Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 24 Jan 2020 20:51:16 GMT2020-01-24T20:51:16Z50711From hypersymplectic structures to compatible pairs of tensors on a lie algebroidhttp://hdl.handle.net/10316/44544Title: From hypersymplectic structures to compatible pairs of tensors on a lie algebroid
Authors: Antunes, Paulo; Nunes da Costa, Joana Margarida
Abstract: A hypersymplectic structure on a Lie algebroid determines several Poisson–Nijenhuis, ΩN and PΩ structures on that Lie algebroid. We show that these Poisson–Nijenhuis (respectively, ΩN, PΩ) structures on the Lie algebroid, are pairwise compatible.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445442013-01-01T00:00:00ZAnalytical aspects of the Brownian motor effect in randomly flashing ratchetshttp://hdl.handle.net/10316/43907Title: Analytical aspects of the Brownian motor effect in randomly flashing ratchets
Authors: Vorotnikov, Dmitry
Abstract: The muscle contraction, operation of ATP synthase, maintaining the shape of a cell are believed to be secured by motor proteins, which can be modelled using the Brownian ratchet mechanism. We consider the randomly flashing ratchet model of a Brownian motor, where the particles can be in two states, only one of which is sensitive the applied spatially periodic potential (the mathematical setting is a pair of weakly coupled reaction-diffusion and Fokker-Planck equations). We prove that this mechanism indeed generates unidirectional transport by showing that the amount of mass in the wells of the potential decreases/increases from left to right. The direction of transport is unambiguously determined by the location of each minimum of the potential with respect to the so-called diffusive mean of its adjacent maxima. The transport can be generated not only by an asymmetric potential, but also by a symmetric potential and asymmetric transition rates, and as a consequence of the general result we derive explicit conditions when the latter happens. When the transitions are localized on narrow active sites in the protein conformation space, we find a more explicit characterization of the bulk transport direction, and infer that some common preconditions of the motor effect are redundant.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/439072013-01-01T00:00:00ZOn a System of Adaptive Coupled PDEs for Image Restorationhttp://hdl.handle.net/10316/43903Title: On a System of Adaptive Coupled PDEs for Image Restoration
Authors: Prasath, V. B. Surya; Vorotnikov, Dmitry
Abstract: In this paper, we consider a coupled system of partial differential equations (PDEs) based model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. Some numerical examples are given to highlight the denoising nature of the proposed model along with some comparison results.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10316/439032012-01-01T00:00:00ZInfinitely Divisible Distributions in Integer-Valued Garch Modelshttp://hdl.handle.net/10316/44666Title: Infinitely Divisible Distributions in Integer-Valued Garch Models
Authors: Gonçalves, Esmeralda; Mendes-Lopes, Nazaré; Silva, Filipa
Abstract: We propose an integer-valued stochastic process with conditional marginal distribution belonging to the class of infinitely divisible discrete probability laws. With this proposal, we introduce a wide class of models for count time series that includes the Poisson integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) model (Ferland et al., 2006) and the negative binomial and generalized Poisson INGARCH models (Zhu, 2011, 2012a). The main probabilistic analysis of this process is developed stating, in particular, first-order and second-order stationarity conditions. The existence of a strictly stationary and ergodic solution is established in a subclass including the Poisson and generalized Poisson INGARCH models.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/446662015-01-01T00:00:00ZSasakian nilmanifoldshttp://hdl.handle.net/10316/47659Title: Sasakian nilmanifolds
Authors: Beniamino Cappelletti-Montano; Antonio De Nicola; Juan Carlos Marrero; Ivan Yudin
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/476592015-01-01T00:00:00ZWorst case complexity of direct searchhttp://hdl.handle.net/10316/45707Title: Worst case complexity of direct search
Authors: Vicente, Luís Nunes
