1 Analyzing General Properties of Network Deconvolution 3 1.1 Network deconvolution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Optimality analysis of network deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Modeling assumptions and intuitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. Analogously, a tree is called T -decomposable for a fixed tree T if it has a spanning forest whose components are all isomorphic to T . In this paper, we use a generating functions approach to derive exact and asymptotic results on the number of k-decomposable and T -decomposable trees from a so-call...

We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d − 1)-dimensional faces among all complexes with n faces of dimension d, then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods.

We provide an analytical expression for optimal Lewenstein-Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the KarushKuhn-Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of sep...

We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n−1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there...

We study symmetric correspondences with completely decomposable minimal equation on smooth projective curves C . The Jacobian of then decomposes correspondingly. For all positive integers g and ℓ , we give series examples genus n ( − 1 ) + satisfying equations degree such that the has at least 2 isogeny components.

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 introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.