Departament de Matemàtiques
http://hdl.handle.net/2117/3917
Thu, 20 Jul 2017 03:18:45 GMT2017-07-20T03:18:45ZGreen's function of a weighted $n$-cycle
http://hdl.handle.net/2117/106599
Green's function of a weighted $n$-cycle
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia; Jiménez Jiménez, M. Jose; Mitjana Riera, Margarida
Wed, 19 Jul 2017 08:53:18 GMThttp://hdl.handle.net/2117/1065992017-07-19T08:53:18ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosGago Álvarez, SilviaJiménez Jiménez, M. JoseMitjana Riera, MargaridaExplicit inverse of a tridiagonal (p,r)-Toeplitz matrix
http://hdl.handle.net/2117/106597
Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, M. Jose
Wed, 19 Jul 2017 08:46:53 GMThttp://hdl.handle.net/2117/1065972017-07-19T08:46:53ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, M. JoseBounded solutions of second order lineal difference equations with periodic coefficients
http://hdl.handle.net/2117/106577
Bounded solutions of second order lineal difference equations with periodic coefficients
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, M. Jose
Tue, 18 Jul 2017 11:45:35 GMThttp://hdl.handle.net/2117/1065772017-07-18T11:45:35ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, M. JoseExplicit inverse of a tridiagonal (p,r)-Toeplitz matrix
http://hdl.handle.net/2117/106576
Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, M. Jose
Tue, 18 Jul 2017 11:38:41 GMThttp://hdl.handle.net/2117/1065762017-07-18T11:38:41ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, M. JoseA note on a family of non-gravitational central force potentials in dimension one
http://hdl.handle.net/2117/106571
A note on a family of non-gravitational central force potentials in dimension one
Alvarez-Ramírez, M.; Corbera Subirana, Montserrat; Cors Iglesias, Josep Maria; García, A.
In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|ß, where x is the position of the single particle and ß is some positive real number.
Tue, 18 Jul 2017 10:41:26 GMThttp://hdl.handle.net/2117/1065712017-07-18T10:41:26ZAlvarez-Ramírez, M.Corbera Subirana, MontserratCors Iglesias, Josep MariaGarcía, A.In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|ß, where x is the position of the single particle and ß is some positive real number.Geometric quantization of semitoric systems and almost toric manifolds
http://hdl.handle.net/2117/106532
Geometric quantization of semitoric systems and almost toric manifolds
Miranda Galcerán, Eva; Presas, Francisco; Solha, Romero
Kostant gave a model for the real geometric quantization
associated to polarizations via the cohomology associated to the sheaf of
flat sections of a pre-quantum line bundle. This model is well-adapted
for real polarizations given by integrable systems and toric manifolds.
In the latter case, the cohomology can be computed counting integral
points inside the associated Delzant polytope. In this article we extend
Kostant’s geometric quantization to semitoric integrable systems and
almost toric manifolds. In these cases the dimension of the acting torus
is smaller than half of the dimension of the manifold. In particular, we
compute the cohomology groups associated to the geometric quantization
if the real polarization is the one associated to an integrable system
with focus-focus type singularities in dimension four. As application
we determine models for the geometric quantization of K3 surfaces, a
spin-spin system, the spherical pendulum, and a spin-oscillator system
under this scheme.
Mon, 17 Jul 2017 10:56:24 GMThttp://hdl.handle.net/2117/1065322017-07-17T10:56:24ZMiranda Galcerán, EvaPresas, FranciscoSolha, RomeroKostant gave a model for the real geometric quantization
associated to polarizations via the cohomology associated to the sheaf of
flat sections of a pre-quantum line bundle. This model is well-adapted
for real polarizations given by integrable systems and toric manifolds.
In the latter case, the cohomology can be computed counting integral
points inside the associated Delzant polytope. In this article we extend
Kostant’s geometric quantization to semitoric integrable systems and
almost toric manifolds. In these cases the dimension of the acting torus
is smaller than half of the dimension of the manifold. In particular, we
compute the cohomology groups associated to the geometric quantization
if the real polarization is the one associated to an integrable system
with focus-focus type singularities in dimension four. As application
we determine models for the geometric quantization of K3 surfaces, a
spin-spin system, the spherical pendulum, and a spin-oscillator system
under this scheme.Estimation of the synaptic conductance in a McKean-model neuron
http://hdl.handle.net/2117/106463
Estimation of the synaptic conductance in a McKean-model neuron
Guillamon Grabolosa, Antoni; Prohens Sastre, Rafel; Teruel Aguilar, Antonio E.; Vich Llompart, Catalina
Estimating the synaptic conductances impinging on a single neuron directly from its membrane potential is one of the open problems to be solved in order to understand the flow of information in the brain. Despite the existence of some computational strategies that give circumstantial solutions ([1-3] for instance), they all present the inconvenience that the estimation can only be done in subthreshold activity regimes. The main constraint to provide strategies for the oscillatory regimes is related to the nonlinearity of the input-output curve and the difficulty to compute it. In experimental studies it is hard to obtain these strategies and, moreover, there are no theoretical indications of how to deal with this inverse non-linear problem. In this work, we aim at giving a first proof of concept to address the estimation of synaptic conductances when the neuron is spiking. For this purpose, we use a simplified model of neuronal activity, namely a piecewise linear version of the Fitzhugh-Nagumo model, the McKean model ([4], among others), which allows an exact knowledge of the nonlinear f-I curve by means of standard techniques of non-smooth dynamical systems. As a first step, we are able to infer a steady synaptic conductance from the cell's oscillatory activity. As shown in Figure ¿Figure1,1, the model shows the relative errors of the conductances of order C, where C is the membrane capacitance (C<<1), notably improving the errors obtained using filtering techniques on the membrane potential plus linear estimations, see numerical tests performed in [5].
