In this paper, we study the problem of decomposing a given tensor into train such that tensors at vertices are orthogonally decomposable. When has length two, and decomposable two symmetric, recover decomposition by considering random linear combinations slices. Furthermore, if symmetric low-rank but not decomposable, show whitening procedure can transform orthogonal case. network three or more...

We introduce the notion of an Eulerian graph being strongly evencycle decomposable, and note that a few basic classes have this property. Our main results are that several fundamental composition operations that preserve the property of being Eulerian also preserve the property of being strongly even-cycle decomposable. As an application, our composition operations easily imply that all Euleria...

We use Shelah’s theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem 1. Suppose that λ is a singular cardinal, λ′ < λ, and the ultrafilter D is κ-decomposable for all regular cardinals κ with λ′ < κ < λ. Then D is either λ-decomposable, or λ-decomposable. Corollary 2. If λ is a singular cardinal, then an ultrafilter is (λ, λ)-regular if and only if it is e...

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.

We study completely decomposable torsion-free abelian groups of the form GS := ⊕n∈SQpn for sets S ⊆ ω. We show that GS has a decidable copy if and only if S is Σ2 and has a computable copy if and only if S is Σ 0 3.

The graph G(N; d) has vertex set V = {0; 1; : : : ; N − 1}, with {v; w} an edge if v − w ≡ ±di(modN ) for some 06i6dlogd Ne − 1. We show that the circulant graph G(cd; d) is Hamilton decomposable for all positive integers c; d, and m with c¡d. This extends work of Micheneau and answers a special case of a question of Alspach. c © 2000 Elsevier Science B.V. All rights reserved.

Let D(n)(D(n, k)) denote the maximum possible d such that there exists a d-regular hypergraph (d-regular k-uniform hypergraph, respectively) on n vertices containing no proper regular spanning subhypergraph. The problem of estimating D(n) arises in Game Theory and Huckemann and Jurkat were the first to prove that it is finite. Here we give two new simple proofs that D(n), D(n, k) are finite, an...

In this paper we present some factorization properties for unbounded local positive maps. We show that an map ? on the minimal tensor product of locally C?-algebras A and C?(DE), where DE is a Fréchet quantized domain, dominated by ??id forma ??id, ? ?. As application result, given ?: A? B, ??idMn? decomposable n?2 if only ? CP-map. Also, CCP-map unital C? -algebras ??? ???˜, ?˜ CCP- ?, wheneve...

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...