Abstract: In this paper, we prove that the broad class of direct-search methods of directional type based on imposing sufficient decrease to accept new iterates shares the worst case complexity bound of steepest descent for the unconstrained minimization of a smooth function, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is at most proportional to the inverse of the threshold squared. In direct-search methods, the objective function is evaluated, at each iteration, at a finite number of points. No derivatives are required. The action of declaring an iteration successful (moving into a point of lower objective function value) or unsuccessful (staying at the same iterate) is based on objective function value comparisons. Some of these methods are directional in the sense of moving along predefined directions along which the objective function will eventually decrease for sufficiently small step sizes. The worst case complexity bounds derived measure the maximum number of iterations as well as the maximum number of objective function evaluations required to find a point with a required norm of the gradient of the objective function, and are proved for such directional direct-search methods when a sufficient decrease condition based on the size of the steps is imposed to accept new iterates.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/457072013-01-01T00:00:00ZConvergence of Trust-Region Methods Based on Probabilistic Modelshttp://hdl.handle.net/10316/45698Title: Convergence of Trust-Region Methods Based on Probabilistic Models
Authors: Bandeira, A. S.; Scheinberg, K.; Vicente, Luís Nunes
Abstract: In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic optimization approaches in two principal ways. Firstly, we assume that the value of the function itself can be computed without noise, in other words, that the function is deterministic. Second, we use random models of higher quality than those produced by the usual stochastic gradient methods. In particular, a first order model based on random approximation of the gradient is required to provide sufficient quality of approximation with probability $\geq 1/2$. This is in contrast with stochastic gradient approaches, where the model is assumed to be “correct” only in expectation. As a result of this particular setting, we are able to prove convergence, with probability one, of a trust-region method which is almost identical to the classical method. Moreover, the new method is simpler than its deterministic counterpart as it does not require a criticality step. Hence we show that a standard optimization framework can be used in cases when models are random and may or may not provide good approximations, as long as “good” models are more likely than “bad” models. Our results are based on the use of properties of martingales. Our motivation comes from using random sample sets and interpolation models in derivative-free optimization. However, our framework is general and can be applied with any source of uncertainty in the model. We discuss various applications for our methods in the paper.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/456982014-01-01T00:00:00ZInexact solution of NLP subproblems in MINLPhttp://hdl.handle.net/10316/45710Title: Inexact solution of NLP subproblems in MINLP
Authors: Li, Min; Vicente, Luís Nunes
Abstract: In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness in the limit case. Some numerical results will be presented to illustrate the behavior of the methods under NLP subproblem inexactness.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/457102013-01-01T00:00:00ZSmoothing and worst-case complexity for direct-search methods in nonsmooth optimizationhttp://hdl.handle.net/10316/45705Title: Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization
Authors: Garmanjani, Rohollah; Vicente, Luís Nunes
Abstract: In the context of the derivative-free optimization of a smooth objective function, it has been shown that the worst-case complexity of direct-search methods is of the same order as that of the steepest descent for derivative-based optimization; more precisely, the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is proportional to the inverse of the threshold squared. Motivated by the lack of such a result in the nonsmooth case, we propose, analyse, and test a class of smoothing direct-search methods for the unconstrained optimization of nonsmooth functions. Given a parameterized family of smoothing functions for the nonsmooth objective function dependent on a smoothing parameter, this class of methods consists of applying a direct-search algorithm for a fixed value of the smoothing parameter until the step size is relatively small, after which the smoothing parameter is reduced and the process is repeated. One can show that the worst-case complexity (or cost) of this procedure is roughly one order of magnitude worse than the one for direct search or steepest descent on smooth functions. The class of smoothing direct-search methods is also shown to enjoy asymptotic global convergence properties. Some preliminary numerical experiments indicate that this approach leads to better values of the objective function, in some cases pushing the optimization further, apparently without an additional cost in the number of function evaluations.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/457052013-01-01T00:00:00ZGlobally convergent DC trust-region methodshttp://hdl.handle.net/10316/45702Title: Globally convergent DC trust-region methods
Authors: Le Thi, Hoai An; Huynh, Van Ngai; Dinh, Tao Pham; Vaz, A. Ismael F.; Vicente, Luís Nunes