Fri, 14 Jul 2017 12:07:45 GMThttp://hdl.handle.net/2117/1064632017-07-14T12:07:45ZGuillamon Grabolosa, AntoniProhens Sastre, RafelTeruel Aguilar, Antonio E.Vich Llompart, CatalinaEstimating the synaptic conductances impinging on a single neuron directly from its membrane potential is one of the open problems to be solved in order to understand the flow of information in the brain. Despite the existence of some computational strategies that give circumstantial solutions ([1-3] for instance), they all present the inconvenience that the estimation can only be done in subthreshold activity regimes. The main constraint to provide strategies for the oscillatory regimes is related to the nonlinearity of the input-output curve and the difficulty to compute it. In experimental studies it is hard to obtain these strategies and, moreover, there are no theoretical indications of how to deal with this inverse non-linear problem. In this work, we aim at giving a first proof of concept to address the estimation of synaptic conductances when the neuron is spiking. For this purpose, we use a simplified model of neuronal activity, namely a piecewise linear version of the Fitzhugh-Nagumo model, the McKean model ([4], among others), which allows an exact knowledge of the nonlinear f-I curve by means of standard techniques of non-smooth dynamical systems. As a first step, we are able to infer a steady synaptic conductance from the cell's oscillatory activity. As shown in Figure ¿Figure1,1, the model shows the relative errors of the conductances of order C, where C is the membrane capacitance (C<<1), notably improving the errors obtained using filtering techniques on the membrane potential plus linear estimations, see numerical tests performed in [5].Non-commutative integrable systems on bsymplectic manifolds
http://hdl.handle.net/2117/106379
Non-commutative integrable systems on bsymplectic manifolds
Miranda Galcerán, Eva; Kiesenhoferb, Anna
In this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.
Thu, 13 Jul 2017 12:03:41 GMThttp://hdl.handle.net/2117/1063792017-07-13T12:03:41ZMiranda Galcerán, EvaKiesenhoferb, AnnaIn this paper we study noncommutative integrable systems on b-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a b-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure.On the phase-lag with equation with spatial dependent lags
http://hdl.handle.net/2117/106377
On the phase-lag with equation with spatial dependent lags
Liu, Zhuangyi; Quintanilla de Latorre, Ramón; Wang, Yang
In this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.
Thu, 13 Jul 2017 11:42:19 GMThttp://hdl.handle.net/2117/1063772017-07-13T11:42:19ZLiu, ZhuangyiQuintanilla de Latorre, RamónWang, YangIn this paper we investigate several qualitative properties of the solutions of the dual-phase-lag heat equation and the three-phase-lag heat equation. In the first case we assume that the parameter tTtT depends on the spatial position. We prove that when 2tT-tq2tT-tq is strictly positive the solutions are exponentially stable. When this property is satisfied in a proper sub-domain, but 2tT-tq=02tT-tq=0 for all the points in the case of the one-dimensional problem we also prove the exponential stability of solutions. A critical case corresponds to the situation when 2tT-tq=02tT-tq=0 in the whole domain. It is known that the solutions are not exponentially stable. We here obtain the polynomial stability for this case. Last section of the paper is devoted to the three-phase-lag case when tTtT and t¿¿ depend on the spatial variable. We here consider the case when t¿¿=¿¿tq and tTtT is a positive constant, and obtain the analyticity of the semigroup of solutions. Exponential stability and impossibility of localization are consequences of the analyticity of the semigroup.Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
http://hdl.handle.net/2117/106362
Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, M. Jose
We have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout the discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi–periodic coefficients. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provides the entries of the inverse matrix.
Wed, 12 Jul 2017 11:43:11 GMThttp://hdl.handle.net/2117/1063622017-07-12T11:43:11ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, M. JoseWe have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout the discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi–periodic coefficients. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provides the entries of the inverse matrix.