Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small correction

Bases anatómicas de la lectura y alternativas metodológicas

[Resumen] A través de las técnicas de localización de funciones se ha podido observar en el cerebro del disléxico particularidades que lo distinguen del cerebro de los lectores nonnales. Las exploraciones postmortem, la electroencefalografía, la resonancia magnética, etc. coinciden en señalar la existencia de anomalías anatómicas y funcionales en áreas relacionadas con el lenguaje. El proceso lectoescritor tiene lugar en estas mismas áreas cuando se lleva a cabo a través de la ruta fonológico. Todo parece indicar que este hecho guarda especial relación con el fracaso del disléxico, InáxiIne si se tiene en cuenta que en las lenguas logográficas, en las que se utiliza la ruta visual (que al parecer tiene lugar en el lado derecho del cerebro) para acceder a la lectura, la disléxia como tal síndrome no existe. Nuestra intención con este trabajo es aportar evidencias que hagan reflexionar sobre la necesidad de buscar alternativas a la metodología tradicional (en el mercado la práctica totalidad de los lnétodos de lectura son silábicos o alfabéticos. Los globales son difíciles de encontrar) sobre todo en el caso de alumnos con dificultades lectoescritora

Estudio de caso do entrenamento lingüístico nunha reabilitación logopédica

[Resumo] caso que estamos a presentar nesta comunicación é o estudio de caso dun neno de 7 anos cun linguaxe moi pouco estructrurado a nivel expresivo (vocabulario pobre, ausencia de nexos -palabra frase-, sen ritmo na fala, confusións en fonemas, non pronuncia as consonantes nasais nin os sinfóns, etc.) e con dificultades na lingua escrita tanto a nivel comprensivo coma expresivo. Pódese dicir que posúe carencias nos catro sistemas que compoñen a linguaxe: fonolóxico, lexical, sintáctico-gramatical e simbólico-semántico. Para o análise das suas dificultades non só tivemos en conta ó suxeito se non os seus contextos externos, principalmente o circulo familiar e o colexio dada a importancia que reportan no proceso de comunicación. Nas relacións interpersonais o neno recibe constantemente un feed-back correctivo. Todo-los nenos/as vense sometidos/as a unha intervención intensiva, aínda que inconsciente do entorno sobre a súa comunicación co obxectivo primario de facilita-la interacción e en consecuencia permitirlle adquirir, con maor facilidade, o código característico do grupo social ó que pertence. Este proceso é común a todalas culturas porque pertence ó grupo de conductas máis xerais de transmisión de información entre as xeneracións. Incidimos sobre o clima da clase e elaborarnos pautas a nivel familiar a fin de favorecer o proceso de entrenamento lingüístico e prevenir conductas que poidan xurdir pola falta de coherencia no nivel de esixencia. A nivel suxeito traballáronse os aspectos de mayor incidencia no desenrolo lingüístico, coma a memoria inmediata, a organización temporoauditiva, e os aspectos psicolingüísticos coma entrenamento da conciencia fonolóxica (descompoñer unha palabra nos seus elementos -sílabas ou letrase volvela a componer, etc.). o xogo e a música conformaron o eixe das sesións de reeducación a fin de axeita-Io proceso a idade e madurez do alumno. Os resultados obtidos si ben foron positivos tendo enconta o punto de partida e o de chegada, como se di nas conclusións, pódese falar máis que de logros concretos dunha progresión lenta pero continuada en todolos capítulos a reeducar, porque debemos de considerar permanentemente que tanto o ensino como a aprendizaxe da linguaxe nesta tipoloxía de casos é un continu

Monolingual and bilingual spanish-catalan speech recognizers developed from SpeechDat databases

Under the SpeechDat specifications, the Spanish member of SpeechDat consortium has recorded a Catalan database that includes one thousand speakers. This communication describes some experimental work that has been carried out using both the Spanish and the Catalan speech material. A speech recognition system has been trained for the Spanish language using a selection of the phonetically balanced utterances from the 4500 SpeechDat training sessions. Utterances with mispronounced or incomplete words and with intermittent noise were discarded. A set of 26 allophones was selected to account for the Spanish sounds and clustered demiphones have been used as context dependent sub-lexical units. Following the same methodology, a recognition system was trained from the Catalan SpeechDat database. Catalan sounds were described with 32 allophones. Additionally, a bilingual recognition system was built for both the Spanish and Catalan languages. By means of clustering techniques, the suitable set of allophones to cover simultaneously both languages was determined. Thus, 33 allophones were selected. The training material was built by the whole Catalan training material and the Spanish material coming from the Eastern region of Spain (the region where Catalan is spoken). The performance of the Spanish, Catalan and bilingual systems were assessed under the same framework. The Spanish system exhibits a significantly better performance than the rest of systems due to its better training. The bilingual system provides an equivalent performance to that afforded by both language specific systems trained with the Eastern Spanish material or the Catalan SpeechDat corpus.Peer ReviewedPostprint (published version

On the Parameterized Intractability of Monadic Second-Order Logic

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms, where the parameter is the tree-width plus the size of the formula. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem cannot be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions and is such that the tree-width of C is not bounded by \log^{84} n then MSO_2-model checking is not fpt unless SAT can be solved in sub-exponential time. If the tree-width of C is not poly-logarithmically bounded, then MSO_2-model checking is not fpt unless all problems in the polynomial-time hierarchy can be solved in sub-exponential time

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency

Nonperturbative aspects of ABJM theory

Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published in JHE

Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles

In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula

Interacting fermions and N=2 Chern-Simons-matter theories

The partition function on the three-sphere of N=3 Chern-Simons-matter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N=2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit is the thermodynamic limit of the gas and it can be analyzed with the Hartree and Thomas-Fermi approximations, which lead to the known large N solutions of these models. We use this interacting fermion picture to analyze in detail N=2 theories with one single node. In the case of theories with no long-range forces we incorporate exchange effects and argue that the partition function is given by an Airy function, as in N=3 theories. For the theory with g adjoint superfields and long-range forces, the Thomas-Fermi approximation leads to an integral equation which determines the large N, strongly coupled R-charge.Comment: 29 pages, 4 figure

Spectroscopic measurement of cortical nitric oxide release induced by ascending activation

[Abstract] The transition from sleep to the awake state is regulated by the activation of subcortical nuclei of the brainstem (BS) and basal forebrain (BF), releasing acetylcholine and glutamate throughout the cortex and inducing a tonic state of neural activity. It has been suggested that such activation is also mediated by the massive and diffuse cortical release of nitric oxide (NO). In this work we have combined the spectroscopic measurement of NO levels in the somatosensory cortex of the cat through its marker methemoglobin, as well as two other hemodynamic markers (oxyhemoglobin – oxyHb – and deoxyhemoglobin – deoxyHb), together with the electrical stimulation of BS and BF – to induce an experimental transition from a sleep-like state to an awake-like mode. The results show an increase of NO levels either after BS or BF activation. The response induced by BS stimulation was biphasic in the three studied markers, and lasted for up to 30 s. The changes induced by BF were monophasic lasting for up to 20 s. The systemic blockade of NO production abolished the observed responses to BS whereas responses to BF stimulation were much less affected. These results indicate a crucial role for NO in the neuronal activation induced by the ascending systems.Galicia. Consellería de Economía e Industria; INCITE09137272P