arXiv research

Unified framework recovers and improves classical Brouwer homeomorphism results.

Floer theory connects dynamics on surfaces to their chain-level theory.

The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.

Dans les années 1940-1970, Alexandrov et l'"École de Leningrad" ont développé une théorie très riche des surfaces singulières. Il s'agit de surfaces topologiques, munie d'une métrique intrinsèque pour laquelle on peut définir une notion de courbure, qui est une mesure de Radon. Cette classe de surfaces a de bonnes prop…

We inspect the BNSR-invariants $Σ^m(P_n)$ of the pure braid groups $P_n$, using Morse theory. The BNS-invariants $Σ^1(P_n)$ were previously computed by Koban, McCammond and Meier. We prove that for any $3\le m\le n$, the inclusion $Σ^{m-2}(P_n)\subseteq Σ^{m-3}(P_n)$ is proper, but $Σ^\infty(P_n)=Σ^{n-2}(P_n)$. We writ…

A new framework for robust transfer learning that avoids negative transfer in domains with unequal information.

New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.

The paper finds infinitely many half-volume CMC hypersurfaces on generic or Ricci-positive manifolds.

We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in order to specify the relationship between the two (possibly equal) main universal link invariants: the Kontsevich Integral and the perturbative expression of the Chern-Simons theory. As a corollary, we prove that the Altschuler and Freidel an…

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

We construct a family of morphisms between Artin-Tits groups which generalise the ones constructed by J. Crisp in [Injective maps between Artin groups, Proceedings of the Special Year in Geometric Group Theory, Berlin, (1999), 119 -- 138]. We show that their restrictions to the positive Artin monoids respect normal for…

The paper finds closed hypersurfaces with prescribed mean curvature in non-compact manifolds.

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $α$ lyi…

By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre $D^{2n}\sharp(S^n\times S^n)^{\sharp g}$, relative to the boundary, are for $2n\ge 6$ independent of $g$ in degrees $*\le (g-6)/2$. In this note, we explain how this range can be improved to $*…

The paper resolves compactness and non-compactness for fourth- and sixth-order Q-curvature problems.

We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte général des champs de cones fermés, on décrit l'ensemble des fonctions causales qui peuvent être approchées par des fo…

Proves non-existence of metrics with positive curvature for certain connected sums.

Defines half-volume spectrum for manifolds and proves Weyl law holds.

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…

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 …

Floer homotopy theory applies to Lagrangians, overcoming curvature issues.

We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl_2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U_q sl_2. As an application, we give a formula for the colored Jones polynomial of twist knots, g…

Nous considérons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-variété de dimension k. Les quasi-variétés généralisent les variétés et les V-variétés et représentent le cadre naturel pour la réduction symplectique par rapport à l'action i…

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric spac…

LES reduces over-exploration in LSO, improving solution quality.

Current study aims to provide new empirical evidence on the impact of debt on corporate profitability. This impact can be explained by three essential theories: signaling theory, tax theory and the agency cost theory. Using panel data sample of 2240 French non listed companies of service sector during 1999-2006. By uti…

New invariant prevents minimal submanifolds in curved spaces.

Sharp stability threshold found for deep residual architectures.

Bayesian posterior contraction rates improve with decreasing tails

We give an upper bound for the rank $r$ of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if $r=2^a\cdot b$ with $b$ odd, then $r\le 9$ for $a=0$, $r\le 10$ for $a=1$, $r\le 12$ for $a=2$ and $r\le 16$ for $a\ge 3$. Moreover, we describe t…

Homotopy equivalence found between Milnor-Lê fibers of specific singularities.

In this paper we study the problem of stopping a Brownian bridge $X$ in order to maximise the expected value of an exponential gain function. In particular, we solve the stopping problem $\sup_{0\le τ\le 1}\mathsf{E}[\mathrm{e}^{X_τ}]$ which was posed by Ernst and Shepp in their paper [Commun. Stoch. Anal., 9 (3), 20…

PCR-LE achieves optimal rates for nonparametric regression over Sobolev spaces.

For odd-dimensional spheres, there's always a second short geodesic.

After results by the author (1980, 1981), and by Vinberg (1981), finiteness of the number of maximal arithmetic reflection groups in Lobachevsky spaces was not known in dimensions $2\le n\le 9$ only. Recently (2005), the finiteness was proved in dimension 2 by Long, Maclachlan and Reid, and in dimension 3 by Agol. Here…

The theory of Vassiliev invariants deals with many modules of diagrams on which the algebra Lambda defined by Pierre Vogel acts. By specifying a quadratic simple Lie superalgebra, one obtains a character on Lambda. We show the coherence of these characters by building a map of graded algebras beetwen Lambda and a quoti…

We give an overview of the generalized Calderón-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\BMO$ functions. $L^p-L^q$ of…

Let $(M^n,g)$, $n \ge 4$, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there exists $\eps = \eps (l,L,n)$ satisfying the following: If the scalar curvature $s$ of $g$ satisfies $l \le s \le L$ and the Einstein tensor satisfies $$ | Ric - \fr…

CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k\le n-3. The smooth Yamabe invariants σ(M) and σ(N) satisfy σ(N)\ge min (σ(M),Λ) for Λ>0. We derive explicit lower bounds for Λin dimensions where previous methods failed, namely for (n,k)\in {(4,1),(5,1),…

Using elementary comparison geometry, we prove: Let $(M,g)$ be a simply-connected complete Riemannian manifold of dimension $\ge 3$. Suppose that the sectional curvature $K$ satisfies $-1-s(r) \le K \le -1$, where $r$ denotes distance to a fixed point in $M$. If $\lim_{r \rt \infty} e^{2r}s(r) =0$, then $(M,g)$ has to…

Study correlations of spectral lengths and displacements in higher rank groups.

Continuing the work started in Part I and II of this series (see q-alg/9706004 and math.QA/9801049), we prove the relationship between the Aarhus integral and the invariant $Ω$ (henceforth called LMO) defined by T.Q.T. Le, J. Murakami and T. Ohtsuki in q-alg/9512002. The basic reason for the relationship is that both c…

Improved upper bound for discrete isometric filling of cycles.

This is a translation of Yves Benoist's "Actions propres sur les espaces homogènes réductifs", Ann. of Math., 144:315-347, 1996.

Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\partial M$, admitting a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality in the Eu…

Study compares survival analysis algorithms with missing data methods.

In this article we study the second variation of the energy functional associated to the Allen-Cahn equation on closed manifolds. Extending well known analogies between the gradient theory of phase transitions and the theory of minimal hypersurfaces, we prove the upper semicontinuity of the eigenvalues of the stability…