Conformal deformation of equilibrium measures in normal random ensembles

We investigate the eigenvalue statistics of ensembles of normal random matrices when their order N tends to infinite. In the model, the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of equilibrium measures of normal random ensembles to the real line and give sufficient conditions for it to weakly converge to a Wigner measure.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

The Genetics of Alzheimer`s Disease in Brazil: 10 Years of Analysis in a Unique Population

Alzheimer`s Disease (AD) is the most common type of dementia among the elderly, with devastating consequences for the patient, their relatives, and caregivers. More than 300 genetic polymorphisms have been involved with AD, demonstrating that this condition is polygenic and with a complex pattern of inheritance. This paper aims to report and compare the results of AD genetics studies in case-control and familial analysis performed in Brazil since our first publication, 10 years ago. They include the following genes/markers: Apolipoprotein E (APOE), 5-hidroxytryptamine transporter length polymorphic region (5-HTTLPR), brain-derived neurotrophin factor (BDNF), monoamine oxidase A (MAO-A), and two simple-sequence tandem repeat polymorphisms (DXS1047 and D10S1423). Previously unpublished data of the interleukin-1 alpha (IL-1 alpha) and interleukin-1 beta (IL-1 beta) genes are reported here briefly. Results from others Brazilian studies with AD patients are also reported at this short review. Four local families studied with various markers at the chromosome 21, 19, 14, and 1 are briefly reported for the first time. The importance of studying DNA samples from Brazil is highlighted because of the uniqueness of its population, which presents both intense ethnical miscegenation, mainly at the east coast, but also clusters with high inbreeding rates in rural areas at the countryside. We discuss the current stage of extending these studies using high-throughput methods of large-scale genotyping, such as single nucleotide polymorphism microarrays, associated with bioinformatics tools that allow the analysis of such extensive number of genetics variables, with different levels of penetrance. There is still a long way between the huge amount of data gathered so far and the actual application toward the full understanding of AD, but the final goal is to develop precise tools for diagnosis and prognosis, creating new strategies for better treatments based on genetic profile.

Identification of a novel ligand binding motif in the transthyretin channel

The design of therapeutic compounds targeting transthyretin (TTR) is challenging due to the low specificity of interaction in the hormone binding site. Such feature is highlighted by the interactions of TTR with diclofenac, a compound with high affinity for TTR, in two dissimilar modes, as evidenced by crystal structure of the complex. We report here structural analysis of the interactions of TTR with two small molecules, 1-amino-5-naphthalene sulfonate (1,5-AmNS) and 1-anilino-8-naphthalene sulfonate (1,8-ANS). Crystal structure of TTR: 1,8-ANS complex reveals a peculiar interaction, through the stacking of the naphthalene ring between the side-chain of Lys15 and Leu17. The sulfonate moiety provides additional interaction with Lys15` and a water-mediated hydrogen bond with Thr119`. The uniqueness of this mode of ligand recognition is corroborated by the crystal structure of TTR in complex with the weak analogue 1,5-AmNS, the binding of which is driven mainly by hydrophobic partition and one electrostatic interaction between the sulfonate group and the Lys15. The ligand binding motif unraveled by 1,8-ANS may open new possibilities to treat TTR amyloid diseases by the elucidation of novel candidates for a more specific pharmacophoric pattern. (C) 2009 Published by Elsevier Ltd.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Phytophagous insect fauna tracks host plant responses to exotic grass invasion

The high dependence of herbivorous insects on their host plants implies that plant invaders can affect these insects directly, by not providing a suitable habitat, or indirectly, by altering host plant availability. In this study, we sampled Asteraceae flower heads in cerrado remnants with varying levels of exotic grass invasion to evaluate whether invasive grasses have a direct effect on herbivore richness independent of the current disturbance level and host plant richness. By classifying herbivores according to the degree of host plant specialization, we also investigated whether invasive grasses reduce the uniqueness of the herbivorous assemblages. Herbivorous insect richness showed a unimodal relationship with invasive grass cover that was significantly explained only by way of the variation in host plant richness. The same result was found for polyphagous and oligophagous insects, but monophages showed a significant negative response to the intensity of the grass invasion that was independent of host plant richness. Our findings lend support to the hypothesis that the aggregate effect of invasive plants on herbivores tends to mirror the effects of invasive plants on host plants. In addition, exotic plants affect specialist insects differently from generalist insects; thus exotic plants affect not only the size but also the structural profile of herbivorous insect assemblages.

