Hirota's Solitons in the Affine and the Conformal Affine Toda Models

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.Comment: 36 pages, LaTe

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the $sl_3$ Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete $W_3$ algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.Comment: 12 pages, LaTe

Connection between the Affine and Conformal Affine Toda Models and their Hirota's Solution

It is shown that the Affine Toda models (AT) constitute a ``gauge fixed'' version of the Conformal Affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the corresponding CAT models, each one associated to a point of the orbit of the conformal group. The Hirota's $\tau$-function are introduced and soliton solutions for the AT and CAT models associated to $\hat {SL}(r+1)$ and $\hat {SP}(r)$ are constructed.Comment: 11 pages, LaTe

On the symmetries of BF models and their relation with gravity

The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.Comment: 29 page

Symmetries of topological field theories in the BV-framework

Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page

Regular cosmological solutions in low energy effective action from string theories

The possibility of obtaining singularity free cosmological solutions in four dimensional effective actions motivated by string theory is investigated. In these effective actions, in addition to the Einstein-Hilbert term, the dilatonic and the axionic fields are also considered as well as terms coming from the Ramond-Ramond sector. A radiation fluid is coupled to the field equations, which appears as a consequence of the Maxwellian terms in the Ramond-Ramond sector. Singularity free bouncing solutions in which the dilaton is finite and strictly positive are obtained for models with flat or negative curvature spatial sections when the dilatonic coupling constant is such that $\omega < - 3/2$, which may appear in the so called $F$ theory in 12 dimensions. These bouncing phases are smoothly connected to the radiation dominated expansion phase of the standard cosmological model, and the asymptotic pasts correspond to very large flat spacetimes.Comment: 10 pages, ReVTeX format, 2 figures, to appear in Phys. Rev. D (2003

Topological Yang-Mills theories and their observables: a superspace approach

Théori

Toda lattice field theories, discrete W algebras, Toda lattice hierachies and quantum groups

Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Evaluating classification strategies for detection of circumscribed masses in digital mammograms

This paper reports work to investigate a computer aided diagnosis scheme for detection of circumscribed digitised masses in mammograms. The model used consists of three stages: The first segments the mammogram into regions of interest (ROIs), the second stage tries to eliminate the majority of false positives reported, and finally a third stage utilises more sophisticated processing to make a final decision on the likelihood of an ROI being a genuine mass. The paper is concerned with an evaluation of different classifiers in the difficult task of detection of masses, and the relationship between correct and incorrect detection, but also points the way to developing more sophisticated-and potentially more reliable-techniques based on the integration of multiple classifiers within a single processing structure. The study used 4 different classifiers: multivariate Gaussian classifier (MVG), radial basis function (RBF), Q-vector median (QVM), 1-nearest neighbour (1NN). Three different feature types were used: 3/sup rd/ order normalized Zernike moments, texture features, and a combined moment and textures feature vector. Various feature selection techniques have also been investigated to obtain feature sets which improve the performance of each classifier

Exact correlators of two-matrix models

hep-th--94-12006Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal