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Emerging Trade Patterns in a 3-Region Linear NEG Model: Three ExamplesCommendatore, Pasquale, Kubin, Ingrid, Sushko, Iryna 19 September 2017 (has links) (PDF)
This chapter draws attention to a specific feature of a NEG model that uses linear (and not iso-elastic) demand functions, namely its ability to account for zero trade. Thus, it represents a suitable framework to study how changes in parameters that are typical for NEG models, such as trade costs and regional market size, not only shape the regional distribution of economic activity, but at the same time determine the emergence of additional trade links between formerly autarkic regions. We survey some related papers and present a three-region framework that potentially nests many possible trade patterns. To focus the analysis, we study in more detail three specific trade patterns frequently found in the EU trade network. We start with three autarkic regions; then we introduce the possibility that two regions trade with each other; and, finally, we allow for one region trading with the other two, but the latter are still not trading with each other. We find a surprising plethora of long-run equilibria each involving a specific regional distribution of economic activity and a specific pattern of trade links. We show how a reduction in trade costs shapes simultaneously industry location and the configuration of the trade network.
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Identification de systèmes dynamiques hybrides : géométrie, parcimonie et non-linéarités / Hybrid dynamical system identification : geometry, sparsity and nonlinearitiesLe, Van Luong 04 October 2013 (has links)
En automatique, l'obtention d'un modèle du système est la pierre angulaire des procédures comme la synthèse d'une commande, la détection des défaillances, la prédiction... Cette thèse traite de l'identification d'une classe de systèmes complexes, les systèmes dynamiques hybrides. Ces systèmes impliquent l'interaction de comportements continus et discrets. Le but est de construire un modèle à partir de mesures expérimentales d'entrée et de sortie. Une nouvelle approche pour l'identification de systèmes hybrides linéaires basée sur les propriétés géométriques des systèmes hybrides dans l'espace des paramètres est proposée. Un nouvel algorithme est ensuite proposé pour le calcul de la solution la plus parcimonieuse (ou creuse) de systèmes d'équations linéaires sous-déterminés. Celui-ci permet d'améliorer une approche d'identification basée sur l'optimisation de la parcimonie du vecteur d'erreur. De plus, de nouvelles approches, basées sur des modèles à noyaux, sont proposées pour l'identification de systèmes hybrides non linéaires et de systèmes lisses par morceaux / In automatic control, obtaining a model is always the cornerstone of the synthesis procedures such as controller design, fault detection or prediction... This thesis deals with the identification of a class of complex systems, hybrid dynamical systems. These systems involve the interaction of continuous and discrete behaviors. The goal is to build a model from experimental measurements of the system inputs and outputs. A new approach for the identification of linear hybrid systems based on the geometric properties of hybrid systems in the parameter space is proposed. A new algorithm is then proposed to recover the sparsest solutions of underdetermined systems of linear equations. This allows us to improve an identification approach based on the error sparsification. In addition, new approaches based on kernel models are proposed for the identification of nonlinear hybrid systems and piecewise smooth systems
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Bifurcações genéricas e relações de equivalência em campos de vetores suaves por partes / Generic bifurcations and equivalence relations in piecewise smooth vector fieldsPerez, Otávio Henrique [UNESP] 23 February 2017 (has links)
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Previous issue date: 2017-02-23 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho iremos abordar aspectos qualitativos e geométricos a respeito de campos de vetores suaves por partes. Nosso foco será estudar bifurcações locais e globais de codimensão um e dois e também algumas relações de equivalência para campos vetoriais suaves por partes definidos no plano. Classificaremos e caracterizaremos bifurcações genéricas por meio do retrato de fase e do diagrama de bifurcação dos campos envolvidos. Também faremos uma breve introdução sobre Sistemas Slow-Fast. / In this work we study qualitative and geometric aspects of piecewise smooth vector fields. Our focus is to study local and global bifurcations of codimension one and two and some equivalence relations for piecewise smooth vector fields defined on the plane. We will classify and characterize generic bifurcations using the phase portrait and the bifurcation diagram of the vector fields involved. We also incorporate a brief introduction about Slow-Fast Systems. / FAPESP: 2014/18707-6
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Ciclos limite em sistemas lineares suaves por parte / Limit cycles in discontinuous piecewise linear systemsSilva, Ana Maria Alves da 07 March 2018 (has links)
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Previous issue date: 2018-03-07 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we will study limit cycles in piecewise smooth linear systems. We begin
studying the case where the separation curve is a polygonal and we give an example of a
system having seven limit cycles. The existence of an arbitrary number of limit cycles is
also proved for these systems, as well as an example of a system with 10 limit cycles. The
existence of n limit cycles, n 2 N, is also studied through a perturbation in the separation
curve. Finally, we study limit cycles in planar piecewise linear systems presenting a twofold
singularity in R2, as well as limit cycles sorrounding a T-singularity. / Neste trabalho estudaremos ciclos limite em sistemas lineares suaves por partes. Iniciamos
estudando o caso em que a zona de descontinuidade é uma poligonal e fornecemos
um exemplo de um sistema com sete ciclos limite. A existência de uma quantidade
arbitrária n de ciclos limite para tais sistemas também é provada, assim como fornecemos
um exemplo de um sistema com 10 ciclos limite. A existência de n ciclos limite,
n 2 N, também é estudada através de uma pertubação na zona de descontinuidade. Por
fim, estudamos ciclos limite em sistemas lineares suaves planares com equilíbrios do tipo
dobra-dobra em R2, bem como ciclos limite em torno de uma T-singularidade.
