Abstract The deep theory of approximate subgroups establishes three-step product growth for subsets finite simple groups $G$ Lie type bounded rank. In this paper, we obtain two-step results representations such (including those unbounded rank), where products are replaced by tensor representations. Let be a group and $\chi $ character $G$. $|\chi |$ denote the sum squares degrees all (distinct)...

Let G be a finite simple group. In this paper we consider the existence of small subsets A with property that, if y∈G is chosen uniformly at random, then high probability y invariably generates together some element A. We prove various results in direction, both positive and negative. As corollary, that two randomly elements group Lie type bounded rank generate away from zero. Our method based ...

Several intersection matrices of s-subsets versus k-subsets of a v-set are introduced in the literature. We study these matrices systematically through counting arguments and generating function techniques. A number of new or known identities appear as natural consequences of this viewpoint; especially, use of the derivative operator d/dz and some related operators reveals some connections betw...

An integer-valued function f on the set 2V of all subsets of a finite set V is a connectivity function if it satisfies the following conditions: (1) f(X) + f(Y ) ≥ f(X ∩Y )+ f(X ∪Y ) for all subsets X, Y of V , (2) f(X) = f(V \X) for all X ⊆ V , and (3) f(∅) = 0. Branch-width is defined for graphs, matroids, and more generally, connectivity functions. We show that for each constant k, there is ...

Spines T a tree on a signed ground set V = V− t V. Spine on T = directed and labeled tree S such that • the labels of the nodes of S form a partition of the signed ground set V, • at a node labeled by U = U− t U, the source label sets of the incoming arcs are subsets of distinct connected components of TrU−, and the sink label sets of the outgoing arcs are subsets of distinct connected componen...

For multivariate distributions in the domain of attraction a max-stable distribution, tail copula and stable dependence function are equivalent ways to capture upper tail. The empirical versions these functions rank-based estimators whose inflated estimation errors known converge weakly Gaussian process that is similar structure weak limit process. We extend this result continuous functional da...

We use mutual information as the criterion to rank the Mel frequency cepstral coefficients (MFCCs) and their derivatives according to the information they provide about different articulatory features in acoustic-to-articulatory (AtoA) inversion. It is found that just a small subset of the coefficients encodes maximal information about articulatory features and interestingly, this subset is art...

In multi-criteria decision making the decision maker need to assign weights to criteria for evaluation of alternatives, but decision makers usually find it difficult to assign precise weights to several criteria. On the other hand, decision makers may readily provide a number of preferences regarding the relative importance between two disjoint subsets of criteria. We extend a procedure by L. V...

We consider the poset of all submatrices of a given matrix, ordered by containment. The unique rank function for this poset is given by r(M) = R(M)+C(M)?1, where R(M) and C(M) denote the number of rows and columns of a nonempty matrix M, respectively, and the rank of the empty matrix is 0. For xed k and i our objective is to nd a set M of submatrices M 1 ; M 2 ; : : :; M k such that r(M j) = i ...

In this paper, we propose a new feature evaluation method that forms the basis for feature ranking and feature selection. The method starts by generating a number of feature subsets in a random fashion and evaluates features based on the derived subsets. It then proceeds in a number of stages. In each stage, it inputs the features whose ranks in the previous stage were above the median rank and...