Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

A bidirectional mapping between English and CNF-based reasoners

If language is a transduction between sound and meaning, the target of semantic interpretation should be the meaning representation expected by general cognition. Automated reasoners provide the best available fully-explicit proxies for general cognition, and they commonly expect Clause Normal Form (CNF) as input. There is a well-known algorithm for converting from unrestricted predicate calculus to CNF, but it is not invertible, leaving us without a means to transduce CNF back to English. I present a solution, with possible repercussions for the overall framework of semantic interpretation

Looking for a Rational Thermodynamics in the late XIX century

From Rudolf Clausius’ classical version of Thermodynamics two different traditions of research really emerged. If James C. Maxwell and Ludwig Boltzmann pursued the integration of thermodynamics with the kinetic theory of gases, others relied on a macroscopic and more abstract approach, which set aside specific mechanical models. Starting from 1869, the French engineer François Massieu was able to demonstrate that thermodynamics could be based on two “characteristic functions” or potentials. Josiah W. Gibbs and Hermann von Helmholtz exploited the structural analogy between Mechanics and Thermodynamics: from a mathematical point of view, Helmholtz’s “free energy” was nothing else but Gibb’s first potential. In the meantime, in 1880, the young German physicist Max Planck aimed at filling the gap between thermodynamics and the theory of elasticity. Five years later Arthur von Oettingen put forward a formal theory, where mechanical work and fluxes of heat represented the starting point of a dual mathematical structure. In 1891 Pierre Duhem generalized the concept of “virtual work” under the action of “external actions” by taking into account both mechanical and thermal actions. Between 1892 and 1894 his design of a generalized Mechanics based on thermodynamics was further developed: ordinary mechanics was looked upon as a specific instance of a more general science