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Measurement of stochastic entropy production.

Using fluorescence spectroscopy we directly measure entropy production of a single two-level system realized experimentally as an optically driven defect center in diamond. We exploit a recent suggestion to define entropy on the level of a single stochastic trajectory [Seifert, Phys. Rev. Lett. 95, 040602 (2005)10.1103/PhysRevLett.95.040602]. Entropy production can then be split into one of the system itself and one of the surrounding medium. We demonstrate that the total entropy production obeys various exact relations for finite time trajectories.

Journal Article↗

Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence.

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.

Journal Article↗

Phase determination and extension using X-ray multiple diffraction and the maximum-entropy method.

The extension of the phases of the structure factors of the organic crystal C(25)H(25)NO(2) from 77 starting individual phases using the maximum-entropy method is reported. These starting phases were determined from 90 experimental triplet phases calculated from 215 measured psi-scan three-beam and four-beam diffraction profiles obtained with a rotating-anode X-ray source, where the psi scans were around the reciprocal-lattice vectors of the 001, 002 and 003 reflections. The extension of the structure factors with phase values was carried out using the maximum-entropy method for 2040 measured two-beam Bragg diffraction intensities with 77 starting phases and the symmetry of the space group as the constraints. Use of structure-factor triplets as constraints for entropy maximization was also attempted. The minimum chi(2) criteria were applied to the maximum-entropy extrapolation to discern the best phase set to be used as the new constraints for the next step of generating new phases. With this phase-extension procedure, more than 100 phases were determined and an electron-density map at 1.97 A was deduced.

Journal Article↗

Heat capacity and entropy changes of the major isotype of the toad (Bufo) parvalbumin induced by calcium binding.

The possible structural changes in the major isotype of parvalbumin from the toad (Bufo bufo japonicus) skeletal muscle caused by Ca2+ and Mg2+ binding have been analyzed by microcalorimetric titrations. Parvalbumin was titrated with Ca2+ in both the absence and presence of Mg2+ and with Mg2+ in the absence of Ca2+, at pH 7.0, and at 5 degrees, 15 degrees, and 25 degrees C. The two sites in a molecule were equivalent on Mg2(+)-Ca2+ exchange, but distinguishable on Ca2+ and Mg2+ binding. The reactions of parvalbumin with Ca2+ are exothermic at every temperature in both the absence and presence of Mg2+, but those with Mg2+ are always endothermic except for the binding to site 1 at 25 degrees C. The magnitudes of the hydrophobic and internal vibrational contributions to the heat capacity and entropy changes of parvalbumin on Ca2+ and Mg2+ binding and Mg2(+)-Ca2+ exchange have been estimated by the empirical method of Sturtevant [Sturtevant, J. M. (1977) Proc. Natl Acad. Sci. USA 74, 2236-2240]. Although no major conformational changes were noted between Ca2(+)- and Mg2(+)-bound forms of toad parvalbumin, the conformational difference was larger in Ca2+ (or Mg2+) binding to site 1 than site 2. This may indicate that the metal-free form is much less stable than any form with Ca2+ (or Mg2+) bound at one site at least. On Mg2(+)-Ca2+ exchange, the vibrational as well as hydrophobic entropy is only slightly increased in a parallel manner. In contrast, on Ca2+ (or Mg2+) binding, the hydrophobic entropy increases but the vibrational entropy decreases; the former indicates the sequestering of nonpolar groups from the surface to the interior of a molecule, and the latter suggests that the overall structures are tightened on Ca2+ (or Mg2+) binding but loosened on Mg2(+)-Ca2+ exchange. Despite the clear distinctions in the thermodynamic features, the conformational changes of toad parvalbumin are essentially the same as those of the two isotypes of bullfrog parvalbumins on Ca2+ binding and Mg2(+)-Ca2+ exchange.

Animals↗

Can experiments select the configurational component of excess entropy?

Configurational entropy is frequently used to rationalize the structural dynamics of glass-forming liquids. The main problem with this concept is that it is not directly accessible to experiments. We introduce a procedure to estimate the configurational component of the excess entropy of a liquid --specifically, the configurational-entropy contribution from the structural relaxation process-- through a combined investigation of dynamic and thermodynamic properties as functions of temperature and pressure. We test our method on orthoterphenyl, salol, and glycerol, and find that the fraction of excess entropy that arises from structural configurations is about 70% for all three materials.

Journal Article↗

Joint entropy maximization in kernel-based topographic maps.

A new learning algorithm for kernel-based topographic map formation is introduced. The kernel parameters are adjusted individually so as to maximize the joint entropy of the kernel outputs. This is done by maximizing the differential entropies of the individual kernel outputs, given that the map's output redundancy, due to the kernel overlap, needs to be minimized. The latter is achieved by minimizing the mutual information between the kernel outputs. As a kernel, the (radial) incomplete gamma distribution is taken since, for a gaussian input density, the differential entropy of the kernel output will be maximal. Since the theoretically optimal joint entropy performance can be derived for the case of nonoverlapping gaussian mixture densities, a new clustering algorithm is suggested that uses this optimum as its "null" distribution. Finally, it is shown that the learning algorithm is similar to one that performs stochastic gradient descent on the Kullback-Leibler divergence for a heteroskedastic gaussian mixture density model.

