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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The X-ray of a permutation is defined as the sequence of antidiagonal sums in the associated permutation matrix. X-rays of permutation are interesting in the context of Discrete Tomography since many types of integral matrices can be written as linear combinations of permutation matrices. This paper is an invitation to the study of X-rays of permutations from a combinatorial point of view. We p...

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 ...

Let X = (X1, X2, ...) be a non-deterministic infinite exchangeable sequence with values in {0, 1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Pólya sequence. This completes the results established in Peccati [2004]. The proof uses several combinatorial implications of the correspondence between Hoeffding decomposability and weak independence. O...

Let X be a normal affine T-variety, where T stands for the algebraic torus. We classify Ga-actions on X arising from homogeneous locally nilpotent derivations of fiber type. We deduce that any variety with trivial Makar-Limanov (ML) invariant is birationally decomposable as Y × P, for some Y . Conversely, given a variety Y , there exists an affine variety X with trivial ML invariant birational ...

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...

Let C be an Abelian group. A class X of groups is called a CE• H-class if for any A, B ∈ X, it follows from the existence isomorphisms E• (A) ≅ (B) and Hom(C,A) Hom(C,B) that there isomorphism B. In this paper, conditions are studied under which $$ {\mathfrak{I}}_{\mathrm{cd}}^{\mathrm{ad}} completely decomposable almost divisible {\mathfrak{I}}_{\mathrm{cd}}^{\ast } torsion-free where Ω(A) con...

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...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. In this paper, we focus on decomposable trees. We show that a decomposable tree has degree at most 4. Moreover, each degree-4 vertex of a decomposable tree is adjacent to a leaf. This leads to a polyno...

Aggregates. For aggregates, we build on ideas in (Pelov 2004). We only consider decomposable aggregate functions, i.e., aggregates for which agg(S) = agg({agg(S′), agg(S \S′)}), for sets of domain elements S and S′ ⊂ S. Our transformation of agg({x ∈ T : φ : t}) is based on the decomposability of the considered aggregates and the fact that there is a total order on all domain elements, with a f...