ACTIVE NETWORKS THAT MAXIMIZE THE AMOUNT OF INFORMATION TRANSMISSION

This work clarifies the relationship between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e. g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.

Atomistic simulations of cosolvent/water mixtures

In this thesis, atomistic simulations are performed to investigate hydrophobic solvation and hydrophobic interactions in cosolvent/water binary mixtures. Many cosolvent/water binary mixtures exhibit non-ideal behavior caused by aggregation at the molecular scale level although they are stable and homogenous at the macroscopic scale. Force-field based atomistic simulations provide routes to relate atomistic-scale structure and interactions to thermodynamic solution properties. The predicted solution properties are however sensitive to the parameters used to describe the molecular interactions. In this thesis, a force field for tertiary butanol (TBA) and water mixtures is parameterized by making use of the Kirkwood-Buff theory of solution. The new force field is capable of describing the alcohol-alcohol, water-water and alcohol-water clustering in the solution as well as the solution components’ chemical potential derivatives in agreement with experimental data. With the new force field, the preferential solvation and the solvation thermodynamics of a hydrophobic solute in TBA/water mixtures have been studied. First, methane solvation at various TBA/water concentrations is discussed in terms of solvation free energy-, enthalpy- and entropy- changes, which have been compared to experimental data. We observed that the methane solvation free energy varies smoothly with the alcohol/water composition while the solvation enthalpies and entropies vary nonmonotonically. The latter occurs due to structural solvent reorganization contributions which are not present in the free energy change due to exact enthalpy-entropy compensation. It is therefore concluded that the enthalpy and entropy of solvation provide more detailed information on the reorganization of solvent molecules around the inserted solute. Hydrophobic interactions in binary urea/water mixtures are next discussed. This system is particularly relevant in biology (protein folding/unfolding), however, changes in the hydrophobic interaction induced by urea molecules are not well understood. In this thesis, this interaction has been studied by calculating the free energy (potential of mean force), enthalpy and entropy changes as a function of the solute-solute distance in water and in aqueous urea (6.9 M) solution. In chapter 5, the potential of mean force in both solution systems is analyzed in terms of its enthalpic and entropic contributions. In particular, contributions of solvent reorganization in the enthalpy and entropy changes are studied separately to better understand what are the changes in interactions in the system that contribute to the free energy of association of the nonpolar solutes. We observe that in aqueous urea the association between nonpolar solutes remains thermodynamically favorable (i.e., as it is the case in pure water). This observation contrasts a long-standing belief that clusters of nonpolar molecules dissolve completely in the presence of urea molecules. The consequences of our observations for the stability of proteins in concentrated urea solutions are discussed in the chapter 6 of the thesis.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

The Lum–Chandler–Weeks theory of hydrophobicity [Lum, K., Chandler, D. & Weeks, J. D. (1999) J. Phys. Chem. 103, 4570–4577] is applied to treat the temperature dependence of hydrophobic solvation in water. The application illustrates how the temperature dependence for hydrophobic surfaces extending less than 1 nm differs significantly from that for surfaces extending more than 1 nm. The latter is the result of water depletion, a collective effect, that appears at length scales of 1 nm and larger. Because of the contrasting behaviors at small and large length scales, hydrophobicity by itself can explain the variable behavior of entropies of protein folding.

Deuterium isotope effect on the intramolecular electron transfer in Pseudomonas aeruginosa azurin

Intramolecular electron transfer in azurin in water and deuterium oxide has been studied over a broad temperature range. The kinetic deuterium isotope effect, kH/kD, is smaller than unity (0.7 at 298 K), primarily caused by the different activation entropies in water (−56.5 J K−1 mol−1) and in deuterium oxide (−35.7 J K−1 mol−1). This difference suggests a role for distinct protein solvation in the two media, which is supported by the results of voltammetric measurements: the reduction potential (E0′) of Cu2+/+ at 298 K is 10 mV more positive in D2O than in H2O. The temperature dependence of E0′ is also different, yielding entropy changes of −57 J K−1 mol−1 in water and −84 J K−1 mol−1 in deuterium oxide. The driving force difference of 10 mV is in keeping with the kinetic isotope effect, but the contribution to ΔS‡ from the temperature dependence of E0′ is positive rather than negative. Isotope effects are, however, also inherent in the nuclear reorganization Gibbs free energy and in the tunneling factor for the electron transfer process. A slightly larger thermal protein expansion in H2O than in D2O (0.001 nm K−1) is sufficient both to account for the activation entropy difference and to compensate for the different temperature dependencies of E0′. Thus, differences in driving force and thermal expansion appear as the most straightforward rationale for the observed isotope effect.

Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

Interpretation of the temperature dependence of equilibrium and rate constants

The objective of this review is to draw attention to potential pitfalls in attempts to glean mechanistic information from the magnitudes of standard enthalpies and entropies derived from the temperature dependence of equilibrium and rate constants for protein interactions. Problems arise because the minimalist model that suffices to describe the energy differences between initial and final states usually comprises a set of linked equilibria, each of which is characterized by its own energetics. For example, because the overall standard enthalpy is a composite of those individual values, a positive magnitude for AHO can still arise despite all reactions within the subset being characterized by negative enthalpy changes: designation of the reaction as being entropy driven is thus equivocal. An experimenter must always bear in mind the fact that any mechanistic interpretation of the magnitudes of thermodynamic parameters refers to the reaction model rather than the experimental system For the same reason there is little point in subjecting the temperature dependence of rate constants for protein interactions to transition-state analysis. If comparisons with reported values of standard enthalpy and entropy of activation are needed, they are readily calculated from the empirical Arrhenius parameters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Isomeric distribution and catalyzed isomerization of cobalt(III) complexes with pentadentate macrocyclic ligands. Importance of hydrogen bonding

We have investigated the isomeric distribution and rearrangement of complexes of the type [CoXLn](2+,3+) (where X = Cl-, OH-, H2O, and L-n represents a pentadentate 13-, 14-, and 15-membered tetraaza or diaza-dithia (N-4 or N2S2) macrocycle bearing a pendant primary amine). The preparative procedures for chloro complexes produced almost exclusively kinetically preferred cis isomers (where the pendant primary amine is cis to the chloro ligand) that can be separated by careful cation-exchange chromatography. For L-13 and L-14 the so-called cis-V isomer is isolated as the kinetic product, and for L-15 the cis-VI form (an N-based diastereomer) is the preferred, while for the L-14(S) complex both cis-V and trans-I forms are obtained. All these complexes rearrange to form stable trans isomers in which the pendent primary amine is trans to the monodentate aqua or hydroxo ligand, depending on pH and the workup procedure. In total 11 different complexes have been studied. From these, two different trans isomers of [CoCIL14S](2+) have been characterized crystallographically for the first time in addition to a new structure of cis-V-[CoCIL14S](2+); all were isolated as their chloride perchlorate salts. Two additional isomers have been identified and characterized by NMR as reaction intermediates. The remaining seven forms correspond to the complexes already known, produced in preparative procedures. The kinetic, thermal, and baric activation parameters for all the isomerization reactions have been determined and involve large activation enthalpies and positive volumes of activation. Activation entropies indicate a very important degree of hydrogen bonding in the reactivity of the complexes, confirmed by density functional theory studies on the stability of the different isomeric forms. The isomerization processes are not simple and even some unstable intermediates have been detected and characterized as part of the above-mentioned 11 forms of the complexes. A common reaction mechanism for the isomerization reactions has been proposed for all the complexes derived from the observed kinetic and solution behavior.

Influential DMUs and outlier detection in data envelopment analysis with an application to health care

This paper explains some drawbacks on previous approaches for detecting influential observations in deterministic nonparametric data envelopment analysis models as developed by Yang et al. (Annals of Operations Research 173:89-103, 2010). For example efficiency scores and relative entropies obtained in this model are unimportant to outlier detection and the empirical distribution of all estimated relative entropies is not a Monte-Carlo approximation. In this paper we developed a new method to detect whether a specific DMU is truly influential and a statistical test has been applied to determine the significance level. An application for measuring efficiency of hospitals is used to show the superiority of this method that leads to significant advancements in outlier detection. © 2014 Springer Science+Business Media New York.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Measurement and correlation of the solubility of telmisartan (form A) in nine different solvents from 277.85 to 338.35 K

The solubility of telmisartan (form A) in nine organic solvents (chloroform, dichloromethane, ethanol, toluene, benzene, 2-propanol, ethyl acetate, methanol and acetone) was determined by a laser monitoring technique at temperatures from 277.85 to 338.35 K. The solubility of telmisartan (form A) in all of the nine solvents increased with temperature as did the rates at which the solubility increased except in chloroform and dichloromethane. The mole fraction solubility in chloroform is higher than that in dichloromethane, which are both one order of magnitude higher than those in the other seven solvents at the experimental temperatures. The solubility data were correlated with the modified Apelblat equation and λh equations. The results show that the λh equation is in better agreement with the experimental data than the Apelblat equation. The relative root mean square deviations (σ) of the λh equation are in the range from 0.004 to 0.45 %. The dissolution enthalpies, entropies and Gibbs energies of telmisartan in these solvents were estimated by the Van’t Hoff equation and the Gibbs equation. The melting point and the fusion enthalpy of telmisartan were determined by differential scanning calorimetry.

Desorption isotherms and thermodynamics properties of anchovy in natura and enzymatic modified paste

The thermodynamic properties of anchovy fillets and enzymatic modified pastes in two hydrolysis degrees (3% HD and 14% HD), at 50, 60 and 70 C were evaluated. The GAB model was used to calculate the values of the monolayer moisture content and the thermodynamic properties of the samples. The enzymatic modification led to the increases of the superficial area and differential enthalpies, and decrease of the differential entropies in relation the samples in natura. The enthalpy–entropy compensation showed that the process was controlled by the enthalpy, it was only spontaneous for the samples in natura. Pore size decreased with enzymatic modification, and all samples were in the limit of region between micropores and mesopores (<2 nm) for moisture content of 15%, and mesopores (from 2 to 50 nm) to moisture content above 15%.