Algorithms↗

Relative entropy as a measure of diagnostic information.

Relative entropy is a concept within information theory that provides a measure of the distance between two probability distributions. The author proposes that the amount of information gained by performing a diagnostic test can be quantified by calculating the relative entropy between the posttest and pretest probability distributions. This statistic, in essence, quantifies the degree to which the results of a diagnostic test are likely to reduce our surprise upon ultimately learning a patient's diagnosis. A previously proposed measure of diagnostic information that is also based on information theory (pretest entropy minus posttest entropy) has been criticized as failing, in some cases, to agree with our intuitive concept of diagnostic information. The proposed formula passes the tests used to challenge this previous measure.

Clinical Medicine↗

Entropy of partially polarized light and application to statistical processing techniques.

We have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection tasks.

Journal Article↗

The statistical relationship between the "entropy" of a neuronal signal and its variability.

We used a serial order nonparametric analysis technique to analyze trains of neuronal action potential intervals in terms of classical information theory. We observed a marked correlation between the information theory descriptor, entropy, and several common measures of variability (median interval length, range of interval length, and skewness of the probability density function). The correlation between variability and entropy was accounted for in the following decreasing order: range of intervals, median interval, and skewness. These data suggest a significant relationship between the signal and its variability and entropy, when entropy is calculated by our serial-order pattern detection method.

Action Potentials↗

Entropy concept in relation to brain waves and evoked potentials: critique of a physical approach.

Basar's view that the larger the number of synchronized and coupled participating neural generators, i.e., the lower the entropy of the neural systems, the lower the responsiveness of the system, and vice versa, was reconsidered experimentally and theoretically, in the light of current knowledge about the relationship between EEG states and evoked potentials. It was found that the morphology as well as the magnitude of the somatosensory evoked potentials was the same during synchronized (low entropy) and desynchronized (high entropy) EEG states in normal human subjects. Baclofen caused an increase in the somatosensory evoked potentials without affecting the EEG in unanaesthetized dogs. In the less complicated and more limited systems such as the skeletal muscle and monosynaptic reflex paradigms, an inverse relationship was established between the entropy state and responsiveness. This relationship can be simply explained by the neurophysiological facts such as Na-inactivation process at the excitable membranes and the refractory states of the neural generators. These results are consistent with those from the literature; the evoked potentials are usually large when recorded during synchronized EEG states and vice versa. It is suggested that, at least, the well established neurophysiological facts should not be ignored in physical approaches to neural mechanisms, especially when it concerns highly complex systems such as the brain.

Animals↗

Adolescent psychic entropy: a response to unacknowledged fears.

The purpose of this study was to explore the feasibility of measuring psychic entropy in adolescents and to note the predictability of two variables--gender and grade. The subjects were 22 male and female junior and senior high school Caucasians in a central Kentucky church youth choir. They were given the 20-item Psychic Entropy Measure for Adolescents, which is a list of 20 negatively presented statements rated on a five-point scale. The five highest scoring items specifically reflect the phenomenon of psychic entropy. The findings suggest that unacknowledged adolescent fears may be developmental. The limited sample demonstrated that a revised instrument of the Psychic Entropy Measure for Adolescents could be an effective instrument in therapy.

Adaptation, Psychological↗

Potential energy functions and the role of the conformational entropy of clonidine-like imidazolidines in determining their affinity for alpha-adrenergic receptors.

Energy as a function of the ring interplanar torsional angle was calculated for 12 2-(phenylimino)imidazolidines by the method of perturbation configuration interaction using localized orbitals. The potential energy functions indicate that the molecules may assume any conformation within rather broad limits. The functions were used in calculating the gas phase and solution conformational entropies. The latter were used as the independent variable in regression analysis to derive equations connecting the conformational entropy with pKi (pKi = -log Ki) for [3H]clonidine displacement (literature data). As a comparison, correlations between pKi and several other parameters (modified neglect of diatomic overlap-computed highest occupied and lowest unoccupied molecular orbital energies and dipole moments; pKa; log P; substituent steric parameters) were sought. Correlation coefficients C greater than 0.6 were obtained with the conformational entropy (-0.77), and the ortho steric parameters (-0.71). The correlation with the conformational entropy was not markedly improved by adding other parameters in multiple regression analysis. This result is discussed in terms of the contribution to the ligand-receptor complexation free energy arising from the conformational restriction of the ligands upon binding to the receptor.

Animals↗

Signal transcoding by nonlinear sensory neurons: information-entropy maximization, optimal transfer function, and anti-Hebbian adaptation.

A principle of information-entropy maximization is introduced in order to characterize the optimal representation of an arbitrarily varying quantity by a neural output confined to a finite interval. We then study the conditions under which a neuron can effectively fulfil the requirements imposed by this information-theoretic optimal principle. We show that this can be achieved with the natural properties available to the neuron. Specifically, we first deduce that neural (monotonically increasing and saturating) nonlinearities are potentially efficient for achieving the entropy maximization, for any given input signal. Secondly, we derive simple laws which adaptively adjust modifiable parameters of a neuron toward maximum entropy. Remarkably, the adaptation laws that realize entropy maximization are found to belong to the class of anti-Hebbian laws (a class having experimental groundings), with a special, yet simple, nonlinear form. The present results highlight the usefulness of general information-theoretic principles in contributing to the understanding of neural systems and their remarkable performances for information processing.

