Non Abelian Toda Theory : A Completely Integrable Model for Strings on a Black Hole Background

The present paper studies a completely integrable conformally invariant model in 1+1 dimensions that corresponds to string propagation on the two-dimensional black hole background (semi-ininite cigar). Besides the two space-time string fields there is a third (internal) field with a very specific Liouville-type interaction leading to the complete integrability. This system is known as non-abelian Toda theory. I give the general explicit classical solution. It realizes a rather involved transformation expressing the interacting string fields in terms of (three) functions $\varphi_j(u)$ and $\bar\varphi_j(v)$ of one light-cone variable only. The latter are shown to lead to standard harmonic oscillator (free field) Poisson brackets thus paving the way towards quantization. There are three left-moving and three right-moving conserved quantities. The right (left)-moving conserved quantities form a new closed non-linear, non-local Poisson bracket algebra. This algebra is a Virasoro algebra extended by two conformal dimension-two primaries.Comment: 41 pages, PUPT-143

Does Coupling To Gravity Preserve Integrability ?

These are notes based on a lecture given at the Cargese summer school 1995. I describe evidence that the (two-dimensional) integrable chiral Gross-Neveu model might remain integrable when coupled to gravity. The results presented here were obtained in collaboration with Ian Kogan.Comment: 11 pages, uses PHYZZX, 7 figures (encapsulated postscript), (one reference added

Predictive Capacity of Meteorological Data - Will it rain tomorrow

With the availability of high precision digital sensors and cheap storage medium, it is not uncommon to find large amounts of data collected on almost all measurable attributes, both in nature and man-made habitats. Weather in particular has been an area of keen interest for researchers to develop more accurate and reliable prediction models. This paper presents a set of experiments which involve the use of prevalent machine learning techniques to build models to predict the day of the week given the weather data for that particular day i.e. temperature, wind, rain etc., and test their reliability across four cities in Australia {Brisbane, Adelaide, Perth, Hobart}. The results provide a comparison of accuracy of these machine learning techniques and their reliability to predict the day of the week by analysing the weather data. We then apply the models to predict weather conditions based on the available data.Comment: 7 pages, 2 Result Set

From the Editor

From the Edito

Small-time expansion of the Fokker-Planck kernel for space and time dependent diffusion and drift coefficients

We study the general solution of the Fokker-Planck equation in d dimensions with arbitrary space and time dependent diffusion matrix and drift term. We show how to construct the solution, for arbitrary initial distributions, as an asymptotic expansion for small time. This generalizes the well-known asymptotic expansion of the heat-kernel for the Laplace operator on a general Riemannian manifold. We explicitly work out the general solution to leading and next-to-leading order in this small-time expansion, as well as to next-to-next-to-leading order for vanishing drift. We illustrate our results on a several examples.Comment: 30 page

Consistent string backgrounds and completely integrable 2D field theories

After reviewing the $\beta$-function equations for consistent string backgrounds in the $\sigma$-model approach, including metric and antisymmetric tensor, dilaton and tachyon potential, we apply this formalism to WZW models. We particularly emphasize the case where the WZW model is perturbed by an integrable marginal tachyon potential operator leading to the non-abelian Toda theories. Already in the simplest such theory, there is a large non-linear and non-local chiral algebra that extends the Virasoro algebra. This theory is shown to have two formulations, one being a classical reduction of the other. Only the non-reduced theory is shown to satisfy the $\beta$-function equations.Comment: 12 pages, uses PHYZZ