Invasive grasses and native Asteraceae in the Brazilian Cerrado

Anthropogenic disturbances frequently modify natural disturbance regimes and foster the invasion and spread of nonindigenous species. However, there is some dispute about whether disturbance events or invasive plants themselves are the major factors promoting the local extinction of native plant species. Here, we used a set of savanna remnants comprising a gradient of invasive grass cover to evaluate whether the species richness of Asteraceae, a major component of the Brazilian Cerrado, is affected by invasive grass cover, or alternatively, whether variation in richness can be directly ascribed to disturbance-related variables. Furthermore, we evaluate whether habitat-specialist Asteraceae differ from habitat generalist species in their responses to grass invasion. Abundance and species richness showed unimodal variation along the invasive grass gradient for both total Asteraceae and habitat-generalists. The cerrado-specialist species, however, showed no clear variation from low-to-intermediate levels of grass cover, but declined monotonically from intermediate-to-higher levels. Through a structural equation model, we found that only invasive grass cover had significant effects on both abundance and species density of Asteraceae. The effect of invasive grass cover was especially high on the cerrado-specialist species, whose proportion declined consistently with increasing invasive dominance. Our results support the prediction that invasive grasses reduce the floristic uniqueness of pristine vegetation physiognomies.

A Boolean algebra and a Banach space obtained by push-out iteration

Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(omega)/fin has under CH and in the N(2)-Cohen model. We prove a similar result in the category of Banach spaces. (C) 2011 Elsevier B.V. All rights reserved.

Deterpenation of Bergamot Essential Oil Using Liquid-Liquid Extraction: Equilibrium Data of Model Systems at 298.2 K

The deterpenation of bergamot essential oil can be performed by liquid liquid extraction using hydrous ethanol as the solvent. A ternary mixture composed of 1-methyl-4-prop-1-en-2-yl-cydohexene (limonene), 3,7-dimethylocta-1,6-dien-3-yl-acetate (linalyl acetate), and 3,7-dimethylocta-1,6-dien-3-ol (linalool), three major compounds commonly found in bergamot oil, was used to simulate this essential oil. Liquid liquid equilibrium data were experimentally determined for systems containing essential oil compounds, ethanol, and water at 298.2 K and are reported in this paper. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were lower than 0.0062 in all systems, indicating the good descriptive quality of the molecular models. To verify the effect of the water mass fraction in the solvent and the linalool mass fraction in the terpene phase on the distribution coefficients of the essential oil compounds, nonlinear regression analyses were performed, obtaining mathematical models with correlation coefficient values higher than 0.99. The results show that as the water content in the solvent phase increased, the kappa value decreased, regardless of the type of compound studied. Conversely, as the linalool content increased, the distribution coefficients of hydrocarbon terpene and ester also increased. However, the linalool distribution coefficient values were negatively affected when the terpene alcohol content increased in the terpene phase.

Extraction of free fatty acids from peanut oil and avocado seed oil: Liquid-liquid equilibrium data at 298.2 K

The present paper reports phase equilibrium experimental data for two systems composed by peanut oil or avocado seed oil + commercial oleic acid + ethanol + water at 298.2 K and different water contents in the solvent. The addition of water to the solvent reduces the loss of neutral oil in the alcoholic phase and improves the solvent selectivity. The experimental data were correlated by the NRTL and UNIQUAC models. The global deviations between calculated and experimental values were 0.63 % and 1.08 %, respectively, for the systems containing avocado seed oil. In the case of systems containing peanut oil those deviations were 0.65 % and 0.98 %, respectively. Such results indicate that both models were able to reproduce correctly the experimental data, although the NRTL model presented a better performance.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Aging and stationary properties of non-equilibrium symmetrical three-state models

We consider a non-equilibrium three-state model whose dynamics is Markovian and displays the same symmetry as the three-state Potts model, i.e. the transition rates are invariant under the cyclic permutation of the states. Unlike the Potts model, detailed balance is, in general, not satisfied. The aging and the stationary properties of the model defined on a square lattice are obtained by means of large-scale Monte Carlo simulations. We show that the phase diagram presents a critical line, belonging to the three-state Potts universality class, that ends at a point whose universality class is that of the Voter model. Aging is considered on the critical line, at the Voter point and in the ferromagnetic phase.

Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.