arXiv research

Let $M$ be either $S^2\times S^2$ or the one point blow-up $\cp# \bcp$ of $\cp$. In both cases $M$ carries a family of symplectic forms $\om_\la$, where $\la > -1$ determines the cohomology class $[\om_\la]$. This paper calculates the rational (co)homology of the group $G_\la$ of symplectomorphisms of $(M,\om_\la)$ as …

Nous donnons une méthode naturelle, que nous appelons {\it "la méthode des façons"} pour stratifier la variété asymptotique associée à une application polynomiale dominante $F: \mathbb{C}^n \to \mathbb{C}^n$. La stratification obtenue est différentiable et satisfait la propriété de frontière.

LA-Courant algebroids link double Lie bialgebroids via Manin triples.

Identifies LA-groups via VB-group structure and complementary actions.

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain as particular cases the Lagrange, Finsler and, for trivial nonlinear connections,…

Defines basic sections of LA-groupoids for simpler modeling.

This paper presents practical methods for portfolio selection in investments.

Let (ρ_\la)_{\la\in \La} be a holomorphic family of representations of a surface group π_1(S) into PSL(2,C), where S is a topological (possibly punctured) surface with negative Euler characteristic. Given a structure of Riemann surface of finite type on S we construct a bifurcation current on the parameter space \La, t…

Simplified definition of LA-Courant algebroids and Poisson Lie 2-algebroids.

We show that some curvature operators are locally invertible, in some weithted sobolev spaces, near the euclidian metric. (Nous montrons que certains opérateurs affines en la courbure de Ricci sont localement inversibles, dans des espaces de Sobolev à poids, au voisinage de la métrique euclidienne.)

Defines Learning Analytics' foundational structure and scope.

LA-VDM accelerates VDM using landmarks to improve data analysis.

Laplace approximation improves deep learning efficiency without sacrificing performance.

This paper deals with naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups $(N, \la \,,\,\ra_N)$, such that $\la \,,\,\ra_N$ is invariant under a left action. The case of nondegenerate center is completely characterized. In fact, whenever $\la \,,\, \ra_N$ restricts to a metric in the center it is proved h…

We categorify the coefficients of the Burau representation matrix using elementary geometrical methods. We show the faithfulness of this categorification in the sense that it detects the trivial braid.

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties of sequences of equivalent probability measures induced by $\la_n$--consistent p…

Paper predicts interference for better LA in URLLC.

La-MAML improves fast online continual learning with a look-ahead approach.

We give a complete proof of the fact that the trace of the curvature of the connection associated to a planar d-web (d>3) is the sum of the Blaschke curvatures of its sub 3-webs.

Given a closed subset $\La$ of the open unit ball $B_1\subset \real^n$, $n \geq 3$, we will consider a complete Riemannian metric $g$ on $\bar{B_1} \setminus \La$ of constant scalar curvature equal to $n(n-1)$ and conformally related to the Euclidean metric. In this paper we prove that every closed Euclidean ball $\bar…

In this note a functorial approach to the integration problem of an LA-groupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibred products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns …

We study Bott-Chern and Aeppli cohomologies of a vector space endowed with two anti-commuting endomorphisms whose square is zero. In particular, we prove an inequality à la Frölicher relating the dimensions of the Bott-Chern and Aeppli cohomologies to the dimensions of the Dolbeault cohomologies. We prove that the equa…

VSML unifies meta learning concepts and enables simple backpropagation.

We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, have the standard metric $g\_0$ for critic point, althoug…

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then th…

This text explains how fiber bundle structure is fundamental for classical physics.

We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum…

We prove that the metric completion of a canonical Ricci-flat Kahler metric on the nonsingular part of a projective Calabi-Yau variety $X$ with ordinary double point singularities, is a compact metric length space homeomorphic to the projective variety $X$ itself. As an application, we prove a conjecture of Candelas an…

LA-MCTS learns search space partition for black-box optimization using Monte Carlo Tree Search.

