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

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

Estudi comparatiu de detecció de Virus del Papiloma Humà entre pell psoriàsica i pell normal.

Existeix un debat continu sobre la rellevància del Virus del papiloma humà (VPH) en l’etiopatogènia de la psoriasi. S’ha reportat un elevat percentatge de detecció de VPH en pacients psoriàsics, sobretot el VPH5 i 36, suggerint que podrien correspondre a l’antigen causal de la cascada inmunològica. El propòsit de l’estudi és utilitzar un mètode ampli per a la detecció d’ADN tant de beta com gamma-papilomavirus en 30 biòpsies de pell psoriàsica i 30 biòpsies de pell sana. Avaluarem si els VPH són detectats de forma més freqüent en pell psoriàsica en comparació amb pell sana, i quins són els VPH específics més sobreexpresats.

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent yearsbut at the moment few applications concern the description of natural phenomena withthis type of probability models, as well as the interpretation of their parameters. Theskew–normal distributions family represents an extension of the normal family to whicha parameter (λ) has been added to regulate the skewness. The development of this theoreticalfield has followed the general tendency in Statistics towards more flexible methodsto represent features of the data, as adequately as possible, and to reduce unrealisticassumptions as the normality that underlies most methods of univariate and multivariateanalysis. In this paper an investigation on the shape of the frequency distribution of thelogratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells,has been performed. Samples have been collected around the active center of Vulcanoisland (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals ofabout six months. Data of the logratio have been tentatively modeled by evaluating theperformance of the skew–normal model for each well. Values of the λ parameter havebeen compared by considering temperature and spatial position of the sampling points.Preliminary results indicate that changes in λ values can be related to the nature ofenvironmental processes affecting the data

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Algorithmic aspects of bio-inspired string operations

We present building blocks for algorithms for the efficient reduction of square factor, i.e. direct repetitions in strings. So the basic problem is this: given a string, compute all strings that can be obtained by reducing factors of the form zz to z. Two types of algorithms are treated: an offline algorithm is one that can compute a data structure on the given string in advance before the actual search for the square begins; in contrast, online algorithms receive all input only at the time when a request is made. For offline algorithms we treat the following problem: Let u and w be two strings such that w is obtained from u by reducing a square factor zz to only z. If we further are given the suffix table of u, how can we derive the suffix table for w without computing it from scratch? As the suffix table plays a key role in online algorithms for the detection of squares in a string, this derivation can make the iterated reduction of squares more efficient. On the other hand, we also show how a suffix array, used for the offline detection of squares, can be adapted to the new string resulting from the deletion of a square. Because the deletion is a very local change, this adaption is more eficient than the computation of the new suffix array from scratch.

Impaired fast-spiking, suppressed cortical inhibition and increased susceptibility to seizures in mice lacking Kv3.2 K+ channel proteins

Voltage-gated K+ channels of the Kv3 subfamily have unusual electrophysiological properties, including activation at very depolarized voltages (positive to −10 mV) and very fast deactivation rates, suggesting special roles in neuronal excitability. In the brain, Kv3 channels are prominently expressed in select neuronal populations, which include fast-spiking (FS) GABAergic interneurons of the neocortex, hippocampus, and caudate, as well as other high-frequency firing neurons. Although evidence points to a key role in high-frequency firing, a definitive understanding of the function of these channels has been hampered by a lack of selective pharmacological tools. We therefore generated mouse lines in which one of the Kv3 genes, Kv3.2, was disrupted by gene-targeting methods. Whole-cell electrophysiological recording showed that the ability to fire spikes at high frequencies was impaired in immunocytochemically identified FS interneurons of deep cortical layers (5-6) in which Kv3.2 proteins are normally prominent. No such impairment was found for FS neurons of superficial layers (2-4) in which Kv3.2 proteins are normally only weakly expressed. These data directly support the hypothesis that Kv3 channels are necessary for high-frequency firing. Moreover, we found that Kv3.2 −/− mice showed specific alterations in their cortical EEG patterns and an increased susceptibility to epileptic seizures consistent with an impairment of cortical inhibitory mechanisms. This implies that, rather than producing hyperexcitability of the inhibitory interneurons, Kv3.2 channel elimination suppresses their activity. These data suggest that normal cortical operations depend on the ability of inhibitory interneurons to generate high-frequency firing.

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

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.

Stochastic evolution of rules for playing normal form games

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments ofstochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal formgames that arise. It is shown that many of the folk results of evolutionary game theory typically obtained witha fixed game and fixed strategies carry over to the present case. The results are also related to recent experimentson rules and games.

Beta cell mass and growth after syngeneic islet cell transplantation in normal and streptozocin diabetic C57BL/6 mice

In islet transplantation, nonimmunological factors such as limited growth capacity or increased death rate could reduce the beta cell mass in the graft and lead to failure of the transplant. We studied the evolution of beta cell replication and mass after transplantation of insufficient, minimally sufficient, or excessive islet tissue. Streptozocin diabetic C57BL/6 mice received 150 or 300 syngeneic islets under the kidney capsule and normal mice received 300 islets. In streptozocin diabetic mice 300 islets restored normoglycemia; beta cell replication in transplanted islets was similar to replication in normal pancreas and beta cell mass in the graft remained constant. In contrast, 150 islets were insufficient to achieve normoglycemia; beta cell replication was increased initially but not by 18 or 30 d despite persistent hyperglycemia, and beta cell mass fell progressively. When islets were transplanted into normal recipients, beta cell replication remained normal but beta cells underwent atrophy and mass in the graft was substantially reduced. Therefore, with a successful islet transplant, in diabetic mice beta cell replication and mass remain constant. In contrast, when insufficient islet tissue is transplanted an initial increase in beta cell replication can not compensate for a decline in beta cell mass. When excessive islet tissue is transplanted, beta cell mass is reduced despite normal beta cell replication.