Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.

Nonempirical cluster-model study of the chemisorption of atomic hydrogen on the (111) surface of diamondlike crystals

The interaction of atomic hydrogen with C4H9, Si4H9, and Ge4H9 model clusters has been studied using all-electron and pseudopotential ab initio Hartree-Fock computations with basis sets of increasing flexibility. The results show that the effect of polarization functions is important in order to reproduce the experimental findings, but their inclusion only for the atoms directly involved in the chemisorption bond is usually sufficient. For the systems H-C4H9 and H-Si4H9 all-electron and pseudopotential results are in excellent agreement when basis sets of comparable quality are used. Besides, semiempirical modified-neglect-of-differential-overlap computations provide quite reliable results both for diamond and silicon and have been used to investigate larger model clusters. The results confirm the local nature of chemisorption and further justify the use of minimal X4H9 model clusters.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Viabilitat i rendiment d'un sistema d'informació geogràfica en dispositius mòbils per realitzar càlculs LCP en zona de muntanya sense connexió de xarxa

The aim of this research paper is to present a macroscopic study about the feasibility and the efficiency of mobile devices in computing Least-Cost Path (LCP). This kind of artifact must work in off-line mode and must allow to load data from a mountain zone like digital terrain models and meteorological data.The research strategy has two steps:- First of all, we need to identify the set of software components in order to implement them inside the IT artifact. This set of components should have to be able to do LCP calculations, visualize results and present a well adapted human interface. The main goal of this first steep is to demonstrate the feasibility of a mobile geographic information system by following the ¿Design & Creation¿ research strategy.- In a second time, the goal is to evaluate the reliability and usability of this IT artifact by an ¿Experiments¿ research approach. In this step we want to characterize the behavior of the artifact in terms of fidelity and LCP process speed. This evaluation will be carried out by some external users.During the reading of this paper, we will see that this kind of geographic information system (the IT artifact) has the minimal requirements needed to carry out LCP calculations in mobile devices although it has several limitations and constraints in terms of useability and reliability. We will point out qualitative and quantitative elements related to the IT artifact performances while doing this kind of computations.

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

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.

Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex

Short-term synaptic depression (STD) is a form of synaptic plasticity that has a large impact on network computations. Experimental results suggest that STD is modulated by cortical activity, decreasing with activity in the network and increasing during silent states. Here, we explored different activity-modulation protocols in a biophysical network model for which the model displayed less STD when the network was active than when it was silent, in agreement with experimental results. Furthermore, we studied how trains of synaptic potentials had lesser decay during periods of activity (UP states) than during silent periods (DOWN states), providing new experimental predictions. We next tackled the inverse question of what is the impact of modifying STD parameters on the emergent activity of the network, a question difficult to answer experimentally. We found that synaptic depression of cortical connections had a critical role to determine the regime of rhythmic cortical activity. While low STD resulted in an emergent rhythmic activity with short UP states and long DOWN states, increasing STD resulted in longer and more frequent UP states interleaved with short silent periods. A still higher synaptic depression set the network into a non-oscillatory firing regime where DOWN states no longer occurred. The speed of propagation of UP states along the network was not found to be modulated by STD during the oscillatory regime; it remained relatively stable over a range of values of STD. Overall, we found that the mutual interactions between synaptic depression and ongoing network activity are critical to determine the mechanisms that modulate cortical emergent patterns.

La influència dels continguts numèrics a l’hora de realitzar estratègies de càlcul mental

En aquesta recerca es presenta l’anàlisi de les estratègies que usen els alumnes de 4t de primària de l’escola Barnola d’Avinyó per a resoldre operacions de suma amb nombres de fins a dues xifres. A més, permet observar la seva evolució després d’haver dut a terme una unitat didàctica orientada a treballar i millorar de manera manipulativa i dinàmica, al llarg de set setmanes, els continguts numèrics. Per tant, amb els resultats obtinguts podem valorar si el fet de treballar continguts numèrics influencia en l’ús d’estratègies de càlcul mental i contrastar-ho amb diferents autors destacats en aquest àmbit.

One, two, or many mechanisms? The brain's processing of complex words

The heated debate over whether there is only a single mechanism or two mechanisms for morphology has diverted valuable research energy away from the more critical questions about the neural computations involved in the comprehension and production of morphologically complex forms. Cognitive neuroscience data implicate many brain areas. All extant models, whether they rely on a connectionist network or espouse two mechanisms, are too underspecified to explain why more than a few brain areas differ in their activity during the processing of regular and irregular forms. No one doubts that the brain treats regular and irregular words differently, but brain data indicate that a simplistic account will not do. It is time for us to search for the critical factors free from theoretical blinders.

An Engineering Solution for using Coarse Meshes in the Simulation of Delamination with Cohesive Zone Models

This paper presents a methodology to determine the parameters used in the simulation of delamination in composite materials using decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is proposed. The procedure ensures that the energy dissipated by the fracture process is correctly computed. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used in the simulation of fracture processes