We define a nonnegative integer $\la(L,L_0;φ)$ for a pair of diffeomorphic closed Lagrangian surfaces $L_0,L$ embedded in a symplectic 4-manifold $(M,\w)$ and a diffeomorphism $φ\in\Diff^+(M)$ satisfying $φ(L_0)=L$. We prove that if there exists $φ\in\Diff^+_o(M)$ with $φ(L_0)=L$ and $\la(L,L_0;φ)=0$, then $L_0,L$ are …

Anatomical and biophysical modeling of left atrium (LA) and proximal pulmonary veins (PPVs) is important for clinical management of several cardiac diseases. Magnetic resonance imaging (MRI) allows qualitative assessment of LA and PPVs through visualization. However, there is a strong need for an advanced image segment…

An equivariant bundle gerbe à la Meinrenken over a $G$-manifold $M$ is known to be a special type of $S^1$-gerbe over the differentiable stack $[M/G]$. We prove that the natural morphism relating the Cartan and simplicial models of equivariant cohomology in degree 3 maps the Dixmier-Douady class of an equivariant bundl…

Study improves sugarcane plot prediction using data interpolation.

This paper shows the equivalence of the categories of $N$-manifolds of degree $2$ with the category of double vector bundles endowed with a linear metric. Split Poisson $N$-manifolds of degree $2$ are shown to be equivalent to self-dual representations up to homotopy. As a consequence, the equivalence above induces an …

En nous basant sur les résultats d'Arthur annoncés dans \cite[§30]{Arthur} nous démontrons les conjectures énoncées dans \cite{IMRN,BC,SMF} dans le cas des groupes orthogonaux à l'exclusion des groupes de type ${}^6 - D_4$. En ce qui concerne ces derniers, nous annonçons la démonstration -- encore en préparation - que …

Having a sequence-to-sequence model which can operate in an online fashion is important for streaming applications such as Voice Search. Neural transducer is a streaming sequence-to-sequence model, but has shown a significant degradation in performance compared to non-streaming models such as Listen, Attend and Spell (…

The study investigates linearizability of Poisson structures on groupoids.

On a fixed Riemann surface $(M_0,g_0)$ with $N$ Euclidean ends and genus $g$, we show that, under a topological condition, the scattering matrix $S_V(\la)$ at frequency $\la > 0$ for the operator $Δ+V$ determines the potential $V$ if $V\in C^{1,α}(M_0)\cap e^{-γd(\cdot,z_0)^j}L^\infty(M_0)$ for all $γ>0$ and for some $…

We present Listen, Attend and Spell (LAS), a neural network that learns to transcribe speech utterances to characters. Unlike traditional DNN-HMM models, this model learns all the components of a speech recognizer jointly. Our system has two components: a listener and a speller. The listener is a pyramidal recurrent ne…

Study compares survival analysis algorithms with missing data methods.

In this thesis we develop the notion of LA-Courant algebroids, the infinitesimal analogue of multiplicative Courant algebroids. Specific applications include the integration of q- Poisson (d, g)-structures, and the reduction of Courant algebroids. We also introduce the notion of pseudo-Dirac structures, (possibly non-L…

On décrit ici des relations entre la géométrie globale des variétés de contact closes et celle de certaines variétés symplectiques, à savoir les variétés de Stein compactes. L'origine de ces relations est l'existence de livres ouverts adaptés aux structures de contact. We discuss relations between the global geometry o…

The objective of this article is to analyze the impact of capital structure on profitability. This impact can be explained by three essential theories: signaling theory, tax theory and the agency costs theory. A sample of 1846 French industrial firms are taken over the period 1999-2006, as a dynamic panel study by usin…

We analyze 27 house price indexes of Las Vegas from Jun. 1983 to Mar. 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real-estate bubble, defined as a price acceleration faster than exponential, which is found however to be confined to a rather limited time interval in the recen…

The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA),…

Token-adaptive FFN design improves LLM expressivity.

Equivalent bicategories constructed from action Lie groupoids.

If $(M,g)$ is a compact Riemannian surface then the integrals of $L^2(M)$-normalized eigenfunctions $e_j$ over geodesic segments of fixed length are uniformly bounded. Also, if $(M,g)$ has negative curvature and $γ(t)$ is a geodesic parameterized by arc length, the measures $e_j(γ(t))\, dt$ on $\R$ tend to zero in the …