Quantal information entropies for atoms

The polynomials occurring in the wave functions of hydrogenic excited states are found to present difficulties for a straightforward analytical approach to the study of associated information entropies. A method is suggested to deal with them. It is then applied to calculate the information entropy for the Jacobi polynomial. A model calculation is presented to examine the effect of screening on the entropy sum. It is seen that the sum does not depend on the choice of screening.

Entanglement Entropies in One-Dimensional Systems

In the thesis, we discuss some aspects of 1D quantum systems related to entanglement entropies; in particular, we develop a new numerical method for the detection of crossovers in Luttinger liquids, and we discuss the behaviour of Rényi entropies in open conformal systems, when the boundary conditions preserve their conformal invariance.

Analysis of spontaneous MEG activity in mild cognitive impairment and Alzheimer's disease using spectral entropies and statistical complexity measures

Alzheimer's disease (AD) is the most common cause of dementia. Over the last few years, a considerable effort has been devoted to exploring new biomarkers. Nevertheless, a better understanding of brain dynamics is still required to optimize therapeutic strategies. In this regard, the characterization of mild cognitive impairment (MCI) is crucial, due to the high conversion rate from MCI to AD. However, only a few studies have focused on the analysis of magnetoencephalographic (MEG) rhythms to characterize AD and MCI. In this study, we assess the ability of several parameters derived from information theory to describe spontaneous MEG activity from 36 AD patients, 18 MCI subjects and 26 controls. Three entropies (Shannon, Tsallis and Rényi entropies), one disequilibrium measure (based on Euclidean distance ED) and three statistical complexities (based on Lopez Ruiz–Mancini–Calbet complexity LMC) were used to estimate the irregularity and statistical complexity of MEG activity. Statistically significant differences between AD patients and controls were obtained with all parameters (p < 0.01). In addition, statistically significant differences between MCI subjects and controls were achieved by ED and LMC (p < 0.05). In order to assess the diagnostic ability of the parameters, a linear discriminant analysis with a leave-one-out cross-validation procedure was applied. The accuracies reached 83.9% and 65.9% to discriminate AD and MCI subjects from controls, respectively. Our findings suggest that MCI subjects exhibit an intermediate pattern of abnormalities between normal aging and AD. Furthermore, the proposed parameters provide a new description of brain dynamics in AD and MCI.

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).

Entanglement of Low-Energy Excitations in Conformal Field Theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

Discrete cyanide-bridged mixed-valence Co/Fe complexes: Outer-sphere redox behaviour

The outer-sphere redox behaviour of a series of [LnCoIII-NCFeII(CN)(5)](-) (L-n = n-membered pentadentate aza-macrocycle) complexes have been studied as a function of pH and oxidising agent. All the dinuclear complexes show a double protonation process at pH approximate to 2 that produces a shift in their UV/Vis spectra. Oxidation of the different non-protonated and diprotonated complexes has been carried out with peroxodisulfate, and of the non-protonated complexes also with trisoxalatocobaltate(III). The results are in agreement with predictions from the Marcus theory. The oxidation of [Fe(phen)(3)](3+) and [IrCl6](2-) is too fast to be measured, although for the latter the transient observation of the process has been achieved at pH = 0. The study of the kinetics of the outer-sphere redox process, with the S2O82- and [Co(ox)(3)](3-) oxidants, has been carried out as a function of pH, temperature, and pressure. As a whole, the values found for the activation volumes, entropies, and enthalpies are in the following margins, for the diprotonated and non-protonated dinuclear complexes, respectively: DeltaV(not equal) from 11 to 13 and 15 to 20 cm(3) mol(-1); DeltaS(not equal) from 110 to 30 and -60 to -90 J K-1 mol(-1); DeltaH(not equal) from 115 to 80 and 50 to 65 kJ.mol(-1). The thermal activation parameters are clearly dominated by the electrostriction occurring on outer-sphere precursor formation, while the trends found for the values of the volume of activation indicate an important degree of tuning due to the charge distribution during the electron transfer process. The special arrangement on the amine ligands in the isomer trans[(L14CoNCFeII)-N-III(CN)(5)](-) accounts for important differences in solvent-assisted hydrogen bonding occurring within the outer-sphere redox process, as has been established in redox reactions of similar compounds. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003).

Classification Performance of Multilayer Perceptrons with Different Risk Functionals

In the present paper we assess the performance of information-theoretic inspired risks functionals in multilayer perceptrons with reference to the two most popular ones, Mean Square Error and Cross-Entropy. The information-theoretic inspired risks, recently proposed, are: HS and HR2 are, respectively, the Shannon and quadratic Rényi entropies of the error; ZED is a risk reflecting the error density at zero errors; EXP is a generalized exponential risk, able to mimic a wide variety of risk functionals, including the information-thoeretic ones. The experiments were carried out with multilayer perceptrons on 35 public real-world datasets. All experiments were performed according to the same protocol. The statistical tests applied to the experimental results showed that the ubiquitous mean square error was the less interesting risk functional to be used by multilayer perceptrons. Namely, mean square error never achieved a significantly better classification performance than competing risks. Cross-entropy and EXP were the risks found by several tests to be significantly better than their competitors. Counts of significantly better and worse risks have also shown the usefulness of HS and HR2 for some datasets.

