Further results on geometric properties of a family of relative entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

Renyi entropies of free bosons on the torus and holography

We analytically evaluate the Renyi entropies for the two dimensional free boson CFT. The CFT is considered to be compactified on a circle and at finite temperature. The Renyi entropies S-n are evaluated for a single interval using the two point function of bosonic twist fields on a torus. For the case of the compact boson, the sum over the classical saddle points results in the Riemann-Siegel theta function associated with the A(n-1) lattice. We then study the Renyi entropies in the decompactification regime. We show that in the limit when the size of the interval becomes the size of the spatial circle, the entanglement entropy reduces to the thermal entropy of free bosons on a circle. We then set up a systematic high temperature expansion of the Renyi entropies and evaluate the finite size corrections for free bosons. Finally we compare these finite size corrections both for the free boson CFT and the free fermion CFT with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces as its boundary. One-loop corrections in these geometries are entirely determined by quantum numbers of the excitations present in the bulk. This implies that the leading finite size corrections contributions from one-loop determinants of the Chern-Simons gauge field and the Dirac field in the dual geometry should reproduce that of the free boson and the free fermion CFT respectively. By evaluating these corrections both in the bulk and in the CFT explicitly we show that this expectation is indeed true.

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity.

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).

The use of acoustic indices to determine avian species richness in audio-recordings of the environment

Interpreting acoustic recordings of the natural environment is an increasingly important technique for ecologists wishing to monitor terrestrial ecosystems. Technological advances make it possible to accumulate many more recordings than can be listened to or interpreted, thereby necessitating automated assistance to identify elements in the soundscape. In this paper we examine the problem of estimating avian species richness by sampling from very long acoustic recordings. We work with data recorded under natural conditions and with all the attendant problems of undefined and unconstrained acoustic content (such as wind, rain, traffic, etc.) which can mask content of interest (in our case, bird calls). We describe 14 acoustic indices calculated at one minute resolution for the duration of a 24 hour recording. An acoustic index is a statistic that summarizes some aspect of the structure and distribution of acoustic energy and information in a recording. Some of the indices we calculate are standard (e.g. signal-to-noise ratio), some have been reported useful for the detection of bioacoustic activity (e.g. temporal and spectral entropies) and some are directed to avian sources (spectral persistence of whistles). We rank the one minute segments of a 24 hour recording in descending order according to an "acoustic richness" score which is derived from a single index or a weighted combination of two or more. We describe combinations of indices which lead to more efficient estimates of species richness than random sampling from the same recording, where efficiency is defined as total species identified for given listening effort. Using random sampling, we achieve a 53% increase in species recognized over traditional field surveys and an increase of 87% using combinations of indices to direct the sampling. We also demonstrate how combinations of the same indices can be used to detect long duration acoustic events (such as heavy rain and cicada chorus) and to construct long duration (24 h) spectrograms.

Automated diagnosis of Age-related Macular Degeneration using greyscale features from digital fundus images

Age-related Macular Degeneration (AMD) is one of the major causes of vision loss and blindness in ageing population. Currently, there is no cure for AMD, however early detection and subsequent treatment may prevent the severe vision loss or slow the progression of the disease. AMD can be classified into two types: dry and wet AMDs. The people with macular degeneration are mostly affected by dry AMD. Early symptoms of AMD are formation of drusen and yellow pigmentation. These lesions are identified by manual inspection of fundus images by the ophthalmologists. It is a time consuming, tiresome process, and hence an automated diagnosis of AMD screening tool can aid clinicians in their diagnosis significantly. This study proposes an automated dry AMD detection system using various entropies (Shannon, Kapur, Renyi and Yager), Higher Order Spectra (HOS) bispectra features, Fractional Dimension (FD), and Gabor wavelet features extracted from greyscale fundus images. The features are ranked using t-test, Kullback–Lieber Divergence (KLD), Chernoff Bound and Bhattacharyya Distance (CBBD), Receiver Operating Characteristics (ROC) curve-based and Wilcoxon ranking methods in order to select optimum features and classified into normal and AMD classes using Naive Bayes (NB), k-Nearest Neighbour (k-NN), Probabilistic Neural Network (PNN), Decision Tree (DT) and Support Vector Machine (SVM) classifiers. The performance of the proposed system is evaluated using private (Kasturba Medical Hospital, Manipal, India), Automated Retinal Image Analysis (ARIA) and STructured Analysis of the Retina (STARE) datasets. The proposed system yielded the highest average classification accuracies of 90.19%, 95.07% and 95% with 42, 54 and 38 optimal ranked features using SVM classifier for private, ARIA and STARE datasets respectively. This automated AMD detection system can be used for mass fundus image screening and aid clinicians by making better use of their expertise on selected images that require further examination.

