On estimating extremal dependence structures by parametric spectral measures

Estimation of extreme value copulas is often required in situations where available data are sparse. Parametric methods may then be the preferred approach. A possible way of defining parametric families that are simple and, at the same time, cover a large variety of multivariate extremal dependence structures is to build models based on spectral measures. This approach is considered here. Parametric families of spectral measures are defined as convex hulls of suitable basis elements, and parameters are estimated by projecting an initial nonparametric estimator on these finite-dimensional spaces. Asymptotic distributions are derived for the estimated parameters and the resulting estimates of the spectral measure and the extreme value copula. Finite sample properties are illustrated by a simulation study

Wilson loops and Riemann theta functions II

In this paper we extend and simplify previous results regarding the computation of Euclidean Wilson loops in the context of the AdS/CFT correspondence, or, equivalently, the problem of finding minimal area surfaces in hyperbolic space (Euclidean AdS3). If the Wilson loop is given by a boundary curve X(s) we define, using the integrable properties of the system, a family of curves X(lambda,s) depending on a complex parameter lambda known as the spectral parameter. This family has remarkable properties. As a function of lambda, X(lambda,s) has cuts and therefore is appropriately defined on a hyperelliptic Riemann surface, namely it determines the spectral curve of the problem. Moreover, X(lambda,s) has an essential singularity at the origin lambda=0. The coefficients of the expansion of X(lambda,s) around lambda=0, when appropriately integrated along the curve give the area of the corresponding minimal area surface. Furthermore we show that the same construction allows the computation of certain surfaces with one or more boundaries corresponding to Wilson loop correlators. We extend the area formula for that case and give some concrete examples. As the main example we consider a surface ending on two concentric circles and show how the boundary circles can be deformed by introducing extra cuts in the spectral curve.Comment: LaTeX, 45 pages, 10 figures. v2: typos corrected, references adde

Learning alters theta-nested gamma oscillations in inferotemporal cortex

How coupled brain rhythms influence cortical information processing to support learning is unresolved. Local field potential and neuronal activity recordings from 64- electrode arrays in sheep inferotemporal cortex showed that visual discrimination learning increased the amplitude of theta oscillations during stimulus presentation. Coupling between theta and gamma oscillations, the theta/gamma ratio and the regularity of theta phase were also increased, but not neuronal firing rates. A neural network model with fast and slow inhibitory interneurons was developed which generated theta nested gamma. By increasing N-methyl-D-aspartate receptor sensitivity similar learning-evoked changes could be produced. The model revealed that altered theta nested gamma could potentiate downstream neuron responses by temporal desynchronization of excitatory neuron output independent of changes in overall firing frequency. This learning-associated desynchronization was also exhibited by inferotemporal cortex neurons. Changes in theta nested gamma may therefore facilitate learning-associated potentiation by temporal modulation of neuronal firing

Dimers and the Critical Ising Model on Lattices of genus>1

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann Surfaces.Comment: 44 pages, eps figures included; typos corrected, figure and comments added to section

After-effects of 10 Hz tACS over the prefrontal cortex on phonological word decisions

Introduction Previous work in the language domain has shown that 10 Hz rTMS of the left or right posterior inferior frontal gyrus (pIFG) in the prefrontal cortex impaired phonological decision-making, arguing for a causal contribution of the bilateral pIFG to phonological processing. However, the neurophysiological correlates of these effects are unclear. The present study addressed the question whether neural activity in the prefrontal cortex could be modulated by 10 Hz tACS and how this would affect phonological decisions. Methods In three sessions, 24 healthy participants received tACS at 10 Hz or 16.18 Hz (control frequency) or sham stimulation over the bilateral prefrontal cortex before task processing. Resting state EEG was recorded before and after tACS. We also recorded EEG during task processing. Results Relative to sham stimulation, 10 Hz tACS significantly facilitated phonological response speed. This effect was task-specific as tACS did not affect a simple control task. Moreover, 10 Hz tACS significantly increased theta power during phonological decisions. The individual increase in theta power was positively correlated with the behavioral facilitation after 10 Hz tACS. Conclusion Our results show a facilitation of phonological decisions after 10 Hz tACS over the bilateral prefrontal cortex. This might indicate that 10 Hz tACS increased task-related activity in the stimulated area to a level that was optimal for phonological performance. The significant correlation with the individual increase in theta power suggests that the behavioral facilitation might be related to increased theta power during language processing

Theta-modulated place-by-direction cells in the hippocampal formation in the rat

We report the spatial and temporal properties of a class of cells termed theta-modulated place-by-direction (TPD) cells recorded from the presubicular and parasubicular cortices of the rat. The firing characteristics of TPD cells in open-field enclosures were compared with those of the following two other well characterized cell classes in the hippocampal formation: place and head-direction cells. Unlike place cells, which code only for the animal's location, or head-direction cells, which code only for the animal's directional heading, TPD cells code for both the location and the head direction of the animal. Their firing is also strongly theta modulated, firing primarily at the negative-to-positive phase of the locally recorded theta wave. TPD theta modulation is significantly stronger than that of place cells. In contrast, the firing of head-direction cells is not modulated by theta at all. In repeated exposures to the same environment, the locational and directional signals of TPD cells are stable. When recorded in different environments, TPD locational and directional fields can uncouple, with the locational field shifting unpredictably ("remapping"), whereas the directional preference remains similar across environments