A logic-based agent that plans for extended reachability goals

Planning to reach a goal is an essential capability for rational agents. In general, a goal specifies a condition to be achieved at the end of the plan execution. In this article, we introduce nondeterministic planning for extended reachability goals (i.e., goals that also specify a condition to be preserved during the plan execution). We show that, when this kind of goal is considered, the temporal logic CTL turns out to be inadequate to formalize plan synthesis and plan validation algorithms. This is mainly due to the fact that the CTL`s semantics cannot discern among the various actions that produce state transitions. To overcome this limitation, we propose a new temporal logic called alpha-CTL. Then, based on this new logic, we implement a planner capable of synthesizing reliable plans for extended reachability goals, as a side effect of model checking.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

New Improvements in Automatic Structure Elucidation Using the LSD (Logic for Structure Determination) and the SISTEMAT Expert Systems

This article describes the integration of the LSD (Logic for Structure Determination) and SISTEMAT expert systems that were both designed for the computer-assisted structure elucidation of small organic molecules. A first step has been achieved towards the linking of the SISTEMAT database with the LSD structure generator. The skeletal descriptions found by the SISTEMAT programs are now easily transferred to LSD as substructural constraints. Examples of the synergy between these expert systems are given for recently reported natural products.