RASCAL: calculation of graph similarity using maximum common edge subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

New Concepts in Particle Physics from Solution of an Old Problem

Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new nonperturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh like thermal aspects (KMS property, entropy attached to horizons) of quantum matter behind causal horizons, aspects which hitherto were exclusively related with Killing horizons in curved spacetime rather than with localization aspects in Minkowski space particle physics. The scope of this modular framework is amazingly wide and ranges from providing a conceptual basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models to a decomposition theory of QFT's in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d=1+1 a holographic relation and in higher dimensions more like a scanning). The new framework gives a spacetime interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate

Modular feature selection using relative importance factors

Feature selection plays an important role in finding relevant or irrelevant features in classification. Genetic algorithms (GAs) have been used as conventional methods for classifiers to adaptively evolve solutions for classification problems. In this paper, we explore the use of feature selection in modular GA-based classification. We propose a new feature selection technique, Relative Importance Factor (RIF), to find irrelevant features in the feature space of each module. By removing these features, we aim to improve classification accuracy and reduce the dimensionality of classification problems. Benchmark classification data sets are used to evaluate the proposed approaches. The experiment results show that RIF can be used to determine irrelevant features and help achieve higher classification accuracy with the feature space dimension reduced. The complexity of the resulting rule sets is also reduced which means the modular classifiers with irrelevant features removed will be able to classify data with a higher throughput

Extended Rate, more GFUN

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler's program Rate, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann's GFUN, the univariate case of Manuel Kauers' Guess.m and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m.Comment: 26 page