Abstract: In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where projecting onto the feasible region is computationally affordable). We consider DC local models for the quadratic model of the objective function used to compute the trust-region step, and apply a primal-dual subgradient method to the solution of the corresponding trust-region subproblems. One is able to prove that the resulting scheme is globally convergent to first-order stationary points. The theory requires the use of exact second-order derivatives but, in turn, the computation of the trust-region step asks only for one projection onto the feasible region (in comparison to the calculation of the generalized Cauchy point which may require more). The numerical efficiency and robustness of the proposed new scheme when applied to bound-constrained problems is measured by comparing its performance against some of the current state-of-the-art nonlinear programming solvers on a vast collection of test problems.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/457022014-01-01T00:00:00ZA surrogate management framework using rigorous trust-region stepshttp://hdl.handle.net/10316/45703Title: A surrogate management framework using rigorous trust-region steps
Authors: Gratton, S.; Vicente, Luís Nunes
Abstract: Surrogate models are frequently used in the optimization engineering community as convenient approaches to deal with functions for which evaluations are expensive or noisy, or lack convexity. These methodologies do not typically guarantee any type of convergence under reasonable assumptions. In this article, we will show how to incorporate the use of surrogate models, heuristics, or any other process of attempting a function value decrease in trust-region algorithms for unconstrained derivative-free optimization, in a way that global convergence of the latter algorithms to stationary points is retained. Our approach follows the lines of search/poll direct-search methods and corresponding surrogate management frameworks, both in algorithmic design and in the form of organizing the convergence theory.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/457032014-01-01T00:00:00ZInduced hypersymplectic and hyperkähler structures on the dual of a Lie algebroidhttp://hdl.handle.net/10316/44545Title: Induced hypersymplectic and hyperkähler structures on the dual of a Lie algebroid
Authors: Antunes, Paulo; Nunes da Costa, Joana Margarida
Abstract: We show that every hypersymplectic structure on a Lie algebroid A determines a hypersymplectic and a hyperkähler structure on the dual A*. This result is illustrated with an example on the Lie algebroid T(H^3 × I), where H^3 is the Heisenberg group.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/445452014-01-01T00:00:00ZWell-Pointed Coalgebrashttp://hdl.handle.net/10316/43898Title: Well-Pointed Coalgebras
Authors: Adámek, Jiří; Milius, Stefan; Moss, Lawrence S; Sousa, Lurdes
Abstract: For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius and Taylor. And initial algebras are precisely the final well-founded coalgebras. Finally, the initial iterative algebra consists of all finite well-pointed coalgebras. Numerous examples are discussed e.g. automata, graphs, and labeled transition systems.
Fri, 09 Aug 2013 00:00:00 GMThttp://hdl.handle.net/10316/438982013-08-09T00:00:00ZCovariant Lie derivatives and Frölicher-Nijenhuis bracket on Lie Algebroidshttp://hdl.handle.net/10316/47482Title: Covariant Lie derivatives and Frölicher-Nijenhuis bracket on Lie Algebroids
Authors: De Nicola, Antonio; Yudin, Ivan
Mon, 08 Dec 2014 00:00:00 GMThttp://hdl.handle.net/10316/474822014-12-08T00:00:00ZExamples of compact K-contact manifolds with no Sasakian metrichttp://hdl.handle.net/10316/47483Title: Examples of compact K-contact manifolds with no Sasakian metric
Authors: Cappelletti-Montano, Beniamino; De Nicola, Antonio; Marrero, Juan Carlos; Yudin, Ivan
Wed, 13 Nov 2013 00:00:00 GMThttp://hdl.handle.net/10316/474832013-11-13T00:00:00ZA survey on cosymplectic geometryhttp://hdl.handle.net/10316/47481Title: A survey on cosymplectic geometry
Authors: Cappelletti-Montano, Beniamino; De Nicola, Antonio; Yudin, Ivan
Thu, 16 May 2013 00:00:00 GMThttp://hdl.handle.net/10316/474812013-05-16T00:00:00ZThe ARL of modified Shewhart control charts for conditionally heteroskedastic modelshttp://hdl.handle.net/10316/44813Title: The ARL of modified Shewhart control charts for conditionally heteroskedastic models
Authors: Gonçalves, Esmeralda; Leite, Joana; Mendes-Lopes, Nazaré
Abstract: In this article we consider the modified Shewhart control chart for ARCH processes and introduce it for threshold ARCH (TARCH) ones. For both charts, we determine bounds for the distribution of the in-control run length (RL) and, consequently, for its average (ARL), both depending only on the distribution of the generating white noise, the model parameters and the critical value. For the ARCH model, we compare our bounds with others available in literature and show how they improve the existing ones. We present a simulation study to assess the quality of the bounds calculated for the ARL.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/448132013-01-01T00:00:00ZCosymplectic p-sphereshttp://hdl.handle.net/10316/47525Title: Cosymplectic p-spheres