Interacción en los Sistemas Biológicos mediante nuevos índices basados en la Dinámica No Lineal

La majoria de sistemes biològics són complexes, formats per diverses parts connectades mitjançant vincles que contenen informació addicional i oculta a l’observador. Actualment, les aplicacions clíniques enregistren molts i diversos senyals les interaccions dels quals poden ésser estudiades mitjançant diferents tècniques: mètodes clàssics, generalment lineals, com ara la correlació i la coherència espectral; i mètodes no lineals que han estat definits i desenvolupats l’última dècada, com la predicció no lineal, la informació mútua i les entropies. Aquest projecte proposava l’obtenció d’eines pera l’anàlisi de: a) la coordinació dels músculs respiratoris en individus sans i pacients amb patologies respiratòries sotmesos a protocols d’esforç ventilatori, ja que es desconeix com es relacionen les activitats del diafragma i dels músculs accessoris de les vies aèries superiors; b)l’efecte de fàrmacs sobre la connectivitat funcional del cervell, ja que les eines i mètodes estàndard sovint no permeten extreure prou informació. Els resultats aconseguits han permès avaluar l’activitat muscular respiratòria mitjançant la funció d’informació mútua creuada (FIMC), demostrant que existeix un acoblament no lineal entre les activitats de diferents músculs. Aquesta coordinació muscular es veu afectada per una malaltia respiratòria com la Síndrome d’Apnea Obstructiva de la Son (SAOS), i s’han trobat diferències estadísticament significatives entre els pacients amb SAOS i els individus sans, especialment a nivells mitjans i alts d’esforç respiratori.

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Black holes as fundamental strings: Comparing the absorption of scalars

The recently proposed correspondence principle of Horowitz and Polchinski provides a concrete means to relate (among others) black holes with electric Neveu-SchwarzNeveu-Schwarz charges to fundamental strings and correctly match their entropies. We further test this correspondence by examining the greybody factors in the absorption rates of neutral, minimally coupled scalars by a near extremal black hole. Perhaps surprisingly, the results disagree in general with the absorption by weakly coupled strings. Though this does not disprove the correspondence, it indicates that it might not be simple in this region of the black hole parameter space.

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context.

Funciones termodinámicas relativas a la transferencia del ketoprófen desde el agua hasta algunos sistemas orgánicos

The thermodynamics of molal partitioning of ketoprofen (KTP) was studied in cyclohexane/buffer (CH/W), octanol/buffer (ROH/W), and dimyristoyl phosphatidylcholine (DMPC), dipalmitoyl phosphatidylcholine (DPPC), and egg lecithin (EGG/W) liposome systems. In all cases the partition coefficients (Kmo/w)were greater than unity; therefore the standard free energies of transfer were negative indicating affinity of KTP for organic media. The Kmo/w values were approximately seventy-fold higher in the ROH/W system compared with the CH/W system. On the other hand, the Kmo/w values were approximately ten or fifty-fold higher in the liposomes compared with the ROH/W system. In all cases, the standard enthalpies and entropies of transfer of KTP were positive indicating some degree of participation of the hydrophobic hydration on partitioning processes.

Thermodynamic quantities of solvation and dilution for some acetanilide derivatives in octanol and water mutually saturateds

Based on published thermodynamic quantities for solution, partitioning and sublimation of acetanilide (ACN), acetaminophen (ACP) and Phenacetin (PNC), the thermodynamic quantities for drugs solvation in octanol-saturated water (W(ROH)) and water-saturated octanol (ROH(W)) as well as the drugs dilution in ROH(W) were calculated. The Gibbs energies of solvation were favourable in all cases. The respective enthalpies and entropies were negative indicating an enthalpy-driving for the solvation process in all cases. On the other hand, the Gibbs energies of dilution were favourable for ACP and PNC but unfavourable for ACN, whereas the respective enthalpies and entropies were negative for ACP and PNC but positive for ACN indicating enthalpy-driving for the dilution process in the case of the former drugs and entropy-driving for the latter. From the obtained values for the transfer processes, an interpretation based on solute-solvent interactions was developed.

The kinetics and mechanism of the thermal decomposition of bis diphenyl methyl and related peroxides in liquid phase /|nby C. Thankachan. -- 260 St. Catharines, Ont. : [s. n.],

Rates and products have been determined for the thermal decomposition of bis diphenyl methyl peroxide and diphenyl methyl tert* butyl peroxide at 110@~145@C* The decomposition was uniformly unimolecular with activation energies for the bis diphenyl methyl peroxide in tetrachloroethylene* toluene and nitrobenzene 26,6* 28*3f and 27 Kcals/mole respectively. Diphenyl methyl tert* butyl peroxide showed an activation energy of 38*6 Kcals/mole* About 80-90% of the products in the case of diphenyl methyl peroxide could be explained by the concerted process, this coupled with the negative entropies of activation obtained is a conclusive evidence for the reaction adopting a major concerted path* All the products in the case of diphenyl methyl peroxide could be explained by known reactions of alkoxy radicals* About 80-85% of tert butanol and benzophenone formed suggested far greater cage disproportionation than diffusing apart* Rates of bis triphenyl methyl peroxide have been determined in tetrachloroethylene at 100-120@C* The activation energy was found to be 31 Kcals/mole*