Two-sided estimates for order statistics of log-concave random vectors

We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants in the unconditional case for all $k$ and in the isotropic case for $k \leq n-cn^{5/6}$. We also derive two-sided estimates for expectations of sums of $k$ largest moduli of coordinates for some classes of random vectors.Comment: 25 page

Fatigue analysis-based numerical design of stamping tools made of cast iron

This work concerns stress and fatigue analysis of stamping tools made of cast iron with an essentially pearlitic matrix and containing foundry defects. Our approach consists at first, in coupling the stamping numerical processing simulations and structure analysis in order to improve the tool stiffness geometry for minimizing the stress state and optimizing their fatigue lifetime. The method consists in simulating the stamping process by considering the tool as a perfect rigid body. The estimated contact pressure is then used as boundary condition for FEM structure loading analysis of the tool. The result of this analysis is compared with the critical stress limit depending on the automotive model. The acceptance of this test allows calculating the fatigue lifetime of the critical zone by using the S–N curve of corresponding load ratio. If the prescribed tool life requirements are not satisfied, then the critical region of the tool is redesigned and the whole simulation procedures are reactivated. This method is applied for a cast iron EN-GJS-600-3. The stress-failure (S–N) curves for this material is determined at room temperature under push pull loading with different load ratios R0σmin/σmax0−2, R0−1 and R00.1. The effects of the foundry defects are determined by SEM observations of crack initiation sites. Their presence in tested specimens is associated with a reduction of fatigue lifetime by a factor of 2. However, the effect of the load ratio is more important

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Putting fear in its place: remapping of hippocampal place cells during fear conditioning

We recorded hippocampal place cells in two spatial environments: a training environment in which rats underwent fear conditioning and a neutral control environment. Fear conditioning caused many place cells to alter ( or remap) their preferred firing locations in the training environment, whereas most cells remained stable in the control environment. This finding indicates that aversive reinforcement can induce place cell remapping even when the environment itself remains unchanged. Furthermore, contextual fear conditioning caused significantly more remapping of place cells than auditory fear conditioning, suggesting that place cell remapping was related to the rat's learned fear of the environment. These results suggest that one possible function of place cell remapping may be to generate new spatial representations of a single environment, which could help the animal to discriminate among different motivational contexts within that environment

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

Fluorescent oxide nanoparticles adapted to active tips for near-field optics

We present a new kind of fluorescent oxide nanoparticles with properties well suited to active-tip based near-field optics. These particles with an average diameter in the range 5-10 nm are produced by Low Energy Cluster Beam Deposition (LECBD) from a YAG:Ce3+ target. They are studied by transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), classical photoluminescence, cathodoluminescence and near-field scanning optical microscopy (NSOM). Particles of extreme photo-stability as small as 10 nm in size are observed. These emitters are validated as building blocks of active NSOM tips by coating a standard optical tip with a 10 nm thick layer of YAG:Ce3+ particles directly in the LECBD reactor and by subsequently performing NSOM imaging of test surfaces.Comment: Changes made following Referee's comments; added references; one added figure. See story on this article at: http://nanotechweb.org/cws/article/tech/3606

Cognitive appraisal of environmental stimuli induces emotion-like states in fish

The occurrence of emotions in non-human animals has been the focus of debate over the years. Recently, an interest in expanding this debate to non-tetrapod vertebrates and to invertebrates has emerged. Within vertebrates, the study of emotion in teleosts is particularly interesting since they represent a divergent evolutionary radiation from that of tetrapods, and thus they provide an insight into the evolution of the biological mechanisms of emotion. We report that Sea Bream exposed to stimuli that vary according to valence (positive, negative) and salience (predictable, unpredictable) exhibit different behavioural, physiological and neuromolecular states. Since according to the dimensional theory of emotion valence and salience define a two-dimensional affective space, our data can be interpreted as evidence for the occurrence of distinctive affective states in fish corresponding to each the four quadrants of the core affective space. Moreover, the fact that the same stimuli presented in a predictable vs. unpredictable way elicited different behavioural, physiological and neuromolecular states, suggests that stimulus appraisal by the individual, rather than an intrinsic characteristic of the stimulus, has triggered the observed responses. Therefore, our data supports the occurrence of emotion-like states in fish that are regulated by the individual's perception of environmental stimuli.European Commission [265957 Copewell]; Fundacao para a Ciencia e Tecnologia [SFRH/BD/80029/2011, SFRH/BPD/72952/2010]info:eu-repo/semantics/publishedVersio

Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index $n$, on the leading order gravitational waveforms is studied.Comment: 31 pages, 7 figures, typos correcte

Modelling the Autocovariance of the Power Spectrum of a Solar-Type Oscillator

Asteroseismology is able to conduct studies on the interiors of solar-type stars from the analysis of stellar acoustic spectra. However, such an analysis process often has to rely upon subjective choices made throughout. A recurring problem is to determine whether a signal in the acoustic spectrum originates from a radial or a dipolar oscillation mode. In order to overcome this problem, we present a procedure for modelling and fitting the autocovariance of the power spectrum which can be used to obtain global seismic parameters of solar-type stars, doing so in an automated fashion without the need to make subjective choices. From the set of retrievable global seismic parameters we emphasize the mean small frequency separation and, depending on the intrinsic characteristics of the power spectrum, the mean rotational frequency splitting. Since this procedure is automated, it can serve as a useful tool in the analysis of the more than one thousand solar-type stars expected to be observed as part of the Kepler Asteroseismic Investigation (KAI). We apply the aforementioned procedure to simulations of the Sun. Assuming different apparent magnitudes, we address the issues of how accurately and how precisely we can retrieve the several global seismic parameters were the Sun to be observed as part of the KAI.Comment: 10 pages, 8 figures, accepted for publication in MNRA