Authors: Cappelletti-Montano, Beniamino; De Nicola, Antonio; Yudin, Ivan
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/475252016-01-01T00:00:00ZDirect Search Based on Probabilistic Descenthttp://hdl.handle.net/10316/45248Title: Direct Search Based on Probabilistic Descent
Authors: Gratton, S.; Royer, C. W.; Vicente, Luís Nunes; Zhang, Zaikun
Abstract: Direct-search methods are a class of popular derivative-free algorithms characterized by evaluating the objective function using a step size and a number of (polling) directions. When applied to the minimization of smooth functions, the polling directions are typically taken from positive spanning sets, which in turn must have at least n+1 vectors in an $n$-dimensional variable space. In addition, to ensure the global convergence of these algorithms, the positive spanning sets used throughout the iterations are required to be uniformly nondegenerate in the sense of having a positive (cosine) measure bounded away from zero. However, recent numerical results indicated that randomly generating the polling directions without imposing the positive spanning property can improve the performance of these methods, especially when the number of directions is chosen as considerably less than n+1. In this paper, we analyze direct-search algorithms when the polling directions are probabilistic descent, meaning that with a certain probability at least one of them is of descent type. Such a framework enjoys almost-sure global convergence. More interestingly, we will show a global decaying rate of $1/\sqrt{k}$ for the gradient size, with overwhelmingly high probability, matching the corresponding rate for the deterministic versions of the gradient method or of direct search. Our analysis helps us understand numerical behavior and the choice of the number of polling directions.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/452482015-01-01T00:00:00ZHagemann’s theorem for regular categorieshttp://hdl.handle.net/10316/44500Title: Hagemann’s theorem for regular categories
Authors: Janelidze, Zurab; Rodelo, Diana; Van der Linden, Tim
Abstract: In this paper we extend the characterisation of n-permutable varieties of universal algebras due to J. Hagemann to regular categories. In particular, we show that a regular category has n-permutable congruences if and only if every internal reflexive relation R in it satisfies R^\circ \leqslant R^{n-1}, and if and only if every internal reflexive relation R in it satisfies R^n\leqslant R^{n-1}. In the case when n=2 this result is well known.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445002013-01-01T00:00:00ZHyperstructures on Lie algebroidshttp://hdl.handle.net/10316/44529Title: Hyperstructures on Lie algebroids
Authors: Antunes, Paulo; Nunes da Costa, Joana
Abstract: We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic structures and (pseudo-)hyperk\"{a}hler structures. We show that the hypersymplectic framework is very rich in already known compatible pairs of tensors such as Poisson-Nijenhuis, $\Omega N$ and $P \Omega$ structures.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445292013-01-01T00:00:00ZHomological properties of quantised Borel-Schur algebras and resolutions of quantised Weyl moduleshttp://hdl.handle.net/10316/47523Title: Homological properties of quantised Borel-Schur algebras and resolutions of quantised Weyl modules
Authors: Donkin, Stephen; Santana, Ana Paula; Yudin, Ivan
Wed, 17 Apr 2013 00:00:00 GMThttp://hdl.handle.net/10316/475232013-04-17T00:00:00ZProbabilidades - Princípios Teóricoshttp://hdl.handle.net/10316/44831Title: Probabilidades - Princípios Teóricos
Authors: Gonçalves, Esmeralda; Mendes-Lopes, Nazaré
Abstract: Este livro, apresentando e desenvolvendo os principais temas subjacentes a um curso de Probabilidades, pretende contribuir para a aquisição de formação matemática essencial à descrição, análise e interpretação de situações reais não deterministas, bem como ao desenvolvimento de estudos posteriores em áreas, do domínio do aleatório, como a Estatística ou os Processos Estocásticos.
Da modelação matemática de um fenómeno aleatório segundo Kolmogorov passa-se à descrição numérica de um tal modelo através da sua identificação com um espaço de probabilidade gerado por variáveis aleatórias, ou vectores aleatórios, reais. A análise da distribuição probabilista de tais variáveis ou vectores será exaustivamente descrita e caracterizada através do estudo das principais funções e resumos que lhe estão associados. O estudo das convergências estocásticas, de grande importância no domínio das Probabilidades e indispensável no campo da Estatística, encerra os desenvolvimentos teóricos desta obra.