Adaptation, Physiological↗

Entropy-based texture analysis of chromatin structure in advanced prostate cancer.

A new texture operator, gray-level entropy matrix (GLEM), was developed, and nine new textural features were extracted from this matrix. These textural features were applied to light microscopy images of nuclei taken from monolayers of advanced prostate cancer cells representing two different prognostic groups: hormone-sensitive (good prognosis) and hormone-resistant (poor prognosis) tumors. A comparison between the classification results obtained from GLEM features and those obtained from standard textural estimators is also discussed. Single features that gave correct classification rates better than 65% were included in a discriminant analysis in order to find the optimal set of features to discriminate between the two prognostic groups in the training data set. The best combination of features includes three GLEM features together with ENTROPY extracted from gray-level cooccurrence matrix, and this combination gave a correct classification rate of 95% using the leaving-one-out technique. The influences of image sharpness and number of cells were also investigated. The features based on entropy or degree of scatter of minute structures can be used to discriminate between hormone-sensitive and hormone-resistant prostate carcinomas.

Cell Nucleus↗

Darwinian fitness, evolutionary entropy and directionality theory.

Two recent articles provide computational and empirical validation of the following analytical fact: the outcome of competition between an invading genotype and that of a resident population is determined by the rate at which the population returns to its original size after a random perturbation. This phenomenon can be quantitatively described in terms of the demographic parameter termed "evolutionary entropy", a measure of the variability in the age at which individuals produce offspring and die. The two articles also validate certain predictions of directionality theory, an evolutionary model that integrates demography and ecology with population genetics. In particular, directionality theory predicts that in populations that spend the greater part of their life cycle in the stationary growth phase, evolution will result in an increase in entropy. These species will be described by a late age of sexual maturity, small progeny sets and a broad reproductive time-span. In populations that undergo large fluctuations in size, however, the evolutionary outcome will be different. When the average size is large, evolution will result in a decrease in entropy-these populations will be described by early age of sexual maturity, large numbers of offspring and narrow reproductive span but when the average size is small, the evolutionary outcome will be random and non-directional.

Age Factors↗

Effects of entropy on the gas-phase pyrolysis of ethyl N,N-dimethylcarbamate.

In this study, we examined the gas-phase pyrolysis of ethyl N,N-dimethylcarbamate theoretically at various theoretical levels. The reaction consists of a two-step mechanism, with N,N-dimethylcarbamic acid and ethylene as reaction intermediates. In the first step, the reaction proceeds via a six-membered cyclic transition state (TS), which is more favorable than that via a four-membered cyclic TS. Here, the contribution of entropy to the overall potential energy surface was found to play an important role in determining the rate-limiting step, which was found to be the second step when viewed in terms of the enthalpy of activation (DeltaH(not equal)), but the first step when entropy changes (-TDeltaS(not equal)) were considered. These results are consistent with experimental findings. Moreover, the experimental activation entropy can be reproduced by using the hindered rotor approximation, which converts some low vibration frequencies that correspond to internal rotational modes into hindered rotors.

Entropy↗

Insights into the local residual entropy of proteins provided by NMR relaxation.

A simple model is used to illustrate the relationship between the dynamics measured by NMR relaxation methods and the local residual entropy of proteins. The expected local dynamic behavior of well-packed extended amino acid side chains are described by employing a one-dimensional vibrator that encapsulates both the spatial and temporal character of the motion. This model is then related to entropy and to the generalized order parameter of the popular "model-free" treatment often used in the analysis of NMR relaxation data. Simulations indicate that order parameters observed for the methyl symmetry axes in, for example, human ubiquitin correspond to significant local entropies. These observations have obvious significance for the issue of the physical basis of protein structure, dynamics, and stability.

Entropy↗

Computation of conformational entropy from protein sequences using the machine-learning method--application to the study of the relationship between structural conservation and local structural stability.

A complete protein sequence can usually determine a unique conformation; however, the situation is different for shorter subsequences--some of them are able to adopt unique conformations, independent of context; while others assume diverse conformations in different contexts. The conformations of subsequences are determined by the interplay between local and nonlocal interactions. A quantitative measure of such structural conservation or variability will be useful in the understanding of the sequence-structure relationship. In this report, we developed an approach using the support vector machine method to compute the conformational variability directly from sequences, which is referred to as the sequence structural entropy. As a practical application, we studied the relationship between sequence structural entropy and the hydrogen exchange for a set of well-studied proteins. We found that the slowest exchange cores usually comprise amino acids of the lowest sequence structural entropy. Our results indicate that structural conservation is closely related to the local structural stability. This relationship may have interesting implications in the protein folding processes, and may be useful in the study of the sequence-structure relationship.

Amino Acid Sequence↗