Toric grammars: a new statistical approach to natural language modeling

We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many finite recurrent communicating classes and define our language model as the invariant probability measures of the chain on each recurrent communicating class. This Markov chain, that we call a communication model, recombines at each step randomly the set of sentences forming its current state, using some grammar rules. When the grammar rules are fixed and known in advance instead of being estimated on the fly, we can prove supplementary mathematical properties. In particular, we can prove in this case that all states are recurrent states, so that the chain defines a partition of its state space into finite recurrent communicating classes. We show that our approach is a decisive departure from Markov models at the sentence level and discuss its relationships with Context Free Grammars. Although the toric grammars we use are closely related to Context Free Grammars, the way we generate the language from the grammar is qualitatively different. Our communication model has two purposes. On the one hand, it is used to define indirectly the probability distribution of a random sentence of the language. On the other hand it can serve as a (crude) model of language transmission from one speaker to another speaker through the communication of a (large) set of sentences

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On raconte qu’un disciple de Bashô, perplexe devant l’aveu que venait de lui faire son maître — à savoir qu’il avait expliqué le zen durant toute sa vie sans pourtant le comprendre —, l’interrogea afin d’élucider le paradoxe. Comment cela était-il possible ? Bashô, exaspéré, s’empressa de lui demander à son tour : « Oh, dois-je aussi vous expliquer cela ? » À bien des égards, nous pourrions ici remplacer le mot « zen » par le mot « poésie » sans que cette histoire ne perde de sa force, tant i..

A model for reactive porous transport during re-wetting of hardened concrete

A mathematical model is developed that captures the transport of liquid water in hardened concrete, as well as the chemical reactions that occur between the imbibed water and the residual calcium silicate compounds residing in the porous concrete matrix. The main hypothesis in this model is that the reaction product -- calcium silicate hydrate gel -- clogs the pores within the concrete thereby hindering water transport. Numerical simulations are employed to determine the sensitivity of the model solution to changes in various physical parameters, and compare to experimental results available in the literature.Comment: 30 page

Limited diversity associated with duplicated class II MHC-DRB genes in the red squirrel population in the United Kingdom compared with continental Europe

The red squirrel (Sciurus vulgaris) population in the United Kingdom has declined over the last century and is now on the UK endangered species list. This is the result of competition from the eastern grey squirrel (S. carolinensis) which was introduced in the 19th century. However, recent evidence suggests that the rate of population decline is enhanced by squirrelpox disease, caused by a viral infection carried asymptomatically by grey squirrels but to which red squirrels are highly susceptible. Population genetic diversity provides some resilience to rapidly evolving or exotic pathogens. There is currently no data on genetic diversity of extant UK squirrel populations with respect to genes involved in disease resistance. Diversity is highest at loci involved in the immune response including genes clustered within the major histocompatibility complex (MHC). Using the class II DRB locus as a marker for diversity across the MHC region we genotyped 110 red squirrels from locations in the UK and continentalEurope. Twenty four Scvu-DRB alleles at two functional loci; Scvu-DRB1 and Scvu- DRB2, were identified. High levels of diversity were identified at both loci in the continental populations. In contrast, no diversity was observed at the Scvu-DRB2 locus in the mainland UK population while a high level of homozygosity was observed at the Scvu-DRB1 locus. The red squirrel population in the UK appears to lack the extensive MHC diversity associated with continental populations, a feature which may have contributed to their rapid decline