A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Giant monopole energies from a constrained relativistic mean-field approach

Background:Average energies of nuclear collective modes may be efficiently and accurately computed using a nonrelativistic constrained approach without reliance on a random phase approximation (RPA). Purpose: To extend the constrained approach to the relativistic domain and to establish its impact on the calibration of energy density functionals. Methods: Relativistic RPA calculations of the giant monopole resonance (GMR) are compared against the predictions of the corresponding constrained approach using two accurately calibrated energy density functionals. Results: We find excellent agreement at the 2% level or better between the predictions of the relativistic RPA and the corresponding constrained approach for magic (or semimagic) nuclei ranging from 16 O to 208 Pb. Conclusions: An efficient and accurate method is proposed for incorporating nuclear collective excitations into the calibration of future energy density functionals.

Better-quasi-order : ideals and spaces

This thesis deals with combinatorics, order theory and descriptive set theory. The first contribution is to the theory of well-quasi-orders (wqo) and better-quasi-orders (bqo). The main result is the proof of a conjecture made by Maurice Pouzet in 1978 his thèse d'état which states that any wqo whose ideal completion remainder is bqo is actually bqo. Our proof relies on new results with both a combinatorial and a topological flavour concerning maps from a front into a compact metric space. The second contribution is of a more applied nature and deals with topological spaces. We define a quasi-order on the subsets of every second countable To topological space in a way that generalises the Wadge quasi-order on the Baire space, while extending its nice properties to virtually all these topological spaces. The Wadge quasi-order of reducibility by continuous functions is wqo on Borei subsets of the Baire space, this quasi-order is however far less satisfactory for other important topological spaces such as the real line, as Hertling, Ikegami and Schlicht notably observed. Some authors have therefore studied reducibility with respect to some classes of discontinuous functions to remedy this situation. We propose instead to keep continuity but to weaken the notion of function to that of relation. Using the notion of admissible representation studied in Type-2 theory of effectivity, we define the quasi-order of reducibility by relatively continuous relations. We show that this quasi-order both refines the classical hierarchies of complexity and is wqo on the Borei subsets of virtually every second countable To space - including every (quasi-)Polish space. -- Cette thèse se situe dans les domaines de la combinatoire, de la théorie des ordres et de la théorie descriptive. La première contribution concerne la théorie des bons quasi-ordres (wqo) et des meilleurs quasi-ordres (bqo). Le résultat principal est la preuve d'une conjecture, énoncée par Pouzet en 1978 dans sa thèse d'état, qui établit que tout wqo dont l'ensemble des idéaux non principaux ordonnés par inclusion forme un bqo est alors lui-même un bqo. La preuve repose sur de nouveaux résultats, qui allient la combinatoire et la topologie, au sujet des fonctions d'un front vers un espace métrique compact. La seconde contribution de cette thèse traite de la complexité topologique dans le cadre des espaces To à base dénombrable. Dans le cas de l'espace de Baire, le quasi-ordre de Wadge est un wqo sur les sous-ensembles Boréliens qui a suscité énormément d'intérêt. Cependant cette relation de réduction par fonctions continues s'avère bien moins satisfaisante pour d'autres espaces d'importance tels que la droite réelle, comme l'ont fait notamment remarquer Hertling, Schlicht et Ikegami. Nous proposons de conserver la continuité et d'affaiblir la notion de fonction pour celle de relation. Pour ce faire, nous utilisons la notion de représentation admissible étudiée en « Type-2 theory of effectivity » initiée par Weihrauch. Nous introduisons alors le quasi-ordre de réduction par relations relativement continues et montrons que celui-ci à la fois raffine les hiérarchies classiques de complexité topologique et forme un wqo sur les sous-ensembles Boréliens de chaque espace quasi-Polonais.

Un análisis comparativo del papel del bucle fonológico versus la agenda visoespacial en el cálculo en niños de 7-8 años = A comparative analysis of the phonological loop versus the visuo-spatial sketchpad in mental arithmetic tasks in 7-8 y.o. children

En esta investigación se ha estudiado la relación entre dos subsistemas de la memoria de trabajo (buclefonológico y agenda viso-espacial) y el rendimiento en cálculo con una muestra de 94 niños españolesde 7-8 años. Hemos administrado dos pruebas de cálculo diseñadas para este estudio y seis medidassimples de memoria de trabajo (de contenido verbal, numérico y espacial) de la «Batería de Testsde Memoria de Treball» de Pickering, Baqués y Gathercole (1999), y dos pruebas visuales complementarias.Los resultados muestran una correlación importante entre las medidas de contenido verbaly numérico y el rendimiento en cálculo. En cambio, no hemos encontrado ninguna relación con las medidasespaciales. Se concluye, por lo tanto, que en escolares españoles existe una relación importanteentre el bucle fonológico y el rendimiento en tareas de cálculo. En cambio, el rol de la agenda viso-espaciales nulo