Desta reedição salienta-se, para além da natural actualização dos temas tratados, a apresentação, no final de cada capitulo, de um conjunto alargado de exercícios resolvidos que permitem clarificar e ilustrar os estudos teóricos desenvolvidos.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/448312013-01-01T00:00:00ZOn the Finite Dimensional Laws of Threshold GARCH Processeshttp://hdl.handle.net/10316/44834Title: On the Finite Dimensional Laws of Threshold GARCH Processes
Authors: Gonçalves, Esmeralda; Leite, Joana; Mendes-Lopes, Nazaré
Abstract: In this chapter we establish bounds for the finite dimensional laws of a threshold GARCH process, X, with generating process Z. In this class of models the conditional standard deviation has different reactions according to the sign of past values of the process. So, we firstly find lower and upper bounds for the law of \left ({X}_{1}^{+},-{X}_{1}^{+},\ldots,{X}_{n}^{+},-{X}_{n}^{+}\right), in certain regions of R^{2n}, and use them to find bounds of the law of \left ({X}_{1},\ldots,{X}_{n}\right). Some of these bounds only depend on the parameters of the model and on the distribution function of the independent generating process, Z. An application of these bounds to control charts for time series is presented.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/448342013-01-01T00:00:00ZHomogeneous Symmetric Antiassociative Quasialgebrashttp://hdl.handle.net/10316/43825Title: Homogeneous Symmetric Antiassociative Quasialgebras
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: Our main purpose is to provide for homogeneous (even or odd) symmetric antiassociative quasialgebras a structure theory analogous to that for homogeneous symmetric associative superalgebras given in [5] and to present an inductive description of these classes of algebras.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/438252014-01-01T00:00:00ZGeometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Accelerationhttp://hdl.handle.net/10316/44982Title: Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Clemente-Gallardo, Jesús
Abstract: In this work we consider a second order variational problem depending on the covariant acceleration, which is related with the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of the Pontryagin's maximum principle, allows us to study the dynamics of the control problem.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449822013-01-01T00:00:00ZA Splitting Algorithm for Medical Image Denoisinghttp://hdl.handle.net/10316/45004Title: A Splitting Algorithm for Medical Image Denoising
Authors: Araújo, Adérito
Abstract: In this work we consider a stable algorithm for integrating a mathematical model based on mean curvature motion equation proposed in (Alvarez, Lions, Morel 1992) for image denoising. The scheme is constructed using a finite difference space discretisation and semi-implicit time discretisation and is considered with a splitting algorithm that can be implemented in parallel. We apply this algorithm to the problem of denoising optical coherence tomograms from the human retina while preserving image features.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/450042013-01-01T00:00:00ZNumerical solution for a non-Fickian diffusion in a periodic potentialhttp://hdl.handle.net/10316/45003Title: Numerical solution for a non-Fickian diffusion in a periodic potential
Authors: Araújo, Adérito; Das, Amal K.; Neves, Cidália; Sousa, Ercília
Abstract: Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider
a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/450032013-01-01T00:00:00ZSemi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapeshttp://hdl.handle.net/10316/44041Title: Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes
Authors: Azenhas, Olga; Emami, Aram
Abstract: Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏(i,j)∈η(1−x_i y_j)−1, where the product is over all cell-coordinates (i,j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest stair shape. In the spirit of the classical Cauchy kernel expansion for rectangle shapes, this RSK variation provides an interpretation of the kernel for stair-type shapes as a family of pairs of semi-skyline augmented fillings whose key tableaux, determined by their shapes, lead to expansions as a sum of products of two families of key polynomials, the basis of Demazure characters of type A, and the Demazure atoms. A previous expansion of the Cauchy kernel in type A, for the stair shape was given by Alain Lascoux, based on the structure of double crystal graphs, and by Amy M. Fu and Alain Lascoux, relying on Demazure operators, which was also used to recover expansions for Ferrers shapes.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/440412013-01-01T00:00:00ZLaplace transform – Finite element method for non Fickian flowshttp://hdl.handle.net/10316/44548Title: Laplace transform – Finite element method for non Fickian flows
Authors: Barbeiro, Sílvia; Bardeji, Somaye Gh.; Ferreira, José Augusto
Abstract: In this paper we consider numerical methods for integro-differential problems based on time discretization via Laplace transformation. We focus our attention in models arising in the context of non Fickian solute transport phenomena in porous media. The mathematical models which describe the evolution of the solute concentrations are characterized by Volterra equations. We present and analyze an hybrid method which combines the Laplace transformation with respect to the time variable with the finite element discretization in the spatial variables. Numerical results illustrate the performance of the method.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445482013-01-01T00:00:00ZAn analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircaseshttp://hdl.handle.net/10316/44032Title: An analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircases
Authors: Azenhas, Olga; Emami, Aram
Abstract: We prove a restriction of an analogue of the Robinson-Schensted-Knuth correspondence for semi-skyline augmented fillings, due to Mason, to multisets of cells of a staircase possibly truncated by a smaller staircase at the upper left end corner, or at the bottom right end corner. The restriction to be imposed on the pairs of semi-skyline augmented fillings is that the pair of shapes, rearrangements of each other, satisfies an inequality in the Bruhat order, w.r.t. the symmetric group, where one shape is bounded by the reverse of the other. For semi-standard Young tableaux the
inequality means that the pair of their right keys is such that one key is bounded by the Sch\"utzenberger evacuation of the other. This bijection is then used to obtain %recover an expansion formula of the non-symmetric Cauchy kernel, over staircases or truncated staircases, in the basis of Demazure characters of type $A$, and the basis of Demazure atoms. The expansion implies
Lascoux expansion formula, when specialised to staircases or truncated staircases, and make explicit, in the latter, the Young tableaux in the Demazure crystal by interpreting Demazure operators via elementary bubble sorting operators acting on weak compositions.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/440322015-01-01T00:00:00ZNumerical simulation of aqueous humor flow: From healthy to pathologic situationshttp://hdl.handle.net/10316/44673Title: Numerical simulation of aqueous humor flow: From healthy to pathologic situations
Authors: Ferreira, José Augusto; Oliveira, Paula de; Silva, Pascoal; Murta, J.N.
