Information-entropic measure of energy-degenerate kinks in two-field models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alternative fidelity measure between quantum states

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa's axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Constraint solving over multi-valued logics - application to digital circuits

Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘black-box’ agent modelled by a set of propositional logic rules, in which just a subset of components is externally visible, such faults may only be recognised by examining some output function of the agent. A (fault-free) model of the agent’s system provides the expected output given some input. If the real output differs from that predicted output, then the system is faulty. However, some faults may only become apparent in the system output when appropriate inputs are given. A number of problems regarding both testing and diagnosis thus arise, such as testing a fault, testing the whole system, finding possible faults and differentiating them to locate the correct one. The corresponding optimisation problems of finding solutions that require minimum resources are also very relevant in industry, as is minimal diagnosis. In this dissertation we use a well established set of benchmark circuits to address such diagnostic related problems and propose and develop models with different logics that we formalise and generalise as much as possible. We also prove that all techniques generalise to agents and to multiple faults. The developed multi-valued logics extend the usual Boolean logic (suitable for faultfree models) by encoding values with some dependency (usually on faults). Such logics thus allow modelling an arbitrary number of diagnostic theories. Each problem is subsequently solved with CLP solvers that we implement and discuss, together with a new efficient search technique that we present. We compare our results with other approaches such as SAT (that require substantial duplication of circuits), showing the effectiveness of constraints over multi-valued logics, and also the adequacy of a general set constraint solver (with special inferences over set functions such as cardinality) on other problems. In addition, for an optimisation problem, we integrate local search with a constructive approach (branch-and-bound) using a variety of logics to improve an existing efficient tool based on SAT and ILP.

Approximate entropy normalized measures for analyzing social neurobiological systems

When considering time series data of variables describing agent interactions in social neurobiological systems, measures of regularity can provide a global understanding of such system behaviors. Approximate entropy (ApEn) was introduced as a nonlinear measure to assess the complexity of a system behavior by quantifying the regularity of the generated time series. However, ApEn is not reliable when assessing and comparing the regularity of data series with short or inconsistent lengths, which often occur in studies of social neurobiological systems, particularly in dyadic human movement systems. Here, the authors present two normalized, nonmodified measures of regularity derived from the original ApEn, which are less dependent on time series length. The validity of the suggested measures was tested in well-established series (random and sine) prior to their empirical application, describing the dyadic behavior of athletes in team games. The authors consider one of the ApEn normalized measures to generate the 95th percentile envelopes that can be used to test whether a particular social neurobiological system is highly complex (i.e., generates highly unpredictable time series). Results demonstrated that suggested measures may be considered as valid instruments for measuring and comparing complexity in systems that produce time series with inconsistent lengths.

Comparing clustering solutions: the use of adjusted paired indices

In the present paper we compare clustering solutions using indices of paired agreement. We propose a new method - IADJUST - to correct indices of paired agreement, excluding agreement by chance. This new method overcomes previous limitations known in the literature as it permits the correction of any index. We illustrate its use in external clustering validation, to measure the accordance between clusters and an a priori known structure. The adjusted indices are intended to provide a realistic measure of clustering performance that excludes agreement by chance with ground truth. We use simulated data sets, under a range of scenarios - considering diverse numbers of clusters, clusters overlaps and balances - to discuss the pertinence and the precision of our proposal. Precision is established based on comparisons with the analytical approach for correction specific indices that can be corrected in this way are used for this purpose. The pertinence of the proposed correction is discussed when making a detailed comparison between the performance of two classical clustering approaches, namely Expectation-Maximization (EM) and K-Means (KM) algorithms. Eight indices of paired agreement are studied and new corrected indices are obtained.