El papel de la memoria de trabajo en el cálculo mental un cuarto de siglo después de Hitch = The role of working memory in mental arithmetic a quarter of century after Hitch

Desde que Hitch (1978) publicó el primer estudio sobre el rol de la memoria de trabajo en el cálculo han idoaumentando las investigaciones en este campo. Muchos trabajos han estudiado un único subsistema, pero nuestroobjetivo es identificar qué subsistema de la memoria de trabajo (bucle fonológico, agenda viso-espacial o ejecutivocentral) está más implicado en el cálculo mental. Para ello hemos realizado un estudio correlacional en el quehemos administrado dos pruebas aritméticas y nueve pruebas de la “Bateria de Test de Memòria de Treball” dePickering, Baqués y Gathercole (1999) a una muestra de 94 niños españoles de 7-8 años. Nuestros resultadosindican que el bucle fonológico y sobretodo el ejecutivo central inciden de forma estadísticamente significativa enel rendimiento aritmético

Eixo quinário: um elemento de simetria presente em moléculas e quasi-cristais - um experimento didático em cristalografia

Axis of quinary symmetry occur in molecular symmetry, as in the case of fullerenes, and in crystalline symmetry, in the quasicrystals. Minerals with pentagonal faces do not have this element of symmetry, as the pyrite (FeS2) which shows a ridge that is different from the other ones, in any face of the crystal. The purpose of this paper is to demonstrate conceptual differences between pyritohedron and regular pentagonal dodecahedron symmetries, discussing students' difficulties to identify them. Also is proposed a didactic experiment with spatial models of the above-mentioned forms and the demonstration of its symmetries in clinographic projections.

Modelling mean above and below ground litter production based on yield tables

Selective papers of the workshop on "Development of models and forest soil surveys for monitoring of soil carbon", Koli, Finland, April 5-9 2006.

A comparison of electricity spot prices simulation using ARMA-GARCH and mean-reverting models

The aim of this work is to compare two families of mathematical models for their respective capability to capture the statistical properties of real electricity spot market time series. The first model family is ARMA-GARCH models and the second model family is mean-reverting Ornstein-Uhlenbeck models. These two models have been applied to two price series of Nordic Nord Pool spot market for electricity namely to the System prices and to the DenmarkW prices. The parameters of both models were calibrated from the real time series. After carrying out simulation with optimal models from both families we conclude that neither ARMA-GARCH models, nor conventional mean-reverting Ornstein-Uhlenbeck models, even when calibrated optimally with real electricity spot market price or return series, capture the statistical characteristics of the real series. But in the case of less spiky behavior (System prices), the mean-reverting Ornstein-Uhlenbeck model could be seen to partially succeeded in this task.

Quasi allegro

Soitinnus: lauluääni, piano.

A quasi-materialist, quasi-dualist solution to the mind-body problem

If the mental can affect, or be affected by, the physical, then the mental must itself be physical. Otherwise the physical world would not be explanatorily closed. But it is closed. There are reasons to hold that materialism (in both its reductive and non-reductive varieties) is false. So how are we to explain the apparent responsiveness of the physical to the mental and vice versa? The only possible solution seems to be this: physical objects are really projections or isomorphs of objects whose essential properties are mental. (A slightly less accurate way of putting this would be to say: the constitutive - i.e. the non-structural and non-phenomenal - properties of physical objects are mental, i.e. are such as we are used to encountering only in "introspection".) The chair, qua thing that I can know through sense perception, and through hypotheses based strictly thereupon, is a kind of shadow of an object that is exactly like it, except that this other objects essential properties are mental. This line of thought, though radically counterintuitive, explains the apparent responsiveness of the mental to the physical, and vice versa, without being open to any of the criticisms to which materialism, dualistic interaction ism, and epiphenomenalism are open.

Quasi-objects and actors in the web of belief. Formation of a national nuclear waste management system: the case of Finland

Paper presented in ISA RC23 meeting, Gothenburg July 16th 2010

Heritability at family mean level

Based on a polygenic system of a diploid species, without epistasis, and a population in Hardy-Weinberg equilibrium, without inbreeding and under linkage equilibrium, it can be shown that: (1) the narrow sense heritability at half-sib family level is equal to the square of the correlation coefficient between family mean and the additive genetic value of its common parent; (2) the narrow sense heritability at full-sib family level is equal to the square of the correlation coefficient between family mean and the mean of the additive genetic values of its parents; (3) the narrow sense heritability at Sn family level is exactly equal to the square of the correlation coefficient between family mean and the additive genetic value of its parent only in absence of dominance or when allele frequencies are equal; and (4) the broad sense heritability at full-sib or Sn family level can be used to analyze selection efficiency, since the progeny genotypic mean is, in general, a good indicator of parents, or Sn-1 plant superiority with respect to the frequency of favorable genes.