Revisiting the combinatorics of the 2D Ising model

We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants, using the language of Kac-Ward matrices. We also give a brief account of the relations between various alternative formalisms which have been used in the combinatorial study of the planar Ising model: dimers and Grassmann variables, spin and disorder operators, and, more recently, s-holomorphic observables. In addition, we point out that these formulas can be extended to the double-Ising model, defined as a pointwise product of two Ising spin configurations on the same discrete domain, coupled along the boundary.Comment: Minor change in the notation (definition of eta). 55 pages, 4 figure

Probabilistic parsing

Postprin

Flexible RNA design under structure and sequence constraints using formal languages

The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical applications in biology, additional constraints must be taken into account, such as the presence/absence of regulatory motifs, either at a specific location or anywhere in the sequence. In this study, we investigate the design of RNA sequences from their targeted secondary structure, given these additional sequence constraints. To this purpose, we develop a general framework based on concepts of language theory, namely context-free grammars and finite automata. We efficiently combine a comprehensive set of constraints into a unifying context-free grammar of moderate size. From there, we use generic generic algorithms to perform a (weighted) random generation, or an exhaustive enumeration, of candidate sequences. The resulting method, whose complexity scales linearly with the length of the RNA, was implemented as a standalone program. The resulting software was embedded into a publicly available dedicated web server. The applicability demonstrated of the method on a concrete case study dedicated to Exon Splicing Enhancers, in which our approach was successfully used in the design of \emph{in vitro} experiments.Comment: ACM BCB 2013 - ACM Conference on Bioinformatics, Computational Biology and Biomedical Informatics (2013

Computation of distances for regular and context-free probabilistic languages

Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe

Coverage and Vacuity in Network Formation Games

The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter

Properties of ABA+ for Non-Monotonic Reasoning

We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that ABA+ semantics exhibit. These pave way to the satisfaction by ABA+ of some (arguably) desirable principles of preference handling in argumentation and nonmonotonic reasoning, as well as non-monotonic inference properties of ABA+ under various semantics.Comment: This is a revised version of the paper presented at the worksho