Several applications of cognitive informatics are coupled with automatic acquisition and processing of data and images for recognition and classification. There are many algorithms with wide-ranging performance in pattern recognition. A computer recognizes a character as a pattern from its digital image or from a set of parameters picked from its digital representation. This paper explores an o...

The problem of detecting minor quantitative trait loci (QTL) responsible for genetic variation not explained by major QTL is of importance in the complete dissection of quantitative characters. Two extensions of the permutation-based method for estimating empirical threshold values are presented. These methods, the conditional empirical threshold (CET) and the residual empirical threshold (RET)...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii CHAPTER 1. HISTORICAL BACKGROUND . . . . . . . . . . . . . . . . . 1 1.1 Early Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Resolvent Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 More Recent Developments . . . . . . . . . . . . . . . . . ....

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions. For graphs with...

We describe three different methods to compute all those characters of a finite group that have certain properties of transitive permutation characters. First, a combinatorial approach can be used to enumerate vectors of multiplicities. Secondly, these characters can be found as certain integral solutions of a system of inequalities. Thirdly, they are calculated via Gaussian elimination. The me...

We show that in a non-trivial Gassmann triple (G,H,H′) of index n there does not exist an involution τ ∈ G such that the value of the permutation character on τ is n− 2. In addition we describe a GAP program designed to search for examples of Gassmann triples and give a brief summary of the results of this search.

We describe a novel technique to handle big permutation domains for large groups. It is applied to the multiplicity-free action of the sporadic simple Baby Monster group on the cosets of its maximal subgroup Fi23, to determine the character table of the associated endomorphism ring.