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Universitat de Girona

Campus Montilivi

E-17071, Girona

 

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SEMINARIS / SEMINARS

Curs 2011/2012

  • 26 d'octubre de 2011
    David Juher
    L'arbre mínim per a un període d'entropia zero donat
    The minimum tree for a given zero-entropy period
    In this talk, we prove a formula which computes, for any given natural number n, the minimum number of endopoints of a tree so that there exists a zero-entropy continuous map defined on it having a period n orbit. 
  • 23 de novembre (1a part) i 14 de desembre (2a part) de 2011
    Joan Saldaña 
    Les funcions generatrius de probabilitat i epidèmies en xarxes
    Una de les tècniques més utilitzades per a l'anàlisi de procesos en xarxa són les funcions generatrius de probabilitat (FGP). Una de les aplicacions més recents d'aquesta tècnica és l'estudi d'epidèmies en xarxes on neixen i moren nodes (individus). En la xerrada es vol fer una presentació de com s'utilitzen les FGP en uns models senzills d'epidèmies en xarxes i discutir la seva possible aplicació per resoldre problemes oberts en xarxes dinàmiques.
    Probability generating functions and epidemics in networks
    One of the techniques used to analyze processes on networks are the so-called probability generating functions (PGF). One of the recent applications of this technique is the study of epidemics in networks where nodes (individuals) are created (newborns)and deleted (deaths). In the talk we present on how PGF are used in the analysis of simple epidemic models on networks and discuss their application to solve open problems about epidemic models defined on dynamic networks.
  • 1 de febrer de 2012
    Jordi Ripoll
    Graph Spectra with applications to network models
    In this talk we will review some results about Spectra for networks, i.e. basically the set of eigenvalues of the adjacency matrix of the network. We will apply these results to the computation of the basic reproduction number R0 for epidemic network models through the next generation matrix.  

  • 7 de febrer de 2012
    Óscar Angulo
    Estudio numérico y analítico de modelos asociados a la hematopoiesis
    La hematopoiesis es el proceso por el que se producen y regulan las distintas poblaciones de células sanguíneas. Está basado en una sucesión de mecanismos complejos de diferenciación de las células madre. Estas diferentes diferenciaciones, que ocurren en la médula ósea, están principalmente reguladas por la población total de las células hematopoieticas. Este proceso exhibe a menudo anormalidades in la producción de células sanguíneas, que causan las denominadas enfermedades hematológicas. Una enfermedad hematológica severa es la Leucemia Myelogeneous Crónica (CML), un cáncer de los glóbulos blancos. En algunos casos, ésta exhibe oscilaciones periódicas en las contabilidades de todas las células sanguíneas.
    Presentamos un modelo de la dinámica de la hematopoiesis. Analizamos la estabilidad asintótica de los equilibrios y numéricamente ilustramos nuestros resultados y obtenemos la dinámica del modelo que relacionamos con las observaciones de la CML periódica.