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Border Collision Bifurcations in Boom and Bust CyclesKubin, Ingrid, Gardini, Laura 03 1900 (has links) (PDF)
Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The
bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smooth dynamic systems - in particular, results from the theory of border collision bifurcations - and show that the very existence of borders such as capacity constraints or nonnegativity
constraints may lie behind abrupt changes in the dynamic behavior of economic variables. (author's abstract) / Series: Department of Economics Working Paper Series
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Conjuntos minimais e caóticos em campos de vetores planares suaves por partes / Minimal and chaotic sets in planar piecewise smooth vector fieldsGazetta, Daniele Alessandra Reghini [UNESP] 06 January 2016 (has links)
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Previous issue date: 2016-01-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal resultado dessa dissertação é o Teorema de Poincaré-Bendixson para
campos de vetores planares suaves por partes, que nos diz quais são os tipos de conjuntos
limite. Estudaremos também detalhes a respeito dos conceitos de conjuntos
minimais e caóticos em campos de vetores planares suaves por partes. / The main result of this work is the Poincaré - Bendixson Theorem for planar piecewise
smooth vector fields, which tell us what kind of limit sets arise in this context.
We will also study details about the concepts of minimal and chaotic sets in planar
piecewise smooth vector fields.
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Teoria do Averaging para campos de vetores suaves por partes / The Averaging theory for piecewise smooth vector fieldsVelter, Mariana Queiroz 05 February 2016 (has links)
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Previous issue date: 2016-02-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work the first-order Averaging theory will be studied. This theory replaces the
problem of finding and quantifying limit cycles of a vector field by the problem of finding
positive zeros of a function. We present the classical Averaging method (done for C 2
smooth vector fields) and we apply it to some special cases of quadratic polynomial vector
fields in R3. Afterwards, we show a generalization of the Averaging method proposed in
[3], which uses Brouwer degree theory in order to extend the method to continuous vector
field, in other words, the differentiability of a vector field is no longer required. Finally,
we will study the Averaging theory for piecewise smooth vector fields, presented in [14]
using the regularization technique for piecewise smooth vector fields, see [22]. Also we
will apply it to a class of polynomial vector field defined by parts, known as Kukles fields,
see [16]. / Neste trabalho a teoria do Averaging de primeira ordem será estudada. Teoria essa que
consiste em transferir o problema de encontrar e quantificar os ciclos limites de um determinado
campo de vetores para o problema de encontrar zeros positivos de uma determinada
função. Apresentaremos o método do Averaging clássico para campos de vetores
suaves, o qual assume que o referido campo é, no mínimo, de classe C 2 e aplicaremos
o método em alguns campos de vetores polinomiais quadráticos em R3 particulares. Em
seguida, apresentaremos uma generalização do método do Averaging, proposto em [3],
que utiliza a teoria do grau topológico de Brouwer para que esse seja válido para campos
de vetores somente contínuos, ou seja, nesse contexto, a diferenciabilidade não é necessária.
Por fim, estudaremos a teoria do Averaging para campos de vetores suaves por partes,
apresentada em [14] que utiliza a técnica de regularização de campos de vetores suaves
por partes, veja [22], e o aplicaremos a uma classe de campos de vetores polinomiais por
partes, denominada campos Kukles estudada em [16].