Abstract: A mathematical model which simulates drug delivery through the cornea, from a therapeutic lens to the anterior chamber of the eye, is proposed. The model consists of three coupled systems of partial differential equations linked by interface conditions: drug diffusion in the therapeutic lens; diffusion and metabolic consumption in the cornea; diffusion, convection and metabolic consumption in the anterior chamber of the eye. The dependence of intraocular pressure on the obstruction of the trabecular mesh and the production rate of aqueous humor by the ciliary body is modeled. The therapeutic effects of drugs that act on the trabecular mesh or on the ciliary body are analysed. Comparisons between topical administration and drug delivery from a therapeutic lens are included.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/446732014-01-01T00:00:00ZNumerical solution of time-dependent Maxwell’s equations for modeling scattered electromagnetic wave’s propagationhttp://hdl.handle.net/10316/44986Title: Numerical solution of time-dependent Maxwell’s equations for modeling scattered electromagnetic wave’s propagation
Authors: Araújo, Adérito; Barbeiro, Sílvia; Pinto, Luís; Caramelo, Francisco; Correia, António L.; Morgado, Miguel; Serranho, Pedro; Silva, Ana S.C.; Be
Abstract: We present the discontinuous Galerkin method combined with a low-storage Runge-Kutta method as an accurate and efficient way to numerically solve the time-dependent Maxwell’s equations. We investigate the numerical scheme in the context of modeling scattered electromagnetic wave’s propagation through human eye’s structures.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449862013-01-01T00:00:00ZSylvester equations for Laguerre–Hahn orthogonal polynomials on the real linehttp://hdl.handle.net/10316/43844Title: Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line
Authors: Branquinho, Amílcar; Paiva, Anabela; Rebocho, Maria das Neves
Abstract: Matrix Sylvester differential equations are introduced in the study of Laguerre–Hahn orthogonal polynomials. Matrix Sylvester differential systems are shown to yield representations for the Laguerre–Hahn orthogonal polynomials. Lax pairs are given, formed from the differential system and the recurrence relation, that yield discrete non-linear equations for the three term recurrence relation coefficients of the Laguerre–Hahn orthogonal polynomials.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/438442013-01-01T00:00:00ZAn extension of Markov’s Theoremhttp://hdl.handle.net/10316/44496Title: An extension of Markov’s Theorem
Authors: Branquinho, Amílcar; Fidalgo Prieto, Ulises; Foulquié Moreno, Ana
Abstract: We give a general sufficient condition for the uniform convergence of sequences of type II Hermite-Padé approximants associated with Nikishin systems of functions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/444962014-01-01T00:00:00ZDeformed Laguerre–Hahn orthogonal polynomials on the real linehttp://hdl.handle.net/10316/43843Title: Deformed Laguerre–Hahn orthogonal polynomials on the real line
Authors: Branquinho, Amílcar; Rebocho, Maria das Neves
Abstract: One derives discrete dynamical systems related to Laguerre–Hahn orthogonal polynomials. One studies deformations of the recurrence relation coefficients of the orthogonal polynomials under a t-dependence on the coefficients of the Riccati differential equation for the related Stieltjes function.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/438432014-01-01T00:00:00ZThe Modular Class of a Lie Algebroid Comorphismhttp://hdl.handle.net/10316/44502Title: The Modular Class of a Lie Algebroid Comorphism
Authors: Caseiro, Raquel
Abstract: We introduce the definition of modular class of a Lie algebroid comorphism and exploit some of its properties.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445022013-01-01T00:00:00ZThe modular class of a Poisson maphttp://hdl.handle.net/10316/44503Title: The modular class of a Poisson map
Authors: Caseiro, Raquel; Fernandes, Rui Loja
Abstract: We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445032013-01-01T00:00:00ZInversion of a mapping associated with the Aomoto-Forrester systemhttp://hdl.handle.net/10316/44501Title: Inversion of a mapping associated with the Aomoto-Forrester system
Authors: Caseiro, Raquel; Françoise, Jean-Pierre; Sasaki, Ryu
Abstract: This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. The interest for such a class comes from a previous article of Aomoto and Forrester. We consider first the one-degree of freedom case and compute the Birkhoff series defined near each of its stationary points. In general, the analysis of the system motivates finding some expression for the inverses of a rational map introduced by Aomoto and Forrester. We derive here some diagrammatic expansion series for these inverses.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/445012013-01-01T00:00:00ZThe monads of classical algebra are seldom weakly cartesianhttp://hdl.handle.net/10316/44482Title: The monads of classical algebra are seldom weakly cartesian