Resiliência familiar e risco psicossocial: estudo das percepções das famílias e dos profissionais que as acompanham

Dissertação de mestrado em Estudos da Criança (área de especialização em Intervenção Psicossocial com Crianças, Jovens e Famílias)

Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\'enyi relative entropy formula.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

Innovative Solutions for Slope Stability Reinforcement and Characterization: Vol. I, TR-489, 2005

Soil slope instability concerning highway infrastructure is an ongoing problem in Iowa, as slope failures endanger public safety and continue to result in costly repair work. Characterization of slope failures is complicated, because the factors affecting slope stability can be difficult to discern and measure, particularly soil shear strength parameters. While in the past extensive research has been conducted on slope stability investigations and analysis, this research consists of field investigations addressing both the characterization and reinforcement of such slope failures. The current research focuses on applying an infrequently-used testing technique comprised of the Borehole Shear Test (BST). This in-situ test rapidly provides effective (i.e., drained) shear strength parameter values of soil. Using the BST device, fifteen Iowa slopes (fourteen failures and one proposed slope) were investigated and documented. Particular attention was paid to highly weathered shale and glacial till soil deposits, which have both been associated with slope failures in the southern Iowa drift region. Conventional laboratory tests including direct shear tests, triaxial compression tests, and ring shear tests were also performed on undisturbed and reconstituted soil samples to supplement BST results. The shear strength measurements were incorporated into complete evaluations of slope stability using both limit equilibrium and probabilistic analyses. The research methods and findings of these investigations are summarized in Volume 1 of this report. Research details of the independent characterization and reinforcement investigations are provided in Volumes 2 and 3, respectively. Combined, the field investigations offer guidance on identifying the factors that affect slope stability at a particular location and also on designing slope reinforcement using pile elements for cases where remedial measures are necessary. The research findings are expected to benefit civil and geotechnical engineers of government transportation agencies, consultants, and contractors dealing with slope stability, slope remediation, and geotechnical testing in Iowa.

The Hydrophobic interaction: modeling hydrophobic interactions and aggregation of non-polar particles in aqueous solutions

