Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break

Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov's 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov's formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev's theorem. On the other hand, Chirikov's formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.Comment: 25 pages, 9 figures. NOTICE: this is the author's version of a work that was accepted for publication in Physica D. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publicatio

Stochastic approach to diffusion inside the chaotic layer of a resonance

We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus in the diffusion process in the action, $I$, of the FR, obtaining a semi--numerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case the numerically computed probability density function for the action $I$ is well interpolated by the solution of a Fokker-Planck (F-P) equation, whereas it presents a non--constant time delay respect to the concomitant F-P solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in Celestial Mechanics and Accelerator Physics.Comment: This is the author's version of a work that was submitted to Physical Review E (http://pre.aps.org

gDefrag: A graph-based tool to help defragmenting landscapes divided by linear infrastructures

Habitat fragmentation is a major biodiversity threat. Linear infrastructures (e.g. roads) hamper the movement of individuals and cause non-natural mortality. Roadkill hotspots have been used to define priority areas for road effect mitigation, but data availability and reliability is an issue, particularly on wide spatial scales. Additionally, mitigating the whole infrastructure network is unfeasible. Expedite methods are required to address such challenges. We present the gDefrag package, a graph-based approach that builds on habitat value and accessibility after simplifying the landscape as a graph. Its advantages include not requiring roadkill or movement data, and providing effective methods to deliver reliable information, allowing landscape managers to address landscape fragmentation overall. gDefrag prioritizes roads which should be targeted first to defragment the landscape. The software includes a user-friendly manual and currently implements four prioritization criteria: habitat quality, maximum number of inter-habitat paths, overall landscape connectivity, and simultaneously larger and higher-quality habitats

Premisas y antecedentes de la actual revolución educativa. El caso de la Educación Secundaria en España

La educación secundaria en España sufre un proceso de constante reforma legislativa que no consigue más que profundizar en la situación de abandono del sector público y de degradación general del sistema. Desde este artículo se revisa el momento actual de la reforma de la ley básica de ordenación general de la enseñanza y se propone un cambio en los parámetros generales del debate público.Secondary education in Spain suffers a process o permanent legal change that only deepens the helplessness of the public sector and general degradation of the system. In this article, actual moment of general law reform is reviewed and a general change of discussion parameters is proposed

Aplicação das tecnologias de Web-Mapping

"Os Sistemas de Informação Geográfica (SIG), podem ser considerados, sob o ponto de vista da sua funcionalidade, como um conjunto de ferramentas, para a recolha, armazenamento, organização e selecção, transformação e representação da informação de natureza espacial do 'mundo real', para um determinado conjunto de circunstâncias" (Burrough, 1986). A informação geográfica é fundamentalmente produzida e utilizada em ambiente desktop fechado, ou seja, confinado a apenas alguns utilizadores. No entanto, existem vantagens em tornar estes sistemas mais abertos, ou seja, para evitar a repetição de tarefas já efectuadas, é possível publicar “on-line” cartografia para que outros a possam utilizar como base para outros estudos. A disponibilização de informação geográfica nem sempre é pacífica porque a sua produção envolveu custos e também têm direitos de propriedade. A Internet surge como um importante meio, para que dados geográficos possam ser visualizados em qualquer computador, desde que este tenha ligação àWEB. Desta forma, surge o termo WebSIG. Os WebSIG (ou Web-Mapping) não são simples modos de representar cartografia temática na Internet. Estes permitem, também, a disponibilização de ferramentas de consulta, edição e análise da informação geográfica. O estudo desenvolvido tem os seguintes objectivos: • Indicar os procedimentos para instalação e utilização do software ArcIMS; • Criar serviços de visualização, extracção de informação e edição on-line; • Planeamento e criação de um WEB site (Regadio da Cova da Beira – Bloco C42) para disponibilização dos serviços criados; • Planeamento e criação de um WEB site (Faixa de combustíveis – Idanha-a-Nova)