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."

Spanish pension system: population aging and immigration policy

There is a widespread consensus in the literature that, as consequence of the demographic transition, the current Spanish pension system will become unsustainable in the next decades. In this article we evaluate the sustainability of the contributory pensions' sub-system, taking into account the demographic projections by the Spanish Statistical Office (INE). A baseline scenario is projected as well as several reforms are simulated, focusing on: (i) selective immigration policy, (ii) changes in the way of setting the pensions and (iii) increase of the legal age of retirement up to 68. The main results are the following. The current system would not incur deficits until 2018, from then deficits will begin to be accumulated. The expenditure in pensions practically would double (from 8.3 % in 2005 to 17.2 % in 2050). A selective immigration policy -towards foreign young people- would help, but does not solve the long-term sustainability of the current system. A policy that combines a pensions' growth at a pace lower than productivity growth and extends the legal age of retirement up to 68 would give solvency to the system beyond 2029

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.

Anti-aging : Una relectura contemporània de Dorian Gray

Partint de l'estudi del llibre El retrat de Dorian Gray d'Oscar Wilde s'analitzarà, des del punt de vista de la cultura actual, una societat que s'aferra a la joventut i utilitza tots els mètodes tecnològics per defugir de la vellesa.

Proteostasis of aging and stem cells

Estudi realitzat a partir d’una estada a la the Salk Institute, Estats Units, entre 2010 i 2012. L'estabilitat del genoma és essencial per a la supervivència de les cèl • lules mare, però, l'estabilitat del proteoma pot tenir un paper igualment important en la identitat de cèl • lules mare i la seva funció. La nostra hipòtesi és que les cèl • lules mare tenen la capacitat de proteostasis augmentada en comparació amb els seus homòlegs diferenciats i ens varem preguntar si l'activitat del proteasoma és diferent a les cèl • lules mare embrionàries humanes (hESCs). En particular, els nostres resultats mostren que les poblacions de cèl• lules mare presenten una activitat del proteasoma que es correlaciona amb majors nivells de la subunitat 19S del proteasoma PSMD11/RPN-6 i un corresponent augment del ensamblatge del 26S/30S proteasoma. L'expressió ectòpica de PSMD11 és suficient per augmentar l'activitat del proteasoma. Sorprenentment, varem trobar que la llarga vida del GLP-1 C. elegans mutant té també un augment dramàtic en l'activitat del proteasoma associat a nivells augmentats en l'expressió de RPN-6. El factor de transcripció DAF-16 és essencial per l'augment de la longevitat de GLP-1 i els cucs mutants que trobem DAF-16 necessari per a l'augment d'expressió de RPN-6 i, per tant, per l'activació de l'activitat del proteasoma en GLP-1 mutant animals. Una possibilitat interessant és que els gens que regulen la vida i la resistència a l'estrès en C. elegans poden també regular la funció hESCs de mamífer, cèl • lules que son considerades immortals. Aquests resultats ens van portar a la conclusió de que FOXO4, un factor de transcripció sensible a la insulina/IGF-1, regula l'activitat del proteasoma en hESCs, el que suggereix un paper per FOXO4 en la funció d’aquestes cèl • lules. En efecte, FOXO4 es necessari per a la diferenciació en llinatges neuronals de les hESCs. Els nostres resultats estableixen una nova regulació de laproteostasis en hESCs que uneix la longevitat i la resistència a l'estrès en invertebrats amb la funció i identitat de les hESCs.

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.