  • 29 de febrer de 2012
    Xavier Jarque (UB)
    Sierpinski Julia sets for quadratic rational maps
    Sierpinski (1882-1969) discovered, among many other topologically interesting sets, the Sierpisnki carpet. The set is obtained recursively in the following manner. Start with a square of length 1. Remove a central square of length 1/3. The figure can now be naturally divided in 8 squares of length 1/3. Remove the central square of length 1/9 from each one of them. Do the same procedure up to the limit. The set we get is called the Sierpinski carpet. Why is so important? It was proved by Sierpinski that it is a universal plane continuum in the sense that it contains a homeomorphic copy of any planar, one-dimensional, compact and connected set. . 
    Later, in 1953, Whyburn showed that any planar set that is compact, connected, locally connected, nowhere dense (does not contain open sets), and has the property that any two complementary domains are bounded by disjoint simple closes curves is homeomorphic to the Sierpinski carpet. Sets with this property are known as Sierpinski curves.
    The connection of all these previous topological results has a strong relation with complex dynamics because the Julia set of a rational map is always compact and nowhere dense (unless is the whole sphere). Sufficient (and necessary) conditions to get the connectivity and local connectivity 
    are known. So, a natural question is to find out when you can guarantee that the Julia set of a rational map is a Sierpinski curve. 
    I wil present some examples given in the literature and some new results we have found in the family of quadratic rational maps.
  • 28 de març de 2012
    Víctor Mañosa (UPC)
    Birational maps on elliptic curves: blending dynamics and algebraic geometry
    Birational planar maps possessing a rational first integral, preserve a foliation of the plane given by algebraic curves. We will review some results which state that the most typical situation is that this algebraic foliation will be given either by conics and straight lines or by elliptic curves. In the last case we will see some nice results showing that the group structure of the elliptic foliation characterizes the dynamics of any birational map preserving it. All these results are classical and well-known in algebraic geometry, see [2] and [3]. This will be the main core of the talk, and it is aimed to be expository and addressed to a general audience.
    To exemplify the above stuff we will see how it works on the Lyness map F(x,y)=(y,(a+y)/x). This map preserves an algebraic foliation given by curves which are, generically, elliptic. We will see how on each of these elliptic curves the map is an affine action in terms of the group structure of the curve. In fact, we will see that the Lyness’ one is a universal family of elliptic curves.
    Finally we will review the group structure of rational elliptic curves and its relation with the existence of rational periodic orbits; we will do a brief digression on numerical experiments; and will give a negative answer to a conjecture of Zeeman (and an open problem of Bastien an Rogalski) about the existence of rational 9-periodic orbits of the Lyness map, see [1,4] and [5].

    [1] G. Bastien, M. Rogalski, Global behavior of the solutions of Lyness' difference equation u_{n+2}u_n=u_{n+1}+a, J. Difference Equations and Appl. 10 (2004), 977-1003.
    [2] J. Duistermaat. Discrete Integrable Systems. QRT Maps and Elliptic Surfaces. Springer-Verlag, 2010.
    [3] D. Jogia. J.A.G. Roberts, F. Vivaldi, An algebraic geometric approach to integrable maps of the plane. Journal of Physics A, 39 (2006), 1133--1149.
    [4] A. Gasull, V. Mañosa, X. Xarles. Rational Periodic Sequences for the Lyness Equation. Discrete and Continuous Dynamical Systems -series A. 32 (2012), 587-604.
    [5] E.C. Zeeman. Geometric unfolding of a difference equation, Preprint Hertford College, Oxford (1996). Unpublished.  
  • 25 d'abril de 2012
    Pau Roldan (UPC)
    Difusió al llarg de resonàncies al problema restringit de tres cossos
    És ben conegut pels astrònoms que, al Cinturó d'Asteroides situat entre les òrbites de Mart i Júpiter, la distribució dels asteroides presenta els nomenats "forats de Kirkwood"  (http://en.wikipedia.org/wiki/Kirkwood_gap). Aquests forats coincideixen exactament amb les ressonàncies orbitals entre Asteroide i Júpiter.
    Nosaltres demostrem l'existència d'òrbites de difusió per a l'Asteroide que mostren un canvi dràstic en la seva excentricitat, mentre que el seu semieix major es manté casi constant. Per tant, el nostre mecanisme dóna una justificació rigorosa dels forats de Kirkwood. Aquest treball és una col·laboració amb el Jacques Féjoz (Université Paris-Dauphine and Observatoire de Paris), el Marcel Guàrdia (University of Maryland at College Park), i el Vadim Kaloshin (University of Maryland at College Park). Per a més informació, veure el "preprint" http://arxiv.org/abs/1109.2892

  • 20 de juny de 2012
    M.C. Ricardo Meraz Sánchez (Universidad Nacional Autónoma de México)
    Estado de la pesquería de camarón café, Farfantepenaeus californiensis (Holmes, 1900) en el suroeste del golfo de California evaluando el error en el proceso de evaluación.

