Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

A Petri Nets-based Scheduling Methodology forMultipurpose Batch Plants.

This article presents an optimization methodology of batch production processes assembled by shared resources which rely on a mapping of state-events into time-events allowing in this way the straightforward use of a well consolidated scheduling policies developed for manufacturing systems. A technique to generate the timed Petri net representation from a continuous dynamic representation (Differential-Algebraic Equations systems (DAEs)) of the production system is presented together with the main characteristics of a Petri nets-based tool implemented for optimization purposes. This paper describes also how the implemented tool generates the coverability tree and how it can be pruned by a general purpose heuristic. An example of a distillation process with two shared batch resources is used to illustrate the optimization methodology proposed.

Evolution and cellular function of monothiol glutaredoxins: involvement in iron-sulphur cluster assembly

A number of bacterial species, mostly proteobacteria, possess monothiol glutaredoxins homologous to the Saccharomyces cerevisiae mitochondrial protein Grx5, which is involved in iron–sulphur cluster synthesis. Phylogenetic profiling is used to predict that bacterial monothiol glutaredoxins also participate in the iron–sulphur cluster (ISC) assembly machinery, because their phylogenetic profiles are similar to the profiles of the bacterial homologues of yeast ISC proteins. High evolutionary cooccurrence is observed between the Grx5 homologues and the homologues of the Yah1 ferredoxin, the scaffold proteins Isa1 and Isa2, the frataxin protein Yfh1 and the Nfu1 protein. This suggests that a specific functional interaction exists between these ISC machinery proteins. Physical interaction analyses using low-definition protein docking predict the formation of strong and specific complexes between Grx5 and several components of the yeast ISC machinery. Two-hybrid analysis has confirmed the in vivo interaction between Grx5 and Isa1. Sequence comparison techniques and cladistics indicate that the other two monothiol glutaredoxins of S. cerevisiae, Grx3 and Grx4, have evolved from the fusion of a thioredoxin gene with a monothiol glutaredoxin gene early in the eukaryotic lineage, leading to differential functional specialization. While bacteria do not contain these chimaeric glutaredoxins, in many eukaryotic species Grx5 and Grx3/4-type monothiol glutaredoxins coexist in the cell.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Regional response differences across the human amygdaloid complex during social conditioning

The amygdala is consistently implicated in biologically relevant learning tasks such as Pavlovian conditioning. In humans, the ability to identify individual faces based on the social outcomes they have predicted in the past constitutes a critical form of associative learning that can be likened to “social conditioning.” To capture such learning in a laboratory setting, participants learned about faces that predicted negative, positive, or neutral social outcomes. Participants reported liking or disliking the faces in accordance with their learned social value. During acquisition, we observed differential functional magnetic resonance imaging activation across the human amygdaloid complex consistent with previous lesion, electrophysiological, and functional neuroimaging data. A region of the medial ventral amygdala and a region of the dorsal amygdala/substantia innominata showed signal increases to both Negative and Positive faces, whereas a lateral ventral region displayed a linear representation of the valence of faces such that Negative > Positive > Neutral. This lateral ventral locus also differed from the dorsal and medial loci in that the magnitude of these responses was more resistant to habituation. These findings document a role for the human amygdala in social learning and reveal coarse regional dissociations in amygdala activity that are consistent with previous human and nonhuman animal data.

Dynamic data reconciliation for sequential modular simulators: application to a mixing process

This paper describes a method for dynamic data reconciliation of nonlinear systems that are simulated using the sequential modular approach, and where individual modules are represented by a class of differential algebraic equations. The estimation technique consists of a bank of extended Kalman filters that are integrated with the modules. The paper reports a study based on experimental data obtained from a pilot scale mixing process.

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

On the construction of explicit exponential based schemes for Stiff SDEs

Trabalho apresentado Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-14), Halle, 7-11 Sep 2015

Implementação de um modelo computacional para estudo do processo Fischer-Tropsch em reator de leito de lama

This work aims at the implementation and adaptation of a computational model for the study of the Fischer-Tropsch reaction in a slurry bed reactor from synthesis gas (CO+H2) for the selective production of hydrocarbons (CnHm), with emphasis on evaluation of the influence of operating conditions on the distribution of products formed during the reaction.The present model takes into account effects of rigorous phase equilibrium in a reactive flash drum, a detailed kinetic model able of predicting the formation of each chemical species of the reaction system, as well as control loops of the process variables for pressure and level of slurry phase. As a result, a system of Differential Algebraic Equations was solved using the computational code DASSL (Petzold, 1982). The consistent initialization for the problem was based on phase equilibrium formed by the existing components in the reactor. In addition, the index of the system was reduced to 1 by the introduction of control laws that govern the output of the reactor products. The results were compared qualitatively with experimental data collected in the Fischer-Tropsch Synthesis plant installed at Laboratório de Processamento de Gás - CTGÁS-ER-Natal/RN

Evaluation of laser level populations of erbium-doped glasses

A simulation of erbium-doped glass systems, which provides population density for the excited states involved in the 1.5 mu m and also for 2.7 mu m emissions when pumped around 980 nm, is presented. To describe the diode pump laser processes, a theoretical model based in a coupled system of differential rate equations was developed. The approach used and the obtained spectroscopic parameters are discussed. The materials under study are two oxide glasses, lead fluoroborate (PbO-PbF2-B2O3), and heavy metal oxide (Bi2O3 PbO-Ga2O3) and a fluoride glass (ZrF4-BaF2-LaF3-AlF3-NaF), all of them doped with Er3+. (c) 2006 Elsevier B.V. All rights reserved.

Modelagem matemática nas aulas de cálculo: uma estratégia que pode contribuir com a aprendizagem dos alunos de engenharia

Este trabalho objetiva analisar os possíveis efeitos que o uso da Modelagem Matemática, enquanto estratégia de ensino, provoca no processo de aprendizagem dos alunos da disciplina Cálculo III – EDO (Equações Diferenciais Ordinárias). A pesquisa foi desenvolvida em uma turma de alunos do 2° ano do curso de Engenharia da Computação, na Universidade Federal do Pará. O trabalho é de cunho qualitativo onde foram levados em consideração os aspectos sociais que permeiam uma sala de aula universitária. Importante destacar que houve a participação direta da professora-pesquisadora de Matemática. Para que eu pudesse fazer a coleta dos dados, utilizei alguns instrumentos que considerei essenciais, tais como: observações, gravações em áudio, questionários semiestruturados e registros escritos dos alunos. De posse de alguns resultados preliminares, me foi possível observar o quanto a Modelagem Matemática desempenha um papel relevante na aprendizagem dos conteúdos matemáticos por parte dos alunos, pois foi possível eles interagirem com outras áreas do conhecimento sendo, desta forma, estimulados a realizarem pesquisa e, simultaneamente, serem parte do processo de ensino e aprendizagem que foi gerado no ambiente de sala de aula. Observei, também, que a utilização da Modelagem Matemática, enquanto estratégia de ensino e aprendizagem, conduziu os alunos a despertarem para os aspectos reflexivos e críticos até então adormecidos, uma vez que são necessários para uma aprendizagem com qualidade para, assim, construírem seus conhecimentos acadêmicos e profissionais.