A Shannon-Tsallis transformation

Via a first-order linear differential equation, we determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon’s or Tsallis’ entropies in the concomitant variational problem. It is shown that the two variations lead to equivalent solutions that have different appearances but contain the same information. These solutions are linked by our transformation. However, the so-called collision entropy (Tsallis’ one with q=2) does not have a Shannon counterpart.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Simulations and integral-equation theories for dipolar density interacting disks

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in 2D systems, a relevant inter-domain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), Modified Hypernetted Chain (MHNC), and Variational Modified Hypernetted Chain (VMHNC). For the last two closures the bridge function of a reference system is required, being the hard disk the most convenient reference system. Given that in 2D there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick approximation (PY), and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke parameterization (LB). The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is only satisfactory for low-structured regimes. MHNC and VMHNC closures perform globally well and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB--based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB--based closures do not have a solution for all studied interaction strength parameters, and, in general, PY--based closures are numerically preferable.Comment: 9 pages, 4 figure

Domain size polydispersity effects on the structural and dynamical properties in lipid monolayers with phase coexistence

In lipid monolayers with phase coexistence, domains of the liquid-condensed phase always present size polydispersity. However, very few theoretical works consider size distribution effects on the monolayer properties. Because of the difference in surface densities, domains have excess dipolar density with respect to the surrounding liquid expanded phase, originating a dipolar inter-domain interaction. This interaction depends on the domain area, and hence the presence of a domain size distribution is associated with interaction polydispersity. Inter-domain interactions are fundamental to understanding the structure and dynamics of the monolayer. For this reason, it is expected that polydispersity significantly alters monolayer properties. By means of Brownian dynamics simulations, we study the radial distribution function (RDF), the average mean square displacement and the average time-dependent self-diffusion coefficient, D(t), of lipid monolayers with normally distributed size domains. For this purpose, we vary the relevant system parameters, polydispersity and interaction strength, within a range of experimental interest. We also analyze the consequences of using a monodisperse model to determine the interaction strength from an experimental RDF. We find that polydispersity strongly affects the value of the interaction strength, which is greatly underestimated if polydispersity is not considered. However, within a certain range of parameters, the RDF obtained from a polydisperse model can be well approximated by that of a monodisperse model, by suitably fitting the interaction strength, even for 40% polydispersities. For small interaction strengths or small polydispersities, the polydisperse systems obtained from fitting the experimental RDF have an average mean square displacement and D(t) in good agreement with that of the monodisperse system.Fil: Rufeil Fiori, Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Banchio, Adolfo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

A Shannon-Tsallis transformation

Via a first-order linear differential equation, we determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon’s or Tsallis’ entropies in the concomitant variational problem. It is shown that the two variations lead to equivalent solutions that have different appearances but contain the same information. These solutions are linked by our transformation. However, the so-called collision entropy (Tsallis’ one with q=2) does not have a Shannon counterpart.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Dinámica coherente de excitaciones de carga y espín en sistemas unidimensionales /

Tesis (Doctor en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2009.El control y diseño de la dinámica cuántica constituye el núcleo del procesamiento de información cuántica. Sin embargo, en sistemas de espines acoplados la alta conectividad de las interacciones y la complejidad de los estados accesibles a temperatura ambiente dificultan la obtención del grado de control necesario. En esta tesis mostramos alternativas para obtener una dinámica coherente controlada que puede obtenerse en sistemas de espines interactuantes en experimentos de NMR. La clave para obtener el grado de simplicidad deseado es el adecuado diseño de las interacciones efectivas y la elección de la topología de los acoplamientos

Influence of spontaneous curvature on the line tension of phase-coexisting domains in a lipid monolayer: A Landau-Ginzburg model

The line tension between two coexisting phases of a binary lipid monolayer in its fluid state has contributions not only from the chemical mismatch energy between the two different lipid types but also from the elastic deformation of the lipid tails. We investigate to what extent differences in the spontaneous curvature of the two lipids affect the line tension. To this end, we supplement the standard Landau-Ginzburg model for the line tension between coexisting phases by an elastic energy that accounts for lipid splay and tilt. The spontaneous curvature of the two lipids enters into our model through the splay deformation energy. We calculate the structure of the interfacial region and the line tension between the coexisting domains numerically and analytically, the former based on the full non-linear model and the latter upon employing an approximation in the free energy that linearizes the resulting Euler-Lagrange equations. We demonstrate that our analytical approximation is in excellent agreement with the full non-linear model and use it to identify relevant length scales and two physical regimes of the interfacial profile, double-exponential decay, and damped oscillations. The dependence of the line tension on the spontaneous curvatures of the individual lipids is crucially dependent on how the bulk phases are affected. In the special case that the bulk phases remain inert, the line tension decreases when the difference between the spontaneous curvatures of the two lipid types grows.Fil: Rufeil Fiori, Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Downing, Rachel. North Dakota State University. Department Of Physics.; Estados UnidosFil: Bossa, Guilherme Volpe. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: May, Sylvio. North Dakota State University. Department Of Physics.; Estados Unido

Unbalance between Excitation and Inhibition in Phenylketonuria, a Genetic Metabolic Disease Associated with Autism

Phenylketonuria (PKU) is the most common genetic metabolic disease with a well-documented association with autism spectrum disorders. It is characterized by the deficiency of the phenylalanine hydroxylase activity, causing plasmatic hyperphenylalaninemia and variable neurological and cognitive impairments. Among the potential pathophysiological mechanisms implicated in autism spectrum disorders is the excitation/inhibition (E/I) imbalance which might result from alterations in excitatory/inhibitory synapse development, synaptic transmission and plasticity, downstream signalling pathways, and intrinsic neuronal excitability. Here, we investigated functional and molecular alterations in the prefrontal cortex (pFC) of BTBR-Pah(enu2) (ENU2) mice, the animal model of PKU. Our data show higher frequency of inhibitory transmissions and significant reduced frequency of excitatory transmissions in the PKU-affected mice in comparison to wild type. Moreover, in the pFC of ENU2 mice, we reported higher levels of the post-synaptic cell-adhesion proteins neuroligin1 and 2. Altogether, our data point toward an imbalance in the E/I neurotransmission favouring inhibition in the pFC of ENU2 mice, along with alterations of the molecular components involved in the organization of cortical synapse. In addition to being the first evidence of E/I imbalance within cortical areas of a mouse model of PKU, our study provides further evidence of E/I imbalance in animal models of pathology associated with autism spectrum disorders