We define the degenerate two boundary affine Hecke-Clifford algebra H d , and show it admits a well-defined q ( n ) -linear action on tensor space M ? N V where is natural module for are arbitrary modules Lie superalgebra of Type Q. When irreducible highest weight parameterized by staircase partition single row, respectively, this factors through quotient . then construct explicit quotient, p u...

The data clustering problem consists in dividing a set into prescribed groups of homogeneous data. This is an NP-hard that can be relaxed the spectral graph theory, where optimal cuts are related to eigenvalues 1-Laplacian. In this paper, we first give new notations describe paths, among critical eigenvectors 1-Laplacian, realizing sets with genus. We introduce pseudo-orthogonality characterize...

This paper defines a class of labeled stratified order structures that characterizes exactly the notion of combined traces (i.e., comtraces) proposed by Janicki and Koutny in 1995. Our main technical contributions are the representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization a...

In this second talk we will introduce the Rayleigh quotient and the CourantFischer Theorem and give some applications for the normalized Laplacian. Our applications will include structural characterizations of the graph, interlacing results for addition or removal of subgraphs, and interlacing for weak coverings. We also will introduce the idea of “weighted graphs”.

We provide axiomatizations for six variants of the Public Good Index for games with a priori unions. Two such coalitional PGIs have been introduced and alternatively axiomatized in Alonso-Meijide et al. (2008b). They assign power in two steps. In the first step, power is distributed between unions according to the PGI of the quotient game. In a second step, the Solidarity PGI splits power equal...

We prove here that a finitely presented group with a free quotient of rank n is an HNN-extension with n stable letters of a finitely generated group where the associated subgroups are finitely generated. This theorem has a number of consequences. In particular, in the event that the free quotient is cyclic it reduces to an elementary and quick proof of a theorem of Bieri and Strebel. 1. Finitel...

This paper elaborates on the novel intelligence assessment method using the brainwave sub-band power ratio features. The study focuses only on the left hemisphere brainwave in its relaxed state. Distinct intelligence quotient groups have been established earlier from the score of the Raven Progressive Matrices. Sub-band power ratios are calculated from energy spectral density of theta, alpha an...

An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v  in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set....