On the stochastic Strichartz estimates and the stochastic nonlinear Schr\"odinger equation on a compact riemannian manifold

We prove the existence and the uniqueness of a solution to the stochastic NSLE on a two-dimensional compact riemannian manifold. Thus we generalize a recent work by Burq, G\'erard and Tzvetkov in the deterministic setting, and a series of papers by de Bouard and Debussche, who have examined similar questions in the case of the flat euclidean space with random perturbation. We prove the existence and the uniqueness of a local maximal solution to stochastic nonlinear Schr\"odinger equations with multiplicative noise on a compact d-dimensional riemannian manifold. Under more regularity on the noise, we prove that the solution is global when the nonlinearity is of defocusing or of focusing type, d=2 and the initial data belongs to the finite energy space. Our proof is based on improved stochastic Strichartz inequalities

Learning to detect dysarthria from raw speech

Speech classifiers of paralinguistic traits traditionally learn from diverse hand-crafted low-level features, by selecting the relevant information for the task at hand. We explore an alternative to this selection, by learning jointly the classifier, and the feature extraction. Recent work on speech recognition has shown improved performance over speech features by learning from the waveform. We extend this approach to paralinguistic classification and propose a neural network that can learn a filterbank, a normalization factor and a compression power from the raw speech, jointly with the rest of the architecture. We apply this model to dysarthria detection from sentence-level audio recordings. Starting from a strong attention-based baseline on which mel-filterbanks outperform standard low-level descriptors, we show that learning the filters or the normalization and compression improves over fixed features by 10% absolute accuracy. We also observe a gain over OpenSmile features by learning jointly the feature extraction, the normalization, and the compression factor with the architecture. This constitutes a first attempt at learning jointly all these operations from raw audio for a speech classification task.Comment: 5 pages, 3 figures, submitted to ICASS

Large deviation principle and inviscid shell models

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by the square root of the viscosity, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0,T],V) for the topology of uniform convergence on [0,T], but where V is endowed with a topology weaker than the natural one. The initial condition has to belong to V and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation

Rate of Convergence of Implicit Approximations for stochastic evolution equations

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators are considered. Under some regularity condition assumed for the solution, the rate of convergence of implicit Euler approximations is estimated under strong monotonicity and Lipschitz conditions. The results are applied to a class of quasilinear stochastic PDEs of parabolic type.Comment: 25 page

Adapted pairs in type AA and regular nilpotent elements

Let $\mathfrak g$ be a simple Lie algebra over an algebraically closed field $\bf k$ of characteristic zero and $\bf G$ its adjoint group. Let $\mathfrak q$ be a biparabolic subalgebra of $\mathfrak g$. The algebra $Sy(\mathfrak q)$ of semi-invariants on $\mathfrak q^*$ is polynomial in most cases, in particular when $\mathfrak g$ is simple of type $A$ or $C$. On the other hand $\mathfrak q$ admits a canonical truncation $\mathfrak q_{\Lambda}$ such that $Sy(\mathfrak q)=Sy(\mathfrak q_{\Lambda})=Y(\mathfrak q_{\Lambda})$ where $Y(\mathfrak q_{\Lambda})$ denotes the algebra of invariant functions on $\mathfrak q_{\Lambda}^*$. An adapted pair for $\mathfrak q_{\Lambda}$ is a pair $(h,\,\eta)\in \mathfrak q_{\Lambda}\times\mathfrak q_{\Lambda}^*$ such that $\eta$ is regular and $(ad\,h)\eta=-\eta$. In a previous paper of A. Joseph (2008) adapted pairs for every truncated biparabolic subalgebra $\mathfrak q_{\Lambda}$ of a simple Lie algebra $\mathfrak g$ of type $A$ were constructed and then provide Weierstrass sections for $Y(\mathfrak q_{\Lambda})$ in $\mathfrak q_{\Lambda}^*$. These latter are linear subvarieties $\eta+V$ of $\mathfrak q_{\Lambda}^*$ such that the restriction map induces an algebra isomorphism of $Y(\mathfrak q_{\Lambda})$ onto the algebra of regular functions on $\eta+V$. Here we show that for each of the adapted pairs $(h,\,\eta)$ constructed in the paper mentioned above one can express $\eta$ as the image of a regular nilpotent element $y$ of $\mathfrak g^*$ under the restriction to $\mathfrak q$. Since $y$ must be a $\bf G$ translate of the standard regular nilpotent element defined in terms of the already chosen set $\pi$ of simple roots, one may attach to $y$ a unique element of the Weyl group. Ultimately one can then hope to be able to describe adapted pairs (in general) through the Weyl group.Comment: This is a rewriting of the version submitted on the arXiv in June 201

Large deviations for rough paths of the fractional Brownian motion

Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.Comment: 32 page

Slices for biparabolics of index one

Let $\mathfrak a$ be an algebraic Lie subalgebra of a simple Lie algebra $\mathfrak g$ with index \mathfrak a \leq \rank \mathfrak g. Let $Y(\mathfrak a)$ denote the algebra of $\mathfrak a$ invariant polynomial functions on $\mathfrak a^*$. An algebraic slice for $\mathfrak a$ is an affine subspace $\eta+V$ with $\eta \in \mathfrak a^*$ and $V \subset \mathfrak a^*$ a subspace of dimension index $\mathfrak a$ such that restriction of function induces an isomorphism of $Y(\mathfrak a)$ onto the algebra $R[\eta+V]$ of regular functions on $\eta+V$. Slices have been obtained in a number of cases through the construction of an adapted pair $(h,\eta)$ in which $h \in\mathfrak a$ is ad-semisimple, $\eta$ is a regular element of $\mathfrak a^*$ which is an eigenvector for $h$ of eigenvalue minus one and $V$ is an $h$ stable complement to (\ad \mathfrak a)\eta in $\mathfrak a^*$. The classical case is for $\mathfrak g$ semisimple. Yet rather recently many other cases have been provided. For example if $\mathfrak g$ is of type $A$ and $\mathfrak a$ is a "truncated biparabolic" or a centralizer. In some of these cases (particular when the biparabolic is a Borel subalgebra) it was found that $\eta$ could be taken to be the restriction of a regular nilpotent element in $\mathfrak g$. Moreover this calculation suggested how to construct slices outside type $A$ when no adapted pair exists. This article makes a first step in taking these ideas further. Specifically let $\mathfrak a$ be a truncated biparabolic of index one (and then $\mathfrak g$ is of type $A$). In this case it is shown that the second member of an adapted pair $(h,\eta)$ for $\mathfrak a$ is the restriction of a particularly carefully chosen regular nilpotent element of $\mathfrak g$.Comment: 31 pages, 7 figure

Altruistic behavior as a costly signal of general intelligence.

Unconditional altruism is an enduring puzzle for evolutionary approaches to social behavior. In this paper we argue that costly signaling theory, a well-established framework in biology and economics, may be useful to shed light on the individual differences in human unconditional altruism. Based on costly signaling theory, we propose and show that unconditional altruistic behavior is related to general intelligence. The cost incurred by engaging in unconditional altruism is lower for highly intelligent people than for less intelligent people because they may expect to regain the drained resources. As a result, unconditional altruism can serve as an honest signal of intelligence. Our findings imply that distinguishing altruistic behavior from cooperative behavior in social psychological and economic theories of human behavior might be useful, and that costly signaling theory may provide novel insights on various individual difference variables.Altruistic; Behavior; Costly signaling; Economic theory; Individual differences; General intelligence;