On cutoff effects in lattice QCD from short to long distances

We discuss kinematical enhancements of cutoff effects at short and intermediate distances. Starting from a pedagogical example with periodic boundary conditions, we switch to the case of the Schroedinger Functional, where the theoretical analysis is checked by precise numerical data with Nf=2 dynamical O(a)-improved Wilson quarks. Finally we present an improved determination of the renormalization of the axial current in that theory.Comment: 16 pages, 4 figures and 2 tables. References modifie

Inducing Features of Random Fields

We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the Kullback-Leibler divergence between the model and the empirical distribution of the training data. A greedy algorithm determines how features are incrementally added to the field and an iterative scaling algorithm is used to estimate the optimal values of the weights. The statistical modeling techniques introduced in this paper differ from those common to much of the natural language processing literature since there is no probabilistic finite state or push-down automaton on which the model is built. Our approach also differs from the techniques common to the computer vision literature in that the underlying random fields are non-Markovian and have a large number of parameters that must be estimated. Relations to other learning approaches including decision trees and Boltzmann machines are given. As a demonstration of the method, we describe its application to the problem of automatic word classification in natural language processing. Key words: random field, Kullback-Leibler divergence, iterative scaling, divergence geometry, maximum entropy, EM algorithm, statistical learning, clustering, word morphology, natural language processingComment: 34 pages, compressed postscrip

Non-embeddability of certain classes of Levi flat manifolds

On the basis of a result of Barrett, we show that members of certain classes of abstract Levi flat manifolds with boundary, whose Levi foliation contains a compact leaf with contracting, flat holonomy, admit no $CR$ embedding as a hypersurface of a complex manifold.Comment: 8 pages, no figure

Analysis of a moving mask approximation for martensitic transformations

In this work we introduce a moving mask approximation to describe the dynamics of austenite to martensite phase transitions at a continuum level. In this framework, we prove a new type of Hadamard jump condition, from which we deduce that the deformation gradient must be of the form $\mathsf{1} +\mathbf{a}\otimes \mathbf{n}$ a.e. in the martensite phase. This is useful to better understand the complex microstructures and the formation of curved interfaces between phases in new ultra-low hysteresis alloys such as Zn45Au30Cu25, and provides a selection mechanism for physically-relevant energy-minimising microstructures. In particular, we use the new type of Hadamard jump condition to deduce a rigidity theorem for the two well problem. The latter provides more insight on the cofactor conditions, particular conditions of supercompatibility between phases believed to influence reversibility of martensitic transformations

Supernovae Shedding Light on Gamma-Ray Bursts

We review the observational status of the Supernova (SN)/Gamma-Ray Burst (GRB) connection. In section 2 we provide a short summary of the observational properties of core-collapse SNe. In sections 3-6 we review the circumstantial evidences and the direct observations that support the existence of a deep connection between the death of massive stars and GRBs. Present data suggest that SNe associated with GRBs form a heterogeneous class of objects including both bright and faint Hypernovae and perhaps also `standard' Ib/c events. In section 7, we provide an empirical estimate of the rate of Hypernovae, for a ``MilkyWay-like'' galaxy, of about $\sim 2.6\times 10^{-4}$ yr$^{-1}$ that may imply the ratio GRB/Hypernovae to be in the range $\sim 0.03-0.7$. In the same framework we find the ratio GRB/SNe-Ibc to be $\sim 0.008\div 0.05$. In section 8 we discuss the possible existence of a lag between the SN explosion and the associated gamma-ray event. In the few SN/GRB associations so far discovered the SN explosions and GRB events appear to go off simultaneously. In section 9 we present the conclusions and highlight the open problems that Swift hopefully will allow us to solve.Comment: 20 pages, 13 figures, invited review at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres