Face processing limitation to own species in primates: a comparative study in brown capuchins, Tonkean macaques and humans

Most primates live in social groups which survival and stability depend on individuals' abilities to create strong social relationships with other group members. The existence of those groups requires to identify individuals and to assign to each of them a social status. Individual recognition can be achieved through vocalizations but also through faces. In humans, an efficient system for the processing of own species faces exists. This specialization is achieved through experience with faces of conspecifics during development and leads to the loss of ability to process faces from other primate species. We hypothesize that a similar mechanism exists in social primates. We investigated face processing in one Old World species (genus Macaca) and in one New World species (genus Cebus). Our results show the same advantage for own species face recognition for all tested subjects. This work suggests in all species tested the existence of a common trait inherited from the primate ancestor: an efficient system to identify individual faces of own species only

Empirical Processes of Multidimensional Systems with Multiple Mixing Properties

We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can prove the empirical process CLT for ergodic torus automorphisms. Our results also apply to Markov chains and dynamical systems having a spectral gap on some Banach space of functions. Our proof uses a multivariate extension of the techniques introduced by Dehling, Durieu and Voln\'y \cite{DehDurVol09} in the univariate case. As an important technical ingredient, we prove a $(2p)$th moment bound for partial sums in multiple mixing systems.Comment: to be published in Stochastic Processes and their Application

Harmonic spinors and local deformations of the metric

Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.Comment: minor changes, to appear in Mathematical Research Letter

On higher dimensional black holes with abelian isometry group

We consider (n+1)--dimensional, stationary, asymptotically flat, or Kaluza-Klein asymptotically flat black holes, with an abelian $s$--dimensional subgroup of the isometry group satisfying an orthogonal integrability condition. Under suitable regularity conditions we prove that the area of the group orbits is positive on the domain of outer communications, vanishing only on its boundary and on the "symmetry axis". We further show that the orbits of the connected component of the isometry group are timelike throughout the domain of outer communications. Those results provide a starting point for the classification of such black holes. Finally, we show non-existence of zeros of static Killing vectors on degenerate Killing horizons, as needed for the generalisation of the static no-hair theorem to higher dimensions

Spontaneous electromagnetic superconductivity and superfluidity of QCDxQED vacuum in strong magnetic field

It was recently shown that the vacuum in the background of a strong enough magnetic field may become an electromagnetic superconductor due to interplay between strong and electromagnetic forces. The superconducting ground state of the QCDxQED sector of the vacuum is associated with magnetic-field-assisted emergence of quark-antiquark condensates which carry quantum numbers of charged rho mesons (i.e., of electrically charged vector particles made of lightest, u and d, quarks and antiquarks). Here we demonstrate that this exotic electromagnetic superconductivity of vacuum is also accompanied by even more exotic superfluidity of the neutral rho mesons. The superfluid component -- despite being electrically neutral -- turns out to be sensitive to an external electric field as the superfluid may ballistically be accelerated by a test background electric field along the magnetic-field axis. In the ground state both superconducting and superfluid components are inhomogeneous periodic functions of the transversal (with respect to the axis of the magnetic field) spatial coordinates. The superconducting part of the ground state resembles an Abrikosov ground state in a type-II superconductor: the superconducting condensate organizes itself in periodic structure which possesses the symmetry of an equilateral triangular lattice. Each elementary lattice cell contains a stringlike topological defect (superconductor vortex) in the charged rho condensates as well as three superfluid vortices and three superfluid antivortices made of the neutral rho condensate. The superposition of the superconductor and superfluid vortex lattices has a complicated "kaleidoscopic" pattern.Comment: 6 pages, 2 figures. Talk given at Sixth International Conference on Quarks and Nuclear Physics QNP2012, April 16-20, 2012, Ecole Polytechnique, Palaiseau, Franc

Collisions of Shock Waves in General Relativity

We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous, plane gravitational shock waves each initially traveling in a vacuum containing no cosmological constant. A shock wave in this context has a step function profile in contrast to an impulsive wave which has a delta function profile. Following the collision two light-like signals, each composed of a plane, homogeneous light-like shell of matter and a plane, homogeneous impulsive gravitational wave, travel away from each other and a cosmological constant is generated in the interaction region. Furthermore a plane, light-like signal consisting of an electromagnetic shock wave accompanying a gravitational shock wave is described with the help of two real parameters, one for each wave. The head-on collision of two such light-like signals is examined and we show that if a simple algebraic relation is satisfied between the two pairs of parameters associated with each incoming light-like signal then the space-time in the interaction region following the collision is a Bertotti space-time which is a homogeneous solution of the vacuum Einstein-Maxwell field equations with a cosmological constant.Comment: Latex file, 10 page

Eigenvalues estimate for the Neumann problem on bounded domains

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As application, we get upper bounds for the Neumann spectrum which is clearly in agreement with the Weyl law and which is analogous to Buser's upper bounds of the spectrum of a closed Riemannian manifold with lower bound on the Ricci curvature.Comment: 9 pages, submitted december 200

Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold

For any bounded regular domain $\Omega$ of a real analytic Riemannian manifold $M$, we denote by $\lambda_{k}(\Omega)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $\Omega$. In this paper, we consider $\lambda_k$ and as a functional upon the set of domains of fixed volume in $M$. We introduce and investigate a natural notion of critical domain for this functional. In particular, we obtain necessary and sufficient conditions for a domain to be critical, locally minimizing or locally maximizing for $\lambda_k$. These results rely on Hadamard type variational formulae that we establish in this general setting.Comment: To appear in Illinois J. Mat

Einstein-Maxwell-Dilaton theories with a Liouville potential

We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces of dimension d-2 with constant curvature and analyse in detail the field equations and manifest their symmetries. The field equations of the full system are shown to reduce to a single or couple of ODE's which can be used to solve analytically or numerically the theory for the symmetry at hand. Further solutions can also be generated by a solution generating technique akin to the EM duality in the absence of a cosmological constant. We then find and analyse explicit solutions including black holes and gravitating solitons for the case of four dimensional relativity and the higher-dimensional oxydised 5-dimensional spacetime. The general solution is obtained for a certain relation between couplings in the case of cylindrical symmetry.Comment: v3, Some typos corrected with respect to the published versio

Quantum metric fluctuations and Hawking radiation

In this Letter we study the gravitational interactions between outgoing configurations giving rise to Hawking radiation and in-falling configurations. When the latter are in their ground state, the near horizon interactions lead to collective effects which express themselves as metric fluctuations and which induce dissipation, as in Brownian motion. This dissipation prevents the appearance of trans-Planckian frequencies and leads to a description of Hawking radiation which is very similar to that obtained from sound propagation in condensed matter models.Comment: 4 pages, revte