Articles de revista
http://hdl.handle.net/2117/3228
2016-02-09T14:06:19ZTraveling wave solutions in a half-space for boundary reactions
http://hdl.handle.net/2117/77011
Traveling wave solutions in a half-space for boundary reactions
Cabré Vilagut, Xavier; Consul Porras, M. Nieves; Mande Nieto, José Vicente
We prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the half-plane with a Neumann boundary reaction term of unbalanced bistable type or of combustion type. We also establish the monotonicity of the front and, in the bistable case, its behavior at infinity. In contrast with the classical bistable interior reaction model, its behavior at the side of the invading state is of power type, while at the side of the invaded state its decay is exponential. These decay results rely on the construction of a family of explicit bistable traveling fronts. Our existence results are obtained via a variational method, while the uniqueness of the speed and of the front rely on a comparison principle and the sliding method.
2015-09-22T11:21:36ZCabré Vilagut, XavierConsul Porras, M. NievesMande Nieto, José VicenteWe prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the half-plane with a Neumann boundary reaction term of unbalanced bistable type or of combustion type. We also establish the monotonicity of the front and, in the bistable case, its behavior at infinity. In contrast with the classical bistable interior reaction model, its behavior at the side of the invading state is of power type, while at the side of the invaded state its decay is exponential. These decay results rely on the construction of a family of explicit bistable traveling fronts. Our existence results are obtained via a variational method, while the uniqueness of the speed and of the front rely on a comparison principle and the sliding method.Quasimatter domination parameters in bouncing cosmologies
http://hdl.handle.net/2117/76767
Quasimatter domination parameters in bouncing cosmologies
Elizalde, Emilio; Haro Cases, Jaume; Odintsov, Sergei D.
A fine set of parameters is introduced for bouncing cosmologies in order to describe the nearly matterdominated phase, and which play the same role that the usual slow-roll parameters play in inflationary cosmology. It is shown that, as in the inflation case, the spectral index and the running parameter for scalar perturbations in bouncing cosmologies can be best expressed in terms of these small parameters. Further, they explicitly exhibit the duality that exists between a nearly matter-dominated universe in its contracting phase and the quasi-de Sitter regime in the expanding one. The results obtained also confirm and extend the known evidence that the spectral index for an exactly matter-dominated universe (i.e., a pressureless universe) in the contracting phase is, in fact, the same as the spectral index for an exact de Sitter regime in the expanding phase. Finally, in both the inflationary and the matter bounce scenarios, the theoretical values of the spectral index and of the running parameter are compared with their experimental counterparts, obtained from the most recent Planck data, with the result that the bouncing models discussed here fit accurate astronomical observations well.
2015-09-14T11:12:02ZElizalde, EmilioHaro Cases, JaumeOdintsov, Sergei D.A fine set of parameters is introduced for bouncing cosmologies in order to describe the nearly matterdominated phase, and which play the same role that the usual slow-roll parameters play in inflationary cosmology. It is shown that, as in the inflation case, the spectral index and the running parameter for scalar perturbations in bouncing cosmologies can be best expressed in terms of these small parameters. Further, they explicitly exhibit the duality that exists between a nearly matter-dominated universe in its contracting phase and the quasi-de Sitter regime in the expanding one. The results obtained also confirm and extend the known evidence that the spectral index for an exactly matter-dominated universe (i.e., a pressureless universe) in the contracting phase is, in fact, the same as the spectral index for an exact de Sitter regime in the expanding phase. Finally, in both the inflationary and the matter bounce scenarios, the theoretical values of the spectral index and of the running parameter are compared with their experimental counterparts, obtained from the most recent Planck data, with the result that the bouncing models discussed here fit accurate astronomical observations well.Generic bifurcations of low codimension of planar Filippov Systems
http://hdl.handle.net/2117/26671
Generic bifurcations of low codimension of planar Filippov Systems
Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Teixeira, Marco Antonio
In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of
this article is to develop a systematic method for studying local(and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequences
2015-03-12T10:45:38ZMartínez-Seara Alonso, M. TeresaGuàrdia Munarriz, MarcelTeixeira, Marco AntonioIn this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of
this article is to develop a systematic method for studying local(and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequencesCredit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation
http://hdl.handle.net/2117/26597
Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation
Masdemont Soler, Josep; Ortiz-Gracia, Luis
To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consum-
ing method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek
