Transportation cost metrics, also known as the Wasserstein distances Wp, are a natural choice for defining distances between two pointsets, or distributions, and have been applied in numerous fields. From the computational perspective, there has been an intensive research effort for understanding the Wp metrics over R, with work on the W1 metric (a.k.a earth mover distance) being most successfu...

Photoionization of the Ce Ce process has been studied using the random phase approximation with exchange method in the energy region 100-150 eV. Comparison of our results with the recent measurement [Müller et al, Phys. Rev. Lett. 101, 133001 (2008)] confirms the suppression effect of the carbon cage in the endohedral fullerene Ce@C+82 photoionization. The reasons for the cause of the confineme...

Delsarte showed that for any projective linear code over a finite field GF (p) with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = p u and w2 = p (u + 1). Moreover, he showed that the additive group of such a code has a strongly regular Cayley graph. Here we show that for any proper, regular, projective linear code C over a finite Frobenius ring with tw...

Résumé— Une phase primordiale lors de la modélisation d’un système à l’aide d’un perceptron multicouches reste la détermination de la structure du réseau. Dans ce cadre, nous proposons un algorithme d’élagage du réseau basé sur l’utilisation de l’analyse de la variance de la sensibilité de tous les paramètres du réseau. Cet algorithme sera testé sur deux exemples de simulation et ses performanc...

A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed as association. It turns out that the similarity between two words W1 and W2 strongly increases with a co-occurrence, decreases with the occurrence of W1 wit...

Example. Every non-zero element of ⋀ V is trivially totally decomposable. Example. If dimV = 3, then every non-zero element of ⋀ V is totally decomposable. Proof. Given a sum v1 ∧v2 +v3 ∧v4 of two non-zero elements of ⋀ V , the two-dimensional subspaces Span(v1, v2) and Span(v3, v4) must intersect. If w1 is in the intersection, then we can rewrite v1∧v2 = w1 ∧w2 for some w1 ∈ Span(v1, v2). Simi...

A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed as association. It turns out that the similarity between two words W1 and W2 strongly increases with a co-occurrence, decreases with the occurrence of W1 wit...

Two words w1 and w2 are said to be k-binomial equivalent if every non-empty word x of length at most k over the alphabet of w1 and w2 appears as a scattered factor of w1 exactly as many times as it appears as a scattered factor of w2. We give two different polynomial-time algorithms testing the k-binomial equivalence of two words. The first one is deterministic (but the degree of the correspond...

Let wρ x : |x|exp −Q x , ρ > −1/2, where Q ∈ C2 : −∞,∞ → 0,∞ is an even function. In 2008 we have a relation of the orthonormal polynomial pn w2 ρ;x with respect to the weightw 2 ρ x ; p′ n x An x pn−1 x − Bn x pn x − 2ρnpn x /x, where An x and Bn x are some integrating functions for orthonormal polynomials pn w2 ρ;x . In this paper, we get estimates of the higher derivatives of An x and Bn x ,...

Let Y be a finite CW-complex of dimension at most three and P → Y an SO(3) bundle. Associated with P are its Stiefel–Whitney classes wi(P ) ∈ H i(Y ;Z/2), i = 1, 2, 3. Only one of them, namely, w2(P ) ∈ H (Y ;Z/2), will be of importance to us, for the reason that w1(P ) = 0 since P is orientable, and w3(P ) = Sq (w2(P )) by the Wu formula. The class w2(P ) can be defined as follows. Let {Uα } b...