On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Characterization of myocardial deformation in patients with different etiologies of left ventricular hypertrophy by using strain distribution from Magnetic Resonance Imaging

Introducción y objetivos. Se ha señalado que, en la miocardiopatía hipertrófica (MCH), la desorganización de las fibras regionales da lugar a segmentos en los que la deformación es nula o está gravemente reducida, y que estos segmentos tienen una distribución no uniforme en el ventrículo izquierdo (VI). Esto contrasta con lo observado en otros tipos de hipertrofia como en el corazón de atleta o la hipertrofia ventricular izquierda hipertensiva (HVI-HT), en los que puede haber una deformación cardiaca anormal, pero nunca tan reducida como para que se observe ausencia de deformación. Así pues, proponemos el empleo de la distribución de los valores de strain para estudiar la deformación en la MCH. Métodos. Con el empleo de resonancia magnética marcada (tagged), reconstruimos la deformación sistólica del VI de 12 sujetos de control, 10 atletas, 12 pacientes con MCH y 10 pacientes con HVI-HT. La deformación se cuantificó con un algoritmo de registro no rígido y determinando los valores de strain sistólico máximo radial y circunferencial en 16 segmentos del VI. Resultados. Los pacientes con MCH presentaron unos valores medios de strain significativamente inferiores a los de los demás grupos. Sin embargo, aunque la deformación observada en los individuos sanos y en los pacientes con HVI-HT se concentraba alrededor del valor medio, en la MCH coexistían segmentos con contracción normal y segmentos con una deformación nula o significativamente reducida, con lo que se producía una mayor heterogeneidad de los valores de strain. Se observaron también algunos segmentos sin deformación incluso en ausencia de fibrosis o hipertrofia. Conclusiones. La distribución de strain caracteriza los patrones específicos de deformación miocárdica en pacientes con diferentes etiologías de la HVI. Los pacientes con MCH presentaron un valor medio de strain significativamente inferior, así como una mayor heterogeneidad de strain (en comparación con los controles, los atletas y los pacientes con HVI-HT), y tenían regiones sin deformación.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Are one factor logarithmic volatility models useful to fit the features of financial data? An application to microsoft data.

This paper provides empirical evidence that continuous time models with one factor of volatility, in some conditions, are able to fit the main characteristics of financial data. It also reports the importance of the feedback factor in capturing the strong volatility clustering of data, caused by a possible change in the pattern of volatility in the last part of the sample. We use the Efficient Method of Moments (EMM) by Gallant and Tauchen (1996) to estimate logarithmic models with one and two stochastic volatility factors (with and without feedback) and to select among them.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Polynomial and linearized normal forms for almost periodic differential systems

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Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Terrestrial laser scanning for landslides deformation monitoring

Within last few years a new type of instruments called Terrestrial Laser Scanners (TLS) entered to the commercial market. These devices brought a possibility to obtain completely new type of spatial, three dimensional data describing the object of interest. TLS instruments are generating a type of data that needs a special treatment. Appearance of this technique made possible to monitor deformations of very large objects, like investigated here landslides, with new quality level. This change is visible especially with relation to the size and number of the details that can be observed with this new method. Taking into account this context presented here work is oriented on recognition and characterization of raw data received from the TLS instruments as well as processing phases, tools and techniques to do them. Main objective are definition and recognition of the problems related with usage of the TLS data, characterization of the quality single point generated by TLS, description and investigation of the TLS processing approach for landslides deformation measurements allowing to obtain 3D deformation characteristic and finally validation of the obtained results. The above objectives are based on the bibliography studies and research work followed by several experiments that will prove the conclusions.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

On continuity of the Álvarez class under deformation

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Interferència dels trastorns de personalitat en la capacitat parental. Comparació entre població normal i diagnosticada

En aquesta investigació, hem comparat tres mostres (amb diagnòstic de transtorn de la personalitat, amb trets disfuncionals de la personalitat i sans) per tal de valorar quina disposa d’un funcionament parental més acurat. Dels resultats obtinguts, malgrat el petit tamany de la mostra, podem afirmar que els progenitors sans obtenen millors resultats que els altres dos, i que els que disposen de trets disfuncionals tenen un funcionament més adequats que els que tenen un diagnòstic.