    El camarón café es la especie de camarón mas abundante en el Pacifico mexicano. En el suroeste del golfo de california existe la flota camaronera más grande de México, con más de 700 barcos que capturan anualmente cerca de 7,000 toneladas. El estado de la pesquería de camarón café fue evaluado utilizando datos comerciales de captura y esfuerzo del suroeste del golfo de California de 1995-2011. Un modelo dinámico de biomasa de Schaefer y técnicas de re-muestreos fueron utilizadas para analizar la captura por unidad de esfuerzo de la pesquería. Dos hipótesis en el proceso de evaluación fueron examinada: Error de observación y de proceso. El estimador de error de observación tuvo un mejor ajuste a los datos que el estimador de error de proceso. Este resultado puede deberse a que en actualmente es imposible discriminar el esfuerzo de pesca para las diferentes especies de camarón, cambios en el poder de pesca por la mejora de las embarcaciones y el sub-reporte que pudiera haber de las capturas. La pesquería de camarón café en el suroeste del golfo de california presento síntomas de sobrexplotación. Sin embargo, las capturas reportadas en los últimos años pareciera que el recurso presenta una rápida recuperación de la población.


Curs 2010/2011
  • 22 de febrer de 2011
    Albert Avinyó
    Obtenció de funcions que equalitzen una densitat donada mitjançant el mètode del transport de la calor
    Heat transport method to construct density-equalizing maps
     
    The problem of producing a transformation of a domain into itself such that its jacobian determinant is given at each point is an interesting geometrical problem with some applications in others areas of science and technology. When this transformation is applied to geographical maps in order to make each country or region to have an area proportional to a given quantity, like the number of inhabitants, the gross domestic product or others, the output is usually called a Geographical Cartogram.
    In this talk we analyze mathematically the heat transport method to produce these transformations, but in some particular cases where the initial data has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with the experience of the extensive numerical uses of it in the last years.
    Joint work with J. Solà-Morales and M. València of Universitat Politècnica de Catalunya
  • 22 de març de 2011
    David Juher
    Maximitzant entropia de cicles en arbres
    Maximizing entropy of cycles on trees

    In this talk we give a partial characterization of the periodic tree patterns of maximum entropy. More precisely, let n be a natural number and let K be the maximum of the topological entropies of all n-periodic tree patterns. We prove that each n-periodic pattern with entropy K is irreducible and simplicial, and that all such patterns are maximodal -in the sense that its monotone representative has no local homeomorphisms at the points of the invariant set.
    Joint work with Ll. Alsedà i F. Mañosas (U. Autònoma de Barcelona)
  • 12 d'abril de 2011
    Laura Garcia
    Evitant collisions entre satèl.lits al voltant de la Terra
    Avoiding collisions between satellites around the Earth 

    Whether talking about formations of spacecraft around Earth, or one spacecraft which can collide with an obstacle (such as space junk), we must find a rapid methodology to identify collisions and find a new trajectory which spend as little fuel as possible and avoids collisions between spacecraft. The methodology presented is a combination of a methodology based on finite elements (which gives better results in terms of fuel consumption) and an analytical methodology (which is much faster in terms of computing time).
    Joint work with
    Luke Sauter and Phil Palmer from Surrey Space Centre
  • 17 de maig de 2011
    Sara Costa
    Coexistència d'un conjunt innombrable de conjunts atractors en el cilindre
    Coexistence of uncountable many attracting sets on the cylinder
We work with two-dimensional skew-products defined on the cylinder from two functions f and p sucht that f is a continuous degree-one circle map, and p satisfies some properties of concavity and monotonicity. We prove that  when f has no periodic points (rotation interval is a singleton), there exists finitely many attracting sets. In contrast, when the rotation interval of any of the lifting of f is non-degenerate, we prove the existence of uncountably many attracting sets, each of them related with an irrational rotation number.
Joint work wiht Ll. Alsedà from UAB.