Human Primary Auditory Cortex Follows the Shape of Heschl's Gyrus.

The primary auditory cortex (PAC) is central to human auditory abilities, yet its location in the brain remains unclear. We measured the two largest tonotopic subfields of PAC (hA1 and hR) using high-resolution functional MRI at 7 T relative to the underlying anatomy of Heschl's gyrus (HG) in 10 individual human subjects. The data reveals a clear anatomical-functional relationship that, for the first time, indicates the location of PAC across the range of common morphological variants of HG (single gyri, partial duplications, and complete duplications). In 20/20 individual hemispheres, two primary mirror-symmetric tonotopic maps were clearly observed with gradients perpendicular to HG. PAC spanned both divisions of HG in cases of partial and complete duplications (11/20 hemispheres), not only the anterior division as commonly assumed. Specifically, the central union of the two primary maps (the hA1-R border) was consistently centered on the full Heschl's structure: on the gyral crown of single HGs and within the sulcal divide of duplicated HGs. The anatomical-functional variants of PAC appear to be part of a continuum, rather than distinct subtypes. These findings significantly revise HG as a marker for human PAC and suggest that tonotopic maps may have shaped HG during human evolution. Tonotopic mappings were based on only 16 min of fMRI data acquisition, so these methods can be used as an initial mapping step in future experiments designed to probe the function of specific auditory fields.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

Parallel spinors on pseudo-riemannian spin(q) manifolds

We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors.

Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Collective victimisation and collective guilt in the former Yugoslavia : the interplay between individual, local and societal levels

The thesis examines the impact of collective war victimization on individuals' readiness to accept or assign collective guilt for past war atrocities. As a complement to previous studies, its aim is to articulate an integrated approach to collective victimization, which distinguishes between individual-, communal-, and societal-level consequences of warfare. Building on a social representation approach, it is guided by the assumption that individuals form beliefs about a conflict through their personal experiences of victimization, communal experiences of warfare that occur in their proximal surrounding, and the mass- mediatised narratives that circulate in a society's public sphere. Four empirical studies test the hypothesis that individuals' beliefs about the conflict depend on the level and type of war experiences to which they have been exposed, that is, on informative and normative micro and macro contexts in which they are embedded. The studies have been conducted in the context of the Yugoslav wars that attended the breakup of Yugoslavia, a series of wars fought between 1991 and 2001 during which numerous war atrocities were perpetrated causing a massive victimisation of population. To examine the content and impact of war experiences at each level of analysis, the empirical studies employed various methodological strategies, from quantitative analyses of a representative public opinion survey, to qualitative analyses of media content and political speeches. Study 1 examines the impact of individual- and communal- level war experiences on individuals' acceptance and assignment of collective guilt. It further examines the impact of the type of communal level victimization: exposure to symmetric (i.e., violence that similarly affects members of different ethnic groups, including adversaries) and asymmetric violence. The main goal of Study 2 is to examine the structural and political circumstances that enhance collective guilt assignment. While the previous studies emphasize the role of past victimisation, Study 2 tests the assumption that the political demobilisation strategy employed by elites facing public discontent in the collective system-threatening circumstances can fuel out-group blame. Studies 3 and 4 have been conducted predominantly in the context of Croatia and examine rhetoric construction of the dominant politicized narrative of war in a public sphere (Study 3) and its maintenance through public delegitimization of alternative (critical) representations (Study 4). Study 4 further examines the likelihood that highly identified group members adhere to publicly delegitimized critical stances on war. - Cette thèse étudie l'impact de la victimisation collective de guerre sur la capacité des individus à accepter ou à attribuer une culpabilité collective liée à des atrocités commises en temps de guerre. En compléments aux recherches existantes, le but de ce travail est de définir une approche intégrative de la victimisation collective, qui distingue les conséquences de la guerre aux niveaux individuel, régional et sociétal. En partant de l'approche des représentations sociales, cette thèse repose sur le postulat que les individus forment des croyances sur un conflit au travers de leurs expériences personnelles de victimisation, de leurs expériences de guerre lorsque celle-ci se déroule près d'eux, ainsi qu'au travers des récits relayés par les mass media. Quatre études testent l'hypothèse que les croyances des individus dépendent des niveaux et des types d'expériences de guerre auxquels ils ont été exposés, c'est-à-dire, des contextes informatifs et normatifs, micro et macro dans lesquels ils sont insérés. Ces études ont été réalisées dans le contexte des guerres qui, entre 1991 et 2001, ont suivi la dissolution de la Yougoslavie et durant lesquelles de nombreuses atrocités de guerre ont été commises, causant une victimisation massive de la population. Afin d'étudier le contenu et l'impact des expériences de guerre sur chaque niveau d'analyse, différentes stratégies méthodologiques ont été utilisées, des analyses quantitatives sur une enquête représentative d'opinion publique aux analyses qualitatives de contenu de médias et de discours politiques. L'étude 1 étudie l'impact des expériences de guerre individuelles et régionales sur l'acceptation et l'attribution de la culpabilité collective par les individus. Elle examine aussi l'impact du type de victimisation régionale : exposition à la violence symétrique (i.e., violence qui touche les membres de différents groupes ethniques, y compris les adversaires) et asymétrique. L'étude 2 se penche sur les circonstances structurelles et politiques qui augmentent l'attribution de culpabilité collective. Alors que les recherches précédentes ont mis l'accent sur le rôle de la victimisation passée, l'étude 2 teste l'hypothèse que la stratégie de démobilisation politique utilisée par les élites pour faire face à l'insatisfaction publique peut encourager l'attribution de la culpabilité à l'exogroupe. Les études 3 et 4 étudient, principalement dans le contexte croate, la construction rhétorique du récit de guerre politisé dominant (étude 3) et son entretien à travers la délégitimation publique des représentations alternatives (critiques] (étude 4). L'étude 4 examine aussi la probabilité qu'ont les membres de groupe fortement identifiés d'adhérer à des points de vue sur la guerre critiques et publiquement délégitimés.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Civil war and foreign influence

