0th column an...

In this paper we investigate combinatorial properties and constructions of two recent topics of cryptographic interest namely frameproof codes for digital ngerprinting and traceability schemes for broadcast encryption We rst give combinatorial descriptions of these two objects in terms of set systems and also discuss the Hamming distance of frameproof codes when viewed as error correcting codes...

A few years ago Kramer and Laubenbacher introduced a discrete notion of homotopy for simplicial complexes. In this paper, we compute the discrete fundamental group of the order complex of the Boolean lattice. As it turns out, it is equivalent to computing the discrete homotopy group of the 1-skeleton of the permutahedron. To compute this group we introduce combinatorial techniques that we belie...

We propose kernel block restricted isometry property (KB-RIP) as a generalization of the well-studied RIP and prove a variety of results. First, we present a “sumof-norms”-minimization based formulation of the sparse recovery problem and prove that under suitable conditions on KB-RIP, it recovers the optimal sparse solution exactly. The Group Lasso formulation, widely used as a good heuristic, ...

We describe the application of a physics-inspired renormalization technique to combinatorial games. Although this approach is not rigorous, it allows one to calculate detailed, probabilistic properties of the geometry of the P-positions in a game. The resulting geometric insights provide explanations for a number of numerical and theoretical observations about various games that have appeared i...

A divisible design graph is a graph whose adjacency matrix is the incidence matrix of a divisible design. Divisible design graphs are a natural generalization of (v, k, λ)-graphs, and like (v, k, λ)-graphs they make a link between combinatorial design theory and algebraic graph theory. The study of divisible design graphs benefits from, and contributes to, both parts. Using information of the e...