Effects of new nonlinear couplings in relativistic effective field theory

We extend the relativistic mean field theory model of Sugahara and Toki by adding new couplings suggested by modern effective field theories. An improved set of parameters is developed with the goal to test the ability of the models based on effective field theory to describe the properties of finite nuclei and, at the same time, to be consistent with the trends of Dirac-Brueckner-Hartree-Fock calculations at densities away from the saturation region. We compare our calculations with other relativistic nuclear force parameters for various nuclear phenomena.

Factorial Hidden Markov Models

We present a framework for learning in hidden Markov models with distributed state representations. Within this framework, we derive a learning algorithm based on the Expectation--Maximization (EM) procedure for maximum likelihood estimation. Analogous to the standard Baum-Welch update rules, the M-step of our algorithm is exact and can be solved analytically. However, due to the combinatorial nature of the hidden state representation, the exact E-step is intractable. A simple and tractable mean field approximation is derived. Empirical results on a set of problems suggest that both the mean field approximation and Gibbs sampling are viable alternatives to the computationally expensive exact algorithm.

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

Optimized delta expansion for relativistic nuclear models

The optimized delta-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the lambda phi(4) model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the delta expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.

New historical archeointensity data from Brazil: Evidence for a large regional non-dipole field contribution over the past few centuries

We report new archeointensity data obtained from the analyses of baked clay elements (architectural and kiln brick fragments) sampled in Southeast Brazil and historically and/or archeologically dated between the end of the XVIth century and the beginning of the XXth century AD. The results were determined using the classical Thellier and Thellier protocol as modified by Coe, including partial thermoremanent magnetization (pTRM) and pTRM-tail checks, and the Triaxe protocol, which involves continuous high-temperature magnetization measurements. In both protocols, TRM anisotropy and cooling rate TRM dependence effects were taken into account for intensity determinations which were successfully performed for 150 specimens from 43 fragments, with a good agreement between intensity results obtained from the two procedures. Nine site-mean intensity values were derived from three to eight fragments and defined with standard deviations of less than 8%. The site-mean values vary from similar to 25 mu T to similar to 42 mu T and describe in Southeast Brazil a continuous decreasing trend by similar to 5 mu T per century between similar to 1600 AD and similar to 1900 AD. Their comparison with recent archeointensity results obtained from Northeast Brazil and reduced at a same latitude shows that: (1) the geocentric axial dipole approximation is not valid between these southeastern and northeastern regions of Brazil, whose latitudes differ by similar to 10 degrees, and (2) the available global geomagnetic field models (gufm1 models, their recalibrated versions and the CALSK3 models) are not sufficiently precise to reliably reproduce the non-dipole field effects which prevailed in Brazil for at least the 1600-1750 period. The large non-dipole contribution thus highlighted is most probably linked to the evolution of the South Atlantic Magnetic Anomaly (SAMA) during that period. Furthermore, although our dataset is limited, the Brazilian archeointensity data appear to support the view of a rather oscillatory behavior of the axial dipole moment during the past three centuries that would have been marked in particular by a moderate increase between the end of the XVIIIth century and the middle of the XIXth century followed by the well-known decrease from 1840 AD attested by direct measurements. (C) 2011 Elsevier B.V. All rights reserved.

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Turbulent magnetic pumping in a Babcock-Leighton solar dynamo model

Context. The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. Aims. We explore the effects of turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. Methods. As a first step, only vertical pumping has been considered through the inclusion of a radial diamagnetic term in the induction equation. In the second step, a latitudinal pumping term was included and then, a near-surface shear was included. Results. The results reveal the importance of the pumping mechanism in solving current limitations in mean field dynamo modeling, such as the storage of the magnetic flux and the latitudinal distribution of the sunspots. If a meridional flow is assumed to be present only in the upper part of the convective zone, it is the full turbulent pumping that regulates both the period of the solar cycle and the latitudinal distribution of the sunspot activity. In models that consider shear near the surface, a second shell of toroidal field is generated above r = 0.95 R(circle dot) at all latitudes. If the full pumping is also included, the polar toroidal fields are efficiently advected inwards, and the toroidal magnetic activity survives only at the observed latitudes near the equator. With regard to the parity of the magnetic field, only models that combine turbulent pumping with near-surface shear always converge to the dipolar parity. Conclusions. This result suggests that, under the Babcock-Leighton approach, the equartorward motion of the observed magnetic activity is governed by the latitudinal pumping of the toroidal magnetic field rather than by a large scale coherent meridional flow. Our results support the idea that the parity problem is related to the quadrupolar imprint of the meridional flow on the poloidal component of the magnetic field and the turbulent pumping positively contributes to wash out this imprint.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Duality linking standard and tachyon scalar field cosmologies

In this work we investigate the duality linking standard and tachyon scalar field homogeneous and isotropic cosmologies in N + 1 dimensions. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalar field models can be calculated explicitly.

Identification of optimal structural connectivity using functional connectivity and neural modeling.

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.