we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

introduction abnormal neural impulses in the nervous system may lead to various diseases and disabilities. high frequency alternating currents (hfac) has been used to block the propagation of such impulses and improve the symptoms or disabilities. the technique is safe, reversible, and relatively selective, and its reliability, the optimum stimulation parameters, and elimination of the onset re...

We describe a “concentration on the diagonal” condition on the Khovanov complex of tangles, show that this condition is satisfied by the Khovanov complex of the single crossing tangles (!) and ("), and prove that it is preserved by alternating planar algebra compositions. Hence, this condition is satisfied by the Khovanov complex of all alternating tangles. Finally, in the case of 0-tangles, me...

The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coefficients of the Jones polynomial is bounded from above and from below by const...

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and shows that assuming a generative model of the data, it provably recovers the gro...

Feature Interaction. When engineers design a system with features, they wish to have methods to prove that the features do not interact in ways which are undesirable. A considerable literature is devoted to this ‘feature interaction problem’ [13,5]. One approach to demonstrating that features do not interact undesirably is to equip them with properties which are intended to hold of a system hav...

Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries. In practice, this is typically formulated as a weighted low-rank approximation problem and solved using non-convex optimization heuristics such as alternating minimization. Such non-convex techniques have few guarantees. Even worse, weighted low-rank approximation is NP-hard for even the ...

The SGBEM-FEM alternating method is compared with the recently popularized XFEM, for analyzing mixed-mode fracture and fatigue growth of 3D nonplanar cracks in complex solid and structural geometries. A large set of 3D examples with different degrees of complexity is analyzed by the SGBEM-FEM alternating method, and the numerical results are compared with those obtained by XFEM available in the...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

This study investigates three factors that have been argued to define "canonical form" in sentence comprehension: Syntactic structure, semantic role, and frequency of usage. We first examine the claim that sentences containing unaccusative verbs present difficulties analogous to those of passive sentences. Using a plausibility judgment task, we show that a mixed group of aphasics performed sign...