Energetics of rare earth manganese perovskites A1-xA ' xMnO3 (A = La, Nd, Y and A ' = Sr, La) systems

High temperature reaction calorimetry using molten lead berate as solvent has been used to study the thermochemistry of NdMnO3, YMnO3, La1-xSrxMnO3 (with 0 < x < 0.5), and Ln(0.5)Ca(0.5)MnO(3) (with Ln = La, Nd, Y), The enthalpies of formation of these multicomponent oxides from their binary constituents have been calculated from the measured enthalpy of drop solution, The energetic stability of the perovskite depends on the size of the A cation, The enthalpy of formation of YMnO3 (smallest A cation) is more endothermic than those of NdMnO3 and LaMnO3. The energetics of the perovskite also depends on the oxidation state of the B site's ions. In the La1-xSrxMnO3 system, the energetic stability of the structure increases with the Mn4+/Mn3+ ratio, The new values of the enthalpies of oxidations, with reliable standard entropies, were used to plot the phase stability diagram of the lanthanum-manganese-oxygen system in the temperature range 300-1100 K, The LaMnO3/MnO phase boundary evaluated in this study agrees with the one published by Atsumi et nl. calculated from thermogravimetric and conductivity measurements.

Gibbs Energy of Formation of Cobalt Divanadium Tetroxide

The Gibbs energy of formation of V2O3-saturated spinel CoV2O4 has been measured in the temperature range 900–1700 K using a solid state galvanic cell, which can be represented as Pt, Co + CoV2O4 + V2O3/(CaO) ZrO2/Co + CoO, Pt. The standard free energy of formation of cobalt vanadite from component oxides can be represented as CoO (rs) + V2O3 (cor) → CoV2O4 (sp), ΔG° = −30,125 − 5.06T (± 150) J mole−1. Cation mixing on crystallographically nonequivalent sites of the spinel is responsible for the decrease in free energy with increasing temperature. A correlation between “second law” entropies of formation of cubic 2–3 spinels from component oxides with rock salt and corundum structures and cation distribution is presented. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that copper vanadite is unstable.

Effect of substituent on the thermodynamics of D-glucopyranoside binding to concanavalin A, pea (Pisum sativum) lectin and lentil (Lens culinaris) lectin

Titration calorimetry measurements of the binding of phenyl-alpha (alpha PhOGlu), 3-methoxy (3MeOGlu), fluorodeoxy and deoxy derivatives of alpha-D-glucopyranose (Glu) to concanavalin A (conA), pea lectin and lentil lectin were performed at approx. 10 and 25 degrees C in 0.01 M dimethylglutaric acid/NaOH buffer, pH 6.9, containing 0.15 M NaCl and Mn2+ and Ca2+ ions. Apparently the 3-deoxy, 4-deoxy and 6-deoxy as well as the 4-fluorodeoxy and 6-fluorodeoxy derivatives of Glu do not bind to the lectins because no heat release was observed on the addition of aliquots of solutions of these derivatives to the lectin solutions. The binding enthalpies, delta H0b, and entropies, delta S0b, determined from the measurements were compared with the same thermodynamic binding parameters for Glu, D-mannopyranoside and methyl-alpha- D-glucopyranoside (alpha MeOGlu). The binding reactions are enthalpically driven with little change in the heat capacity on binding, and exhibit enthalpy-entropy compensation. Differences between the thermodynamic binding parameters can be rationalized in terms of the interactions apparent in the known crystal structures of the methyl-alpha-D-mannopyranoside-conA [Derewenda, Yariv, Helliwell, Kalb (Gilboa), Dodson, Papiz, Wan and Campbell (1989) EMBO J. 8, 2189-2193] and pea lectin-trimanno-pyranoside [Rini, Hardman, Einspahr, Suddath and Carber (1993) J. Biol. Chem. 268, 10126-10132] complexes. Increases in the entropy change on binding are observed for alpha MeOGlu binding to pea and lentil lectin, for alpha PhOGlu binding to conA and pea lectin, and for 3MeOGlu binding to pea lectin relative to the entropy change for Glu binding, and imply that the phenoxy and methoxy substituents provide additional hydrophobic interactions in the complex. Increases in the binding enthalpy relative to that of Glu are observed for deoxy and fluoro derivatives in the C-1 and C-2 positions and imply that these substituents weaken the interaction with the surrounding water, thereby strengthening the interaction with the binding site.

Analysis of dynamics and mechanism of ligand binding to Artocarpus integrifolia agglutinin. A 13C and 19F NMR study

Binding of 13C-labeled N-acetylgalactosamine (13C-GalNAc) and N-trifluoroacetylgalactosamine (19F-GalNAc) to Artocarpus integrifolia agglutinin has been studied using 13C and 19F nuclear magnetic resonance spectroscopy, respectively. Binding of these saccharides resulted in broadening of the resonances, and no change in chemical shift was observed, suggesting that the alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc experience a magnetically equivalent environment in the lectin combining site. The alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc were found to be in slow exchange between free and protein bound states. Binding of 13C-GalNAc was studied as a function of temperature. From the temperature dependence of the line broadening, the thermodynamic and kinetic parameters were evaluated. The association rate constants obtained for the alpha-anomers of 13C-GalNAc and 19F-GalNAc (k+1 = 1.01 x 10(5) M-1.s-1 and 0.698 x 10(5) M-1.s-1, respectively) are in close agreement with those obtained for the corresponding beta-anomers (k+1 = 0.95 x 10(5) M-1.s-1 and 0.65 x 10(5) M-1.s-1, respectively), suggesting that the two anomers bind to the lectin by a similar mechanism. In addition these values are several orders of magnitude slower than those obtained for diffusion controlled processes. The dissociation rate constants obtained are 49.9, 56.9, 42, and 43 s-1, respectively, for the alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc. A two-step mechanism has been proposed for the interaction of 13C-GalNAc and 19F-GalNAc with A. integrifolia lectin in view of the slow association rates and high activation entropies. The thermodynamic parameters obtained for the association and dissociation reactions suggest that the binding process is entropically favored and that there is a small enthalpic contribution.

Mechanism of the addition of alcohols to substituted phenylisothiocyanates : Electrical effects of the substituents on the reaction

The addition reaction of alcohols to substituted phenylisothiocyanates is found to be a second-order reaction. The reaction is catalysed by triethylamine. First-order rate constants of the addition reaction have been determined in excess of ethanol, for a number of substituted phenylisothiocyanates and the rate data give a satisfactory linear correlation with Hammett σ constants of groups. While the energies of activation vary randomly with substitution, the entropies of activation bear a linear relationship to the energies of activation. Infra-red spectra indicate that the thiourethanes which are the products of the addition reaction exist in the thioamide form. The most prominent resonance form which can satisfactorily explain both the kinetic and infrared data, has been suggested.