Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) ofdifferent vertebrates using the Compositional Data Analysis (CDA) methodologicalapproach it’s presented.355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda,Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) wereanalyzed with CDA.A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinsondistance has been used as a measure of disparity in limb elements proportions to infersome aspects of functional morphology

Distributions on the simplex

The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties

Sobolev orthogonal polynomials on a simplex

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Towards closure between measured and modelled UV under clear skies at four diverse sites

The purpose of this work is determine the extent of closure between measurements and models of UV irradiances at diverse sites using state of the art instruments, models, and the best available data as inputs to the models. These include information about aerosol optical depth (unfortunately not extending down as far into the UVB region as desirable because such information is not generally available), ozone column amounts, as well as vertical profiles of temperature. We concentrate on clear-sky irradiances, and report the results in terms of UV Index (UVI)

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Lesiones por virus Herpes simplex y estomatitis aftosa recidivante. Estudio epidemiológico en una muestra elegida al azar

De entre las lesiones observadas en la cavidad bucal, las producidas por el virus Herpes simplex (VHS) y las originadas en la estomatitis aftosa recidivante (EAR) representan una parte importante de las lesiones que el odontólogo o estomatólogo encuentra cotidianamente. Aunque cada uno de estos dos procesos posee una etiopatogenia y unas características diferentes, en algunas ocasiones su diagnóstico puede llegar a ser controvertido y difícil, debido a su similar apariencia clínica, planteándose entonces problemas de diagnóstico diferencial. El objetivo de este trabajo es realizar un estudio epidemiológico sobre ambas entidades en un grupo de 100 personas elegidas al azar. Mediante un cuestionario anamnético se identifican los pacientes con historia positiva para cualquiera de los dos tipos de lesiones y se recogen datos respecto a las características clínicas de las lesiones en los pacientes de la muestra, con el fin de definir las características diferenciales entre ambas alteraciones.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Parametric analysis of different compact tension specimens for fracture toughness characterisation in woven composite materials

Estudi elaborat a partir d’una estada a l’ Imperial College London, entre juliol i novembre de 2006. En aquest treball s’ha investigat la geometria més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. L’objectiu és assegurar la propagació de l’esquerda sense que la proveta falli abans per cap altre mecanisme de dany per tal de permetre la caracterització experimental de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. Amb aquesta fi, s’ha dut a terme l’anàlisi paramètrica de diferents tipus de provetes mitjançant el mètode dels elements finits (FE) combinat amb la virtual crack closure technique (VCCT). Les geometries de les provetes analitzades corresponen a la proveta de l’assaig compact tension (CT) i diferents variacions com la extended compact tension (ECT), la proveta widened compact tension (WCT), tapered compact tension (TCT) i doubly-tapered compact tension (2TCT). Com a resultat d’aquestes anàlisis s’han derivat diferents conclusions per obtenir la geometria de proveta més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. A més, també s’han dut a terme una sèrie d’assaigs experimentals per tal de validar els resultats de les anàlisis paramètriques. La concordança trobada entre els resultats numèrics i experimentals és bona tot i la presència d’efectes no previstos durant els assaigs experimentals.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Analog Modelling of N-S anticlines of the External Sierras (Jaca basin, Southern Pyrenees)

Report for the scientific sojourn carried out at the Uppsala Universitet, Sweden, from April to July the 2007. Two series of analogue models are used to explore ductile-frictional contrasts of the basal décollement in the development of oblique and transverse structures simultaneously to thin-skinned shortening. These models simulate the evolution of the Central External Sierras (Southern Pyrenees, Spain), which constitute the frontal emerging part of the southernmost Pyrenean thrust sheet. They are characterized by the presence of transverse N-S to NW-SE anticlines, which are perpendicular to the Pyrenean structural trend and developed in the hangingwall of the Santo Domingo thrust system, detaching on an unevenly distributed Triassic materials (evaporitic-dolomitic interfingerings). Model setup performs a décollement made by three patches of silicone neighbouring pure brittle sand. Model series A test the thickness ratio between overburden and décollement. Model series B test the width of frictional detachment areas. Model results show how deformation reaches further in areas detached on ductile layer whereas frictional décollement areas assimilate the strain by means of an additional uplift. This replicates the structural style of Central External Sierras: higher structural relief of N-S anticlines with regard to orogen-parallel structures, absence of a representative ductile décollement in the core, tilting towards the orogen and foreland-side closure not thrusted by the frontal emerging South-Pyrenean thrust.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.