Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2016-09-25T07:14:27ZNeuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model
http://hdl.handle.net/2117/90099
Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model
Huguet Casades, Gemma; Joglekar, Anoushka; Messi, Leopold Matamba; Buckalew, Richard; Wong, Sarah; Terman, David
A detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ion homeostasis, thereby preventing these pathological waves. Simulations of the model illustrate how properties of spreading depolarizations, such as wave speed and duration of depolarization, depend on several factors, including the neuron and astrocyte Na+-K+ ATPase pump strengths. In particular, we consider the neuroprotective role of astrocyte gap junction coupling. The model demonstrates that a syncytium of electrically coupled astrocytes can maintain a physiological membrane potential in the presence of an elevated extracellular K+ concentration and efficiently distribute the excess K+ across the syncytium. This provides an effective neuroprotective mechanism for delaying or preventing the initiation of spreading depolarizations.
2016-09-21T11:20:27ZHuguet Casades, GemmaJoglekar, AnoushkaMessi, Leopold MatambaBuckalew, RichardWong, SarahTerman, DavidA detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ion homeostasis, thereby preventing these pathological waves. Simulations of the model illustrate how properties of spreading depolarizations, such as wave speed and duration of depolarization, depend on several factors, including the neuron and astrocyte Na+-K+ ATPase pump strengths. In particular, we consider the neuroprotective role of astrocyte gap junction coupling. The model demonstrates that a syncytium of electrically coupled astrocytes can maintain a physiological membrane potential in the presence of an elevated extracellular K+ concentration and efficiently distribute the excess K+ across the syncytium. This provides an effective neuroprotective mechanism for delaying or preventing the initiation of spreading depolarizations.Weakly Hamilltonian actions
http://hdl.handle.net/2117/90097
Weakly Hamilltonian actions
Miranda Galcerán, Eva; Martinez Torres, David
In this paper we generalize constructions of non-commutati
ve integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamil
tonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.
2016-09-21T11:13:05ZMiranda Galcerán, EvaMartinez Torres, DavidIn this paper we generalize constructions of non-commutati
ve integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamil
tonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.A note on the symplectic topology of b-manifolds
http://hdl.handle.net/2117/90070
A note on the symplectic topology of b-manifolds
Miranda Galcerán, Eva; Martinez Torres, David; Frejlich, Pedro
Poisson manifold (M2n; ) is b-symplectic if
Vn is transverse
to the zero section. In this paper we apply techniques native to Symplectic
Topology to address questions pertaining to b-symplectic manifolds. We pro-
vide constructions of b-symplectic structures on open manifolds by Gromov's
h-principle, and of b-symplectic manifolds with a prescribed singular locus, by
means of surgeries.
2016-09-20T12:06:51ZMiranda Galcerán, EvaMartinez Torres, DavidFrejlich, PedroPoisson manifold (M2n; ) is b-symplectic if
Vn is transverse
to the zero section. In this paper we apply techniques native to Symplectic
Topology to address questions pertaining to b-symplectic manifolds. We pro-
vide constructions of b-symplectic structures on open manifolds by Gromov's
h-principle, and of b-symplectic manifolds with a prescribed singular locus, by
means of surgeries.Cotangent models of integrable systems
http://hdl.handle.net/2117/90069
Cotangent models of integrable systems
Miranda Galcerán, Eva; Kiesenhofer, Anna
We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on b-Poisson/b-symplectic manifolds. The semilocal equivalence with such models uses the corresponding action-angle theorems in these settings: the theorem of Liouville–Mineur–Arnold for symplectic manifolds and an action-angle theorem for regular Liouville tori in Poisson manifolds (Laurent- Gengoux et al., IntMath Res Notices IMRN 8: 1839–1869, 2011). Our models comprise regular Liouville tori of Poisson manifolds but also consider the Liouville tori on the singular locus of a b-Poisson manifold. For this latter class of Poisson structures we define a twisted cotangent model. The equivalence with this twisted cotangent model is given by an action-angle theorem recently proved by the authors and Scott (Math. Pures Appl. (9) 105(1):66–85, 2016). This viewpoint of cotangent models provides a new machinery to construct examples of integrable systems, which are especially valuable in the b-symplectic case where not many sources of examples are known. At the end of the paper we introduce non-degenerate singularities as lifted cotangent models on b-symplectic manifolds and discuss some generalizations of these models to general Poisson manifolds.
