We study Markov bases of hierarchical models in general and those of decomposable models in particular for multiway contingency tables by determining the structure of fibers of sample size two. We prove that the number of elements of fibers of sample size two are powers of two and we characterizes the primitive moves of Markov bases in terms of connected components of a certain graph defined fr...

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined ana­ lytically in polynomial time. This fol­ lows from two main results: First, we show that factored distributions over spanni...

Computing the MAP assignment in graphical models is generally intractable. As a result, for discrete graphical models, the MAP problem is often approximated using linear programming relaxations. Much research has focused on characterizing when these LP relaxations are tight, and while they are relatively well-understood in the discrete case, only a few results are known for their continuous ana...

Let G be a finite simple graph and J(G) denote its vertex cover ideal in polynomial ring over field. The k-th symbolic power of is denoted by \(J(G)^{(k)}\). In this paper, we give criterion for ideals decomposable graphs to have the property that all their powers are not componentwise linear. Also, necessary sufficient condition on so \(J(G)^{(k)}\) linear some (equivalently, all) \(k \ge 2\) ...

The purpose of this paper is to study minimal monads associated a rank two vector bundle E ${\mathcal {E}}$ on P n $ {\mathbf {P}}^{n}$ . In particular, we situations where has H ∗ i ( ) = 0 $H^i_*({\mathcal {E}}) =0$ for 1 < − $1<i<n-1$ , except one pair values k $(k,n-k)$ We show that 8 {P}}^{8}$ if 3 4 $H^3_*({\mathcal {E}})=H^4_*({\mathcal {E}})=0$ then must be decomposable. More generally,...

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

This paper is intended as an introduction to the theory of simplicial decompositions of graphs. It presents, in a unified way, new results as well as some basic old ones (with new proofs). Its main result is a structure theorem for infinite graphs with a simplicial tree-decomposition into primes. The existence and uniqueness of such prime decompositions will be investigated in two subsequent pa...

For two graphs $mathrm{G}$ and $mathrm{H}$ with $n$ and $m$ vertices, the corona $mathrm{G}circmathrm{H}$ of $mathrm{G}$ and $mathrm{H}$ is the graph obtained by taking one copy of $mathrm{G}$ and $n$ copies of $mathrm{H}$ and then joining the $i^{th}$ vertex of $mathrm{G}$ to every vertex in the $i^{th}$ copy of $mathrm{H}$. The neighborhood corona $mathrm{G}starmathrm{H}$ of $mathrm{G}$ and $...

We study Markov bases of hierarchical models in general and those of decomposable models in particular for multiway contingency tables by determining the structure of fibers of sample size two. We prove that the number of elements of fibers of sample size two are powers of two and we characterize the primitive moves (i.e. square-free moves of degree two) of Markov bases in terms of connected co...

The notions we study in this paper, those of existentially-atomic structure and effectively existentially-atomic structure, are not really new. The objective of this paper is to single them out, survey their properties from a computability-theoretic viewpoint, and prove a few new results about them. These structures are the simplest ones around, and for that reason alone, it is worth analyzing ...