Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Development of a tool for the construction of "ground truth" for complex color images with text

Aquesta memoria resumeix el treball de final de carrera d’Enginyeria Superior d’Informàtica. Explicarà les principals raons que han motivat el projecte així com exemples que il·lustren l’aplicació resultant. En aquest cas el software intentarà resoldre la actual necessitat que hi ha de tenir dades de Ground Truth per als algoritmes de segmentació de text per imatges de color complexes. Tots els procesos seran explicats en els diferents capítols partint de la definició del problema, la planificació, els requeriments i el disseny fins a completar la il·lustració dels resultats del programa i les dades de Ground Truth resultants.

Infinitely many periodic orbits for the rhomboidal five-body problem

We prove the existence of infinitely many symmetric periodic orbits for a regularized rhomboidal five-body problem with four small masses placed at the vertices of a rhombus centered in the fifth mass. The main tool for proving the existence of such periodic orbits is the analytic continuation method of Poincaré together with the symmetries of the problem. © 2006 American Institute of Physics.

Duration and compliance with antidepressant treatment in immigrant and native-born populations in Spain: a four year follow-up descriptive study

Background: Non-compliance with antidepressant treatment continues to be a complex problem in mental health care. In immigrant populations non-compliance is one of several barriers to adequate management of mental illness; some data suggest greater difficulties in adhering to pharmacological treatment in these groups and an increased risk of therapeutic failure. The aim of this study is to assess differences in the duration and compliance with antidepressant treatment among immigrants and natives in a Spanish health region. Methods: Population-based (n = 206,603), retrospective cohort study including all subjects prescribed ADT between 2007 and 2009 and recorded in the national pharmacy claims database. Compliance was considered adequate when the duration was longer than 4 months and when patients withdrew more than 80% of the packs required. Results: 5334 subjects (8.5% of them being immigrants) initiated ADT. Half of the immigrants abandoned treatment during the second month (median for natives = 3 months). Of the immigrants who continued, only 29.5% presented good compliance (compared with 38.8% in natives). The estimated risk of abandoning/ending treatment in the immigrant group compared with the native group, adjusted for age and sex, was 1.28 (95%CI 1.16-1.42). Conclusions: In the region under study, immigrants of all origins present higher percentages of early discontinuation of ADT and lower median treatment durations than the native population. Although this is a complex, multifactor situation, the finding of differences between natives and immigrants in the same region suggests the need to investigate the causes in greater depth and to introduce new strategies and interventions in this population group.

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

How universal is behavior? A four country comparison of spite, cooperation and errors in voluntary contribution mechanisms

This paper studies behavior in experiments with a linear voluntary contributions mechanism for public goods conducted in Japan, the Netherlands, Spain and the USA. The same experimental design was used in the four countries. Our 'contribution function' design allows us to obtain a view of subjects' behavior from two complementary points of view. If yields information about situations where, in purely pecuniary terms, it is a dominant strategy to contribute all the endowment and about situations where it is a dominant strategy to contribute nothing. Our results show, first, that differences in behavior across countries are minor. We find that when people play "the same game" they behave similarly. Second, for all four countries our data are inconsistent with the explanation that subjects contribute only out of confusion. A common cooperative motivation is needed to explain the date.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

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.