If X is the complement of a hypersurface in P, then Kohno showed in [9] that the nilpotent completion of π1(X) is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks φk of the lower central series quotients of π1(X) are known in only two very special cases: if X is hypersolvable (in which case the quadratic c...

We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWAbased, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin–Courant, as the only rules in certain in...

In this paper, we investigate the interactions between Legendrian satellite construction and existence of exact, orientable Lagrangian cobordisms knots. Given two knots tangles, construct a cobordism satellites by closures with extra twists on both top bottom to compensate for genus cobordism. If original were decomposable, then decomposable exists as well, again twists.

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. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal dist...

In multi-label classification, where the evaluation of predictions is less straightforward than in single-label various meaningful, though different, loss functions have been proposed. Ideally, learning algorithm should be customizable towards a specific choice performance measure. Modern implementations boosting, most prominently gradient boosted decision trees, appear to appealing from this p...

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be group, and let T:= Rep(G) the rigid C*-tensor category of continuous unitary representations G. Mod(T) C*-2-category cofinite semisimple finitely decomposable T-module categories. show that G-C*-algebras can identified with equivalence classes 1-morphisms out object T in Mod(T). For X: -> M1, Y: M2,...

Computing a decomposition of a polynomial f(x) as a functional composition g(h(x)) of polynomials g(x) and h(x), is an important and well-studied problem, both for exact and approximate inputs. In this paper, we re-examine the original (exponential-time) algorithm of Barton and Zippel for this task, which looks for special factors of an associated separated bivariate polynomial. We demonstrate ...