We review the qdeformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket state sum…
Papers in Algebra
Algebra papers in Mathematics, Q
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in Algebra, Q


We introduce a practical stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n < m unknowns over a finite field. The security of the keystream generation of QUAD is…

These are the proceedings of the conference on “Quadratic Forms And Their Applications” which was held at University College Dublin from 5th to 9th July, 1999. The meeting was attended by 82 participants from Europe and elsewhere. There were 13…

Identifying a subset of features that preserves classification accuracy is a problem of growing importance, because of the increasing size and dimensionality of realworld data sets. We propose a new feature selection method, named Quadratic…

Quadrature signal processing is used in many fields of science and engineering, and quadrature signals are necessary to describe the processing and implementation that takes place in modern digital communications systems. In this tutorial we'll…

We examine a theory of competitive innovation in which new ideas are introduced only when diminishing returns to the use of existing ideas sets in. After an idea is introduced, the knowledge capital associated with that idea expands, and its value…

BACKGROUND: Teamwork is a fundamental aspect of many human activities, from business to art and from sports to science. Recent research suggest that team work is of crucial importance to cuttingedge scientific research, but little is known about…

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove…

In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f 2 = I. We describe several generalisations of wellknown results in the theory of boolean functions, including quantum…

On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation does not…

Quantum cryptography could well be the first application of quantum mechanics at the singlequantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues.

It is shown that 2+1 dimensional quantum YangMills theory, with an action consisting purely of the ChernSimons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.…

We introduce a general notion of quantum universal enveloping algebroids (QUE algebroids), or quantum groupoids, as a unification of quantum groups and starproducts. Some basic properties are studied including the twist construction and the…

Lefthanded metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two…

This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of…

This paper outlines an approach to the nonabelian theta functions of the $SU(2)$ChernSimons theory with the methods used by A. Weil for studying classical theta functions. First we translate in knot theoretic language classical theta functions,…

In this paper a programming language, qGCL,is presented for the expression of quantum algorithms. It contains the features re quired to program a ‘universal’ quantum computer (including initiali sation and observation), has a formal semantics and…

We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill one's grandfather in that once the…

We study the discretetime quantum walkbased search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the…

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the…
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