Authors: Clementino, Maria Manuel; Hofmann, Dirk; Janelidze, George
Abstract: This paper begins a systematic study of weakly cartesian properties of monads that determine familiar varieties of universal algebras. While these properties clearly fail to hold for groups, rings, and many other related classical algebraic structures, their analysis becomes non-trivial in the case of semimodules over semirings, to which our main results are devoted. In particular necessary and sufficient conditions on a semiring S, under which the free semimodule monad has: (a) its underlying functor weakly cartesian, (b) its unit a weakly cartesian natural transformation, (c) its multiplication a weakly cartesian natural transformation, are obtained.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/444822013-01-01T00:00:00ZSome operators that preserve the locality of a pseudovariety of semigroupshttp://hdl.handle.net/10316/43883Title: Some operators that preserve the locality of a pseudovariety of semigroups
Authors: Costa, Alfredo; Escada, Ana Paula
Abstract: It is shown that if V is a local monoidal pseudovariety of semigroups, then K o V, D o V and LI o V are local. Other operators of the form Z o (_) are considered. In the process, results about the interplay between operators Z o(_) and (_) * D_k are obtained.
Fri, 15 Mar 2013 00:00:00 GMThttp://hdl.handle.net/10316/438832013-03-15T00:00:00ZGray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitionshttp://hdl.handle.net/10316/43762Title: Gray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitions
Authors: Conflitti, Alessandro; Mamede, Ricardo
Abstract: We present combinatorial Gray codes and explicit designs of efficient algorithms for lexicographical combinatorial generation of the sets of nonnesting and sparse nonnesting set partitions of length n.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/437622015-01-01T00:00:00ZDominant Shi regions with a fixed separating wall: bijective enumerationhttp://hdl.handle.net/10316/44483Title: Dominant Shi regions with a fixed separating wall: bijective enumeration
Authors: Conflitti, Alessandro; Mamede, Ricardo
Abstract: We present a purely combinatorial proof by means of an explicit bijection, of the exact number of dominant regions having as a separating wall the hyperplane associated to the longest root in the m-extended Shi hyperplane arrangement of type A and dimension n-1.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/444832014-01-01T00:00:00ZOn the Largest Size of an Antichain in the Bruhat Order for A(2k,k)http://hdl.handle.net/10316/43917Title: On the Largest Size of an Antichain in the Bruhat Order for A(2k,k)
Authors: Conflitti, Alessandro; da Fonseca, Carlos Martins; Mamede, Ricardo
Abstract: We discuss a problem proposed by Brualdi and Deaett on the largest size of an antichain in the Bruhat order for the interesting combinatorial class of binary matrices of A (2k, k).
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10316/439172011-01-01T00:00:00ZA categorical invariant of flow equivalence of shiftshttp://hdl.handle.net/10316/43881Title: A categorical invariant of flow equivalence of shifts
Authors: Costa, Alfredo; Steinberg, Benjamin
Abstract: We prove that the Karoubi envelope of a shift - defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift -is, up to natural equivalence of categories, an invariant of flow equivalence. More precisely, we show that the action of the Karoubi envelope on the Krieger cover of the shift is a flow invariant. An analogous result concerning the Fischer cover of a synchronizing shift is also obtained. From these main results, several flow equivalence invariants - some new and some old - are obtained. We also show that the Karoubi envelope is, in a natural sense, the best possible syntactic invariant of flow equivalence of sofic shifts. Another application concerns the classification of Markov-Dyck and Markov-Motzkin shifts: it is shown that, under mild conditions, two graphs define flow equivalent shifts if and only if they are isomorphic. Shifts with property (A)
and their associated semigroups, introduced by Wolfgang Krieger, are interpreted in terms of the Karoubi envelope, yielding a proof of the flow invariance of the associated semigroups in the cases usually considered (a result recently announced by Krieger), and also a proof that property (A) is
decidable for sofic shifts.