We study a symmetric information bargaining model of civil war where a third (foreign) party can affect the probabilities of winning the conflict and the size of the post conflict spoils. We show that the possible alliance with a third party makes peaceful agreements difficult to reach and might lead to new commitment problems that trigger war. Also, we argue that the foreign party is likely to induce persistent informational asymmetries which might explain long lasting civil wars. We explore both political and economic incentives for a third party to intervene. The explicit consideration of political incentives leads to two predictions that allow for identifying the influence of foreign intervention on civil war incidence. Both predictions are confirmed for the case of the U.S. as a potential intervening nation: (i) civil wars around the world are more likely under Republican governments and (ii) the probability of civil wars decreases with U.S. presidential approval rates.

Tight open knots.

The tightest open conformations of a few prime knots (3(1), 4(1), 5(1), 5(2), and 6(3)) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 3(1) and 4(1) open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

Anàlisi i disseny d'un reflector per banda W

Les ones passives mil·limètriques (30 a 300GHz) tenen la peculiaritat de propagar-se en medis com la boira o la roba, a diferència del rang visible o l’infraroig. D’aquesta peculiaritat, surt l’interès de reproduir imatges per diverses aplicacions (seguretat, vigilància, etc...). És per aquest motiu que es treballa en el disseny d’un reflector per aquest tipus d’aplicació, treballant a una de les finestres de propagació d’aquest rang, la de la banda W. Es dissenyen i analitzen tres tipus de reflector: parabòlic simètric, offset i Cassegrain. D’aquests, s’estudien les seves figures de mèrit i directivitats buscant que aquestes siguin el més elevades possibles per obtenir una bona resolució, així com l’escaneig de l’escena de la qual es vol obtenir una imatge, veient aquí els efectes de les aberracions més comunes.

Candidate quality in a Downsian Model with a continuous policy space

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution over the unit interval. In our equilibrium the advantaged candidate chooses the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. We show that this equilibrium exists if the number of voters is large enough relative to the size of the advantage.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Political Competition in Hard Times

This paper analyzes a spatial model of political competition between two policy- motivated parties in hard times of crisis. Hard times are modeled in terms of policy- making costs carried by a newly elected party. The results predict policy divergence in equilibrium. If the ideological preferences of parties are quite diverse and extreme, there is a unique equilibrium in which the parties announce symmetric platforms and each party wins with probability one half. If one party is extreme while the other is more moderate, there is a unique equilibrium in which the parties announce asymmetric platforms. If the preferred policies of the parties are not very distinct, there are two equilibria with asymmetric platforms. An important property of equilibrium with asymmetric platforms is that a winning party necessarily announces its most preferred policy as a platform. JEL classification: D72. Keywords: Spatial model; Political competition; Two-party system; Policy-motivated parties; Hard times; Crisis.

Differences in whole-body fat oxidation kinetics between cycling and running.

This study aimed to quantitatively describe and compare whole-body fat oxidation kinetics in cycling and running using a sinusoidal mathematical model (SIN). Thirteen moderately trained individuals (7 men and 6 women) performed two graded exercise tests, with 3-min stages and 1 km h(-1) (or 20 W) increment, on a treadmill and on a cycle ergometer. Fat oxidation rates were determined using indirect calorimetry and plotted as a function of exercise intensity. The SIN model, which includes three independent variables (dilatation, symmetry and translation) that account for main quantitative characteristics of kinetics, provided a mathematical description of fat oxidation kinetics and allowed for determination of the intensity (Fat(max)) that elicits maximal fat oxidation (MFO). While the mean fat oxidation kinetics in cycling formed a symmetric parabolic curve, the mean kinetics during running was characterized by a greater dilatation (i.e., widening of the curve, P < 0.001) and a rightward asymmetry (i.e., shift of the peak of the curve to higher intensities, P = 0.01). Fat(max) was significantly higher in running compared with cycling (P < 0.001), whereas MFO was not significantly different between modes of exercise (P = 0.36). This study showed that the whole-body fat oxidation kinetics during running was characterized by a greater dilatation and a rightward asymmetry compared with cycling. The greater dilatation may be mainly related to the larger muscle mass involved in running while the rightward asymmetry may be induced by the specific type of muscle contraction.