Logical analysis of data (LAD) is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T; F ) on attributes set S of size n, in which T (resp., F ) f0; 1g n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge has a decomposable structure;...

Abstract: In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum PSU(N) for N > 2 are generically decomposable. One general decomposition of the representations is induced by the symmetry which exchanges PSU(N) representation labels by their conjugates. The respective summands of a given parity are typically still reducible int...

In this article, we deal with graphs modelling interconnection networks of parallel systems (parallel computers, networks of workstations,..). We want to share the nodes of such a network between many users, each one needing a given number of nodes. Thus, a graph G with N vertices is said to be decomposable if for each set fn 1 We show that determining if a given tripode (three disjoint chains ...

Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...

A (d,h)-decomposition of a graph G is an order pair (D,H) such that H subgraph where has the maximum degree at most h and D acyclic orientation G−E(H) out-degree d. (d,h)-decomposable if (d,h)-decomposition. Let be embeddable in surface nonnegative characteristic. It known (d,h)-decomposable, then h-defective d+1-choosable. In this paper, we investigate graphs prove following four results. (1) ...

We study projective dimension, a graph parameter (denoted by pd(G) for a graph G), introduced by Pudlák and Rödl [13], who showed that proving lower bounds for pd(Gf ) for bipartite graphs Gf associated with a Boolean function f imply size lower bounds for branching programs computing f . Despite several attempts [13, 17], proving super-linear lower bounds for projective dimension of explicit f...

Let F be the function field of a smooth curve over the p-adic number field Qp. We show that for each prime-to-p number n the n-torsion subgroup H(F, μn) = nBr(F ) is generated by Z/n-cyclic classes; in fact the Z/n-length is equal to two. It follows that the Brauer dimension of F is two (first proved in [20]), and any F -division algebra of period n and index n is decomposable.