Malgré son importance dans notre vie de tous les jours, certaines propriétés de l?eau restent inexpliquées. L'étude des interactions entre l'eau et les particules organiques occupe des groupes de recherche dans le monde entier et est loin d'être finie. Dans mon travail j'ai essayé de comprendre, au niveau moléculaire, ces interactions importantes pour la vie. J'ai utilisé pour cela un modèle simple de l'eau pour décrire des solutions aqueuses de différentes particules. Récemment, l?eau liquide a été décrite comme une structure formée d?un réseau aléatoire de liaisons hydrogènes. En introduisant une particule hydrophobe dans cette structure à basse température, certaines liaisons hydrogènes sont détruites ce qui est énergétiquement défavorable. Les molécules d?eau s?arrangent alors autour de cette particule en formant une cage qui permet de récupérer des liaisons hydrogènes (entre molécules d?eau) encore plus fortes : les particules sont alors solubles dans l?eau. A des températures plus élevées, l?agitation thermique des molécules devient importante et brise les liaisons hydrogènes. Maintenant, la dissolution des particules devient énergétiquement défavorable, et les particules se séparent de l?eau en formant des agrégats qui minimisent leur surface exposée à l?eau. Pourtant, à très haute température, les effets entropiques deviennent tellement forts que les particules se mélangent de nouveau avec les molécules d?eau. En utilisant un modèle basé sur ces changements de structure formée par des liaisons hydrogènes j?ai pu reproduire les phénomènes principaux liés à l?hydrophobicité. J?ai trouvé une région de coexistence de deux phases entre les températures critiques inférieure et supérieure de solubilité, dans laquelle les particules hydrophobes s?agrègent. En dehors de cette région, les particules sont dissoutes dans l?eau. J?ai démontré que l?interaction hydrophobe est décrite par un modèle qui prend uniquement en compte les changements de structure de l?eau liquide en présence d?une particule hydrophobe, plutôt que les interactions directes entre les particules. Encouragée par ces résultats prometteurs, j?ai étudié des solutions aqueuses de particules hydrophobes en présence de co-solvants cosmotropiques et chaotropiques. Ce sont des substances qui stabilisent ou déstabilisent les agrégats de particules hydrophobes. La présence de ces substances peut être incluse dans le modèle en décrivant leur effet sur la structure de l?eau. J?ai pu reproduire la concentration élevée de co-solvants chaotropiques dans le voisinage immédiat de la particule, et l?effet inverse dans le cas de co-solvants cosmotropiques. Ce changement de concentration du co-solvant à proximité de particules hydrophobes est la cause principale de son effet sur la solubilité des particules hydrophobes. J?ai démontré que le modèle adapté prédit correctement les effets implicites des co-solvants sur les interactions de plusieurs corps entre les particules hydrophobes. En outre, j?ai étendu le modèle à la description de particules amphiphiles comme des lipides. J?ai trouvé la formation de différents types de micelles en fonction de la distribution des regions hydrophobes à la surface des particules. L?hydrophobicité reste également un sujet controversé en science des protéines. J?ai défini une nouvelle échelle d?hydrophobicité pour les acides aminés qui forment des protéines, basée sur leurs surfaces exposées à l?eau dans des protéines natives. Cette échelle permet une comparaison meilleure entre les expériences et les résultats théoriques. Ainsi, le modèle développé dans mon travail contribue à mieux comprendre les solutions aqueuses de particules hydrophobes. Je pense que les résultats analytiques et numériques obtenus éclaircissent en partie les processus physiques qui sont à la base de l?interaction hydrophobe.<br/><br/>Despite the importance of water in our daily lives, some of its properties remain unexplained. Indeed, the interactions of water with organic particles are investigated in research groups all over the world, but controversy still surrounds many aspects of their description. In my work I have tried to understand these interactions on a molecular level using both analytical and numerical methods. Recent investigations describe liquid water as random network formed by hydrogen bonds. The insertion of a hydrophobic particle at low temperature breaks some of the hydrogen bonds, which is energetically unfavorable. The water molecules, however, rearrange in a cage-like structure around the solute particle. Even stronger hydrogen bonds are formed between water molecules, and thus the solute particles are soluble. At higher temperatures, this strict ordering is disrupted by thermal movements, and the solution of particles becomes unfavorable. They minimize their exposed surface to water by aggregating. At even higher temperatures, entropy effects become dominant and water and solute particles mix again. Using a model based on these changes in water structure I have reproduced the essential phenomena connected to hydrophobicity. These include an upper and a lower critical solution temperature, which define temperature and density ranges in which aggregation occurs. Outside of this region the solute particles are soluble in water. Because I was able to demonstrate that the simple mixture model contains implicitly many-body interactions between the solute molecules, I feel that the study contributes to an important advance in the qualitative understanding of the hydrophobic effect. I have also studied the aggregation of hydrophobic particles in aqueous