Loops versus Matrices

Loops versus Matrices -

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...

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Loops versus Matrices - The Nonperturbative Aspects of Noncritical String -

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...

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Loops versus strings

Two popular attempts to understand the quantum physics of gravitation are critically assessed. The talk on which this paper is based was intended for a general particle-physics audience. Talk given in the meeting What comes beyond the standard model?, Portoroz, Eslovenia, 12-17 July 2003.

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Loops, matchings and alternating-sign matrices

The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes onmatchings is reviewed.New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners. © 2005 Elsevier B.V. All rights reserved.

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Representing Image Matrices: Eigenimages Versus Eigenvectors

We consider the problem of representing image matrices with a set of basis functions. One common solution for that problem is to first transform the 2D image matrices into 1D image vectors and then to represent those 1D image vectors with eigenvectors, as done in classical principal component analysis. In this paper, we adopt a natural representation for the 2D image matrices using eigenimages,...

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Loops versus Matrices

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