one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computa-
tional effort in the approximation while, at the same time, the accuracy increases
2015-03-05T12:53:03ZMasdemont Soler, JosepOrtiz-Gracia, LuisTo measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consum-
ing method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek
one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computa-
tional effort in the approximation while, at the same time, the accuracy increasesCom les Varietats Invariants formen Espirals i Anells en Galàxies barrades
http://hdl.handle.net/2117/26596
Com les Varietats Invariants formen Espirals i Anells en Galàxies barrades
Romero Gómez, Mercè; Sánchez-Martín, Patricia; Masdemont Soler, Josep
L'espectacularitat de les galàxies barrades consisteix no solament en la
presència de la barra, allargada en el centre de la galàxia, sinó també en els braços espirals o anells que es desenvolupen en les parts exteriors. No hi ha una teoria clara per a la formació d'anells i, fins fa poc, només n'hi havia una que explicava l'origen dels braços espirals en galàxies no barrades. En els darrers anys hem desenvolupat una teoria basada en els sistemes dinàmics que relaciona els braços espirals i els anells amb les varietats invariants hiperbòliques associades a òrbites periòdiques i quasiperiòdiques al voltant de punts d'equilibri colineals del sistema
2015-03-05T12:42:01ZRomero Gómez, MercèSánchez-Martín, PatriciaMasdemont Soler, JosepL'espectacularitat de les galàxies barrades consisteix no solament en la
presència de la barra, allargada en el centre de la galàxia, sinó també en els braços espirals o anells que es desenvolupen en les parts exteriors. No hi ha una teoria clara per a la formació d'anells i, fins fa poc, només n'hi havia una que explicava l'origen dels braços espirals en galàxies no barrades. En els darrers anys hem desenvolupat una teoria basada en els sistemes dinàmics que relaciona els braços espirals i els anells amb les varietats invariants hiperbòliques associades a òrbites periòdiques i quasiperiòdiques al voltant de punts d'equilibri colineals del sistemaStructural stability of planar bimodal linear systems
http://hdl.handle.net/2117/26226
Structural stability of planar bimodal linear systems
Ferrer Llop, Josep; Peña Carrera, Marta; Susín Sánchez, Antonio
Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spiral does not appear and when it does we give necessary and sufficient conditions concerning finite periodic orbits and saddle connections. In particular, we study the finite periodic orbits and the homoclinic orbits in the saddle/spiral case.
2015-02-05T10:53:33ZFerrer Llop, JosepPeña Carrera, MartaSusín Sánchez, AntonioStructural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spiral does not appear and when it does we give necessary and sufficient conditions concerning finite periodic orbits and saddle connections. In particular, we study the finite periodic orbits and the homoclinic orbits in the saddle/spiral case.EMtree for phylogenetic topology reconstruction on nonhomogeneous data
http://hdl.handle.net/2117/26031
EMtree for phylogenetic topology reconstruction on nonhomogeneous data
Ibáñez Marcelo, Esther; Casanellas Rius, Marta
2015-01-22T12:04:00ZIbáñez Marcelo, EstherCasanellas Rius, MartaLow degree equations for phylogenetic group-based models
http://hdl.handle.net/2117/26029
Low degree equations for phylogenetic group-based models
Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz
Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we provide an explicit construction of codimX polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U . The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michalek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012) and, on the set U , Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005).
2015-01-22T12:01:03ZCasanellas Rius, MartaFernández Sánchez, JesúsMichalek, MateuszMotivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we provide an explicit construction of codimX polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U . The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michalek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012) and, on the set U , Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005).On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
http://hdl.handle.net/2117/26024
On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
Acosta Humánez, Primitivo Belén; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, Chara
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached.
2015-01-22T11:17:38ZAcosta Humánez, Primitivo BelénLázaro Ochoa, José TomásMorales Ruiz, Juan JoséPantazi, CharaWe study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached.Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
http://hdl.handle.net/2117/25175
Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick
We investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to +/- 1 at any point of the two hemispheres S-+/- subset of partial derivative H-infinity(n) and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane Pi. We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when gamma is close to one.
2015-01-08T12:16:16ZGonzález Nogueras, María del MarSaéz, MarielSire, YannickWe investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to +/- 1 at any point of the two hemispheres S-+/- subset of partial derivative H-infinity(n) and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane Pi. We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when gamma is close to one.