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Estudo qualitativo de campos suaves por partes via problema de perturbação singular / Qualitative study of piecewise smooth vector field via singular pertubation problemSantos, Mayk Joaquim dos 16 January 2017 (has links)
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Previous issue date: 2017-01-16 / In this work we will show that, given a piecewise smooth vector field, we can apply the regularization method and, from it, via blow-up, turn it into a singular perturbation problem. By doing that, we can use the tools from singular perturbation theory to perform a qualitative study of piecewise smooth vector fields. Finally, we will show that, through successive changes of coordinates, a singularity of a discontinuous submanifold of codimension k, where k=1 or k=2, can be transformed into a singularity of codimension 0 in order to study the qualitative behavior in this submanifold, where the Filippov’s convention holds. / Neste trabalho mostraremos que, dado um campo de vetores suaves por partes, podemos aplicar o método de regularização e, a partir deste, via “blow-up”, o transformamos em um problema de perturbação singular. Podemos, dessa forma, fazer uso das ferramentas da teoria de perturbação singular para realizar um estudo qualitativo dos campos de vetores suaves por partes. Por último, mostraremos que através de sucessivas mudanças de coordenadas podemos transformar uma singularidade de uma subvariedade de descontinuidade de codimensão k, onde k=1 ou k=2, em uma uma singularidade de codimensão 0 e estudar o comportamento qualitativo ao longo desta subvariedade, onde é válida a convenção de Filippov.
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Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical SystemsPark, Youngmin 23 August 2013 (has links)
No description available.
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Algorithmes bayésiens variationnels accélérés et applications aux problèmes inverses de grande taille / Fast variational Bayesian algorithms and their application to large dimensional inverse problemsZheng, Yuling 04 December 2014 (has links)
Dans le cadre de cette thèse, notre préoccupation principale est de développer des approches non supervisées permettant de résoudre des problèmes de grande taille le plus efficacement possible. Pour ce faire, nous avons considéré des approches bayésiennes qui permettent d'estimer conjointement les paramètres de la méthode avec l'objet d'intérêt. Dans ce cadre, la difficulté principale est que la loi a posteriori est en général complexe. Pour résoudre ce problème, nous nous sommes intéressés à l'approximation bayésienne variationnelle (BV) qui offre une approximation séparable de la loi a posteriori. Néanmoins, les méthodes d’approximation BV classiques souffrent d’une vitesse de convergence faible. La première contribution de cette thèse consiste à transposer les méthodes d'optimisation par sous-espace dans l'espace fonctionnel impliqué dans le cadre BV, ce qui nous permet de proposer une nouvelle méthode d'approximation BV. Nous avons montré l’efficacité de notre nouvelle méthode par les comparaisons avec les approches de l’état de l’art.Nous avons voulu ensuite confronter notre nouvelle méthodologie à des problèmes de traitement d'images de grande taille. De plus nous avons voulu favoriser les images régulières par morceau. Nous avons donc considéré un a priori de Variation Total (TV) et un autre a priori à variables cachées ressemblant à un mélange scalaire de gaussiennes par changement de positions. Avec ces deux modèles a priori, en appliquant notre méthode d’approximation BV, nous avons développé deux approches non-supervisées rapides et bien adaptées aux images régulières par morceau.En effet, les deux lois a priori introduites précédemment sont corrélées ce qui rend l'estimation des paramètres de méthode très compliquée : nous sommes souvent confronté à une fonction de partition non explicite. Pour contourner ce problème, nous avons considéré ensuite de travailler dans le domaine des ondelettes. Comme les coefficients d'ondelettes des images naturelles sont généralement parcimonieux, nous avons considéré des lois de la famille de mélange scalaire de gaussiennes par changement d'échelle (GSM) pour décrire la parcimonie. Une autre contribution est donc de développer une approche non-supervisée pour les lois de la famille GSM dont la densité est explicitement connue, en utilisant la méthode d'approximation BV proposée. / In this thesis, our main objective is to develop efficient unsupervised approaches for large dimensional problems. To do this, we consider Bayesian approaches, which allow us to jointly estimate regularization parameters and the object of interest. In this context, the main difficulty is that the posterior distribution is generally complex. To tackle this problem, we consider variational Bayesian (VB) approximation, which provides a separable approximation of the posterior distribution. Nevertheless, classical VB methods suffer from slow convergence speed. The first contribution of this thesis is to transpose the subspace optimization methods to the functional space involved in VB framework, which allows us to propose a new VB approximation method. We have shown the efficiency of the proposed method by comparisons with the state of the art approaches. Then we consider the application of our new methodology to large dimensional problems in image processing. Moreover, we are interested in piecewise smooth images. As a result, we have considered a Total Variation (TV) prior and a Gaussian location mixture-like hidden variable model. With these two priors, using our VB approximation method, we have developed two fast unsupervised approaches well adapted to piecewise smooth images.In fact, the priors introduced above are correlated which makes the estimation of regularization parameters very complicated: we often have a non-explicit partition function. To sidestep this problem, we have considered working in the wavelet domain. As the wavelet coefficients of natural images are generally sparse, we considered prior distributions of the Gaussian scale mixture family to enforce sparsity. Another contribution is therefore the development of an unsupervised approach for a prior distribution of the GSM family whose density is explicitly known, using the proposed VB approximation method.
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