Thu, 11 Apr 2013 00:00:00 GMThttp://hdl.handle.net/10316/438812013-04-11T00:00:00ZPresentations of Schützenberger groups of minimal subshiftshttp://hdl.handle.net/10316/43884Title: Presentations of Schützenberger groups of minimal subshifts
Authors: Almeida, Jorge; Costa, Alfredo
Abstract: In previous work, the first author established a natural bijection between minimal subshifts and maximal regular J -classes of free profinite semigroups. In this paper, the Schützenberger groups of such J -classes are investigated, in particular in respect to a conjecture proposed by the first author concerning their profinite presentation. The conjecture is established for all non-periodic minimal subshifts associated with substitutions. It entails that it is decidable whether a finite group is a quotient of such a profinite group. As a further application, the Schützenberger group of the J -class corresponding to the Prouhet-Thue-Morse subshift is shown to admit a somewhat simpler presentation, from which it follows that it has rank three, and that it is non-free relatively to any pseudovariety of groups.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/438842013-01-01T00:00:00ZA 3D Model for Mechanistic Control of Drug Releasehttp://hdl.handle.net/10316/44674Title: A 3D Model for Mechanistic Control of Drug Release
Authors: Ferreira, José Augusto; Grassi, M.; Gudin͂o, Elias; Oliveira, Paula de
Abstract: A three-dimensional mathematical model for sorption/desorption by a cylindrical polymeric matrix with dispersed drug is proposed. The model is based on a system of partial differential equations coupled with boundary conditions over a moving boundary. We assume that the penetrant diffuses into a swelling matrix and causes a deformation, which induces a stress-driven diffusion and consequently a non-Fickian mass flux. A physically sound nonlinear dependence between strain and penetrant concentration is considered and introduced in a Boltzmann integral with a kernel computed from a Maxwell--Wiechert model. Numerical simulations show how the mechanistic behavior can have a role in drug delivery design.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/446742014-01-01T00:00:00ZAnalytical and Numerical Study of Diffusion through Biodegradable Viscoelastic Materialshttp://hdl.handle.net/10316/44925Title: Analytical and Numerical Study of Diffusion through Biodegradable Viscoelastic Materials
Authors: Azhdari, Ebrahim; Ferreira, José Augusto; Oliveira, Paula de; Silva, Pascoal
Abstract: In this paper the transport of a drug through a viscoelastic biodegradable material is studied. The phenomenon is described by a set of three coupled partial differential equations that take into account passive diffusion, stress driven diffusion and the degradation of the material. The stability properties of the system are studied. Numerical simulations show an influence of viscoelastic and degradation parameters in agreement with the expected physical behaviour.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449252013-01-01T00:00:00ZThe role of stiffness in the proliferation of brain tumorshttp://hdl.handle.net/10316/44678Title: The role of stiffness in the proliferation of brain tumors
Authors: Branco, João; Ferreira, José Augusto; Oliveira, Paula de
Abstract: In this paper we present a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. A theoretical stability analysis gives information to design protocols which efficiency is illustrated by a number of numerical simulations.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/446782014-01-01T00:00:00ZA mathematical model for controlled drug delivery in swelling polymershttp://hdl.handle.net/10316/44923Title: A mathematical model for controlled drug delivery in swelling polymers
Authors: Ferreira, José Augusto; Grassi, Mario; Gudiño, Elias; Oliveira, Paula de
Abstract: We propose a one-dimensional model to describe the sorption of a solvent by a polymeric membrane, followed by polymer swelling and drug release. We assume that the solvent diffuses into the membrane and induces a stress driven diffusion, that causes a non-Fickian mass flux. We assume that the drug is present in two states (dissolved and undissolved) and that its transport occurs by Fickian diffusion and non-linear dissolution. Polymer swelling is tracked with a volume conservation equation. The system of partial differential equations that define the model is numerically solved. A qualitative analysis of the dependence of the solutions on the parameters of the model shows a complete agreement with the expected physical behavior.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449232013-01-01T00:00:00Z