solutions in the presence of cosolvents. Here I have demonstrated that the important features of the destabilizing effect of chaotropic cosolvents on hydrophobic aggregates may be described within the same two-state model, with adaptations to focus on the ability of such substances to alter the structure of water. The relevant phenomena include a significant enhancement of the solubility of non-polar solute particles and preferential binding of chaotropic substances to solute molecules. In a similar fashion, I have analyzed the stabilizing effect of kosmotropic cosolvents in these solutions. Including the ability of kosmotropic substances to enhance the structure of liquid water, leads to reduced solubility, larger aggregation regime and the preferential exclusion of the cosolvent from the hydration shell of hydrophobic solute particles. I have further adapted the MLG model to include the solvation of amphiphilic solute particles in water, by allowing different distributions of hydrophobic regions at the molecular surface, I have found aggregation of the amphiphiles, and formation of various types of micelle as a function of the hydrophobicity pattern. I have demonstrated that certain features of micelle formation may be reproduced by the adapted model to describe alterations of water structure near different surface regions of the dissolved amphiphiles. Hydrophobicity remains a controversial quantity also in protein science. Based on the surface exposure of the 20 amino-acids in native proteins I have defined the a new hydrophobicity scale, which may lead to an improvement in the comparison of experimental data with the results from theoretical HP models. Overall, I have shown that the primary features of the hydrophobic interaction in aqueous solutions may be captured within a model which focuses on alterations in water structure around non-polar solute particles. The results obtained within this model may illuminate the processes underlying the hydrophobic interaction.<br/><br/>La vie sur notre planète a commencé dans l'eau et ne pourrait pas exister en son absence : les cellules des animaux et des plantes contiennent jusqu'à 95% d'eau. Malgré son importance dans notre vie de tous les jours, certaines propriétés de l?eau restent inexpliquées. En particulier, l'étude des interactions entre l'eau et les particules organiques occupe des groupes de recherche dans le monde entier et est loin d'être finie. Dans mon travail j'ai essayé de comprendre, au niveau moléculaire, ces interactions importantes pour la vie. J'ai utilisé pour cela un modèle simple de l'eau pour décrire des solutions aqueuses de différentes particules. Bien que l?eau soit généralement un bon solvant, un grand groupe de molécules, appelées molécules hydrophobes (du grecque "hydro"="eau" et "phobia"="peur"), n'est pas facilement soluble dans l'eau. Ces particules hydrophobes essayent d'éviter le contact avec l'eau, et forment donc un agrégat pour minimiser leur surface exposée à l'eau. Cette force entre les particules est appelée interaction hydrophobe, et les mécanismes physiques qui conduisent à ces interactions ne sont pas bien compris à l'heure actuelle. Dans mon étude j'ai décrit l'effet des particules hydrophobes sur l'eau liquide. L'objectif était d'éclaircir le mécanisme de l'interaction hydrophobe qui est fondamentale pour la formation des membranes et le fonctionnement des processus biologiques dans notre corps. Récemment, l'eau liquide a été décrite comme un réseau aléatoire formé par des liaisons hydrogènes. En introduisant une particule hydrophobe dans cette structure, certaines liaisons hydrogènes sont détruites tandis que les molécules d'eau s'arrangent autour de cette particule en formant une cage qui permet de récupérer des liaisons hydrogènes (entre molécules d?eau) encore plus fortes : les particules sont alors solubles dans l'eau. A des températures plus élevées, l?agitation thermique des molécules devient importante et brise la structure de cage autour des particules hydrophobes. Maintenant, la dissolution des particules devient défavorable, et les particules se séparent de l'eau en formant deux phases. A très haute température, les mouvements thermiques dans le système deviennent tellement forts que les particules se mélangent de nouveau avec les molécules d'eau. A l'aide d'un modèle qui décrit le système en termes de restructuration dans l'eau liquide, j'ai réussi à reproduire les phénomènes physiques liés à l?hydrophobicité. J'ai démontré que les interactions hydrophobes entre plusieurs particules peuvent être exprimées dans un modèle qui prend uniquement en compte les liaisons hydrogènes entre les molécules d'eau. Encouragée par ces résultats prometteurs, j'ai inclus dans mon modèle des substances fréquemment utilisées pour stabiliser ou déstabiliser des solutions aqueuses de particules hydrophobes. J'ai réussi à reproduire les effets dûs à la présence de ces substances. De plus, j'ai pu décrire la formation de micelles par des particules amphiphiles comme des lipides dont la surface est partiellement hydrophobe et partiellement hydrophile ("hydro-phile"="aime l'eau"), ainsi que le repliement des protéines dû à l'hydrophobicité, qui garantit le fonctionnement correct des processus biologiques de notre corps. Dans mes études futures je poursuivrai l'étude des solutions aqueuses de différentes particules en utilisant les techniques acquises pendant mon travail de thèse, et en essayant de comprendre les propriétés physiques du liquide le plus important pour notre vie : l'eau.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.