2016-09-20T11:44:44ZMiranda Galcerán, EvaKiesenhofer, AnnaWe associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on b-Poisson/b-symplectic manifolds. The semilocal equivalence with such models uses the corresponding action-angle theorems in these settings: the theorem of Liouville–Mineur–Arnold for symplectic manifolds and an action-angle theorem for regular Liouville tori in Poisson manifolds (Laurent- Gengoux et al., IntMath Res Notices IMRN 8: 1839–1869, 2011). Our models comprise regular Liouville tori of Poisson manifolds but also consider the Liouville tori on the singular locus of a b-Poisson manifold. For this latter class of Poisson structures we define a twisted cotangent model. The equivalence with this twisted cotangent model is given by an action-angle theorem recently proved by the authors and Scott (Math. Pures Appl. (9) 105(1):66–85, 2016). This viewpoint of cotangent models provides a new machinery to construct examples of integrable systems, which are especially valuable in the b-symplectic case where not many sources of examples are known. At the end of the paper we introduce non-degenerate singularities as lifted cotangent models on b-symplectic manifolds and discuss some generalizations of these models to general Poisson manifolds.Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
http://hdl.handle.net/2117/90067
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast frequency vector $\omega/\sqrt\varepsilon$, with $\omega=(1,\Omega),$ where the frequency ratio $\Omega$ is a quadratic irrational number. Applying the Poincaré--Melnikov method, we carry out a careful study of the dominant harmonics of the Melnikov potential. This allows us to provide an asymptotic estimate for the maximal splitting distance and show the existence of transverse homoclinic orbits to the whiskered tori with an asymptotic estimate for the transversality of the splitting. Both estimates are exponentially small in $\varepsilon$, with the functions in the exponents being periodic with respect to $\ln\varepsilon$, and can be explicitly constructed from the continued fraction of $\Omega$. In this way, we emphasize the strong dependence of our results on the arithmetic properties of $\Omega$. In particular, for quadratic ratios $\Omega$ with a 1-periodic or 2-periodic continued fraction (called metallic and metallic-colored ratios, respectively), we provide accurate upper and lower bounds for the splitting. The estimate for the maximal splitting distance is valid for all sufficiently small values of $\varepsilon$, and the transversality can be established for a majority of values of $\varepsilon$, excluding small intervals around some transition values where changes in the dominance of the harmonics take place, and bifurcations could occur. Read More: http://epubs.siam.org/doi/10.1137/15M1032776
2016-09-20T10:43:14ZDelshams Valdés, AmadeuGonchenko, MarinaGutiérrez Serrés, PereThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast frequency vector $\omega/\sqrt\varepsilon$, with $\omega=(1,\Omega),$ where the frequency ratio $\Omega$ is a quadratic irrational number. Applying the Poincaré--Melnikov method, we carry out a careful study of the dominant harmonics of the Melnikov potential. This allows us to provide an asymptotic estimate for the maximal splitting distance and show the existence of transverse homoclinic orbits to the whiskered tori with an asymptotic estimate for the transversality of the splitting. Both estimates are exponentially small in $\varepsilon$, with the functions in the exponents being periodic with respect to $\ln\varepsilon$, and can be explicitly constructed from the continued fraction of $\Omega$. In this way, we emphasize the strong dependence of our results on the arithmetic properties of $\Omega$. In particular, for quadratic ratios $\Omega$ with a 1-periodic or 2-periodic continued fraction (called metallic and metallic-colored ratios, respectively), we provide accurate upper and lower bounds for the splitting. The estimate for the maximal splitting distance is valid for all sufficiently small values of $\varepsilon$, and the transversality can be established for a majority of values of $\varepsilon$, excluding small intervals around some transition values where changes in the dominance of the harmonics take place, and bifurcations could occur. Read More: http://epubs.siam.org/doi/10.1137/15M1032776Inflation and late-time acceleration from a double-well potential with cosmological constant
http://hdl.handle.net/2117/89982
Inflation and late-time acceleration from a double-well potential with cosmological constant
Haro Cases, Jaume; Elizalde, Emilio
A model of a universe without big bang singularity is presented, which displays an early inflationary period ending just before a phase transition to a kination epoch. The model produces enough heavy particles so as to reheat the universe at temperatures in the MeV regime. After the reheating, it smoothly matches the standard Lambda CDM scenario.
2016-09-16T11:01:29ZHaro Cases, JaumeElizalde, EmilioA model of a universe without big bang singularity is presented, which displays an early inflationary period ending just before a phase transition to a kination epoch. The model produces enough heavy particles so as to reheat the universe at temperatures in the MeV regime. After the reheating, it smoothly matches the standard Lambda CDM scenario.José Gómez Martí 1968-2014: in memoriam
http://hdl.handle.net/2117/89974
José Gómez Martí 1968-2014: in memoriam
Fiol Mora, Miquel Àngel
2016-09-16T10:33:15ZFiol Mora, Miquel ÀngelA note on the order of iterated line digraphs
http://hdl.handle.net/2117/89923
A note on the order of iterated line digraphs
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal
polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.
2016-09-14T12:40:26ZDalfó Simó, CristinaFiol Mora, Miquel ÀngelGiven a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal
polynomial of a quotient digraph pi(G) of G. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.Deterministic hierarchical networks
http://hdl.handle.net/2117/89918
Deterministic hierarchical networks
Barrière Figueroa, Eulalia; Comellas Padró, Francesc de Paula; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
It has been shown that many networks associated with complex systems are
small-world (they have both a large local clustering coefficient and a small
diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances
the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.
2016-09-14T12:16:25ZBarrière Figueroa, EulaliaComellas Padró, Francesc de PaulaDalfó Simó, CristinaFiol Mora, Miquel ÀngelIt has been shown that many networks associated with complex systems are
small-world (they have both a large local clustering coefficient and a small
diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances
the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.Weakly Hamiltonian actions
http://hdl.handle.net/2117/89914
Weakly Hamiltonian actions
Miranda Galcerán, Eva; Martinez Torres, David
n this paper we generalize constructions of non-commutative in-
tegrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.
2016-09-14T11:33:24ZMiranda Galcerán, EvaMartinez Torres, Davidn this paper we generalize constructions of non-commutative in-
tegrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.