Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Distance measures to compare real and ideal quantum processes

With growing success in experimental implementations it is critical to identify a gold standard for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate a set of criteria that such a distance measure must satisfy to be both experimentally and theoretically meaningful. We then assess a wide range of possible measures against these criteria, before making a recommendation as to the best measures to use in characterizing quantum information processing.

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Approximate entropy (ApEn) of blood pressure (BP) can be easily measured based on software analysing 24-h ambulatory BP monitoring (ABPM), but the clinical value of this measure is unknown. In a prospective study we investigated whether ApEn of BP predicts, in addition to average and variability of BP, the risk of hypertensive crisis. In 57 patients with known hypertension we measured ApEn, average and variability of systolic and diastolic BP based on 24-h ABPM. Eight of these fifty-seven patients developed hypertensive crisis during follow-up (mean follow-up duration 726 days). In bivariate regression analysis, ApEn of systolic BP (P<0.01), average of systolic BP (P=0.02) and average of diastolic BP (P=0.03) were significant predictors of hypertensive crisis. The incidence rate ratio of hypertensive crisis was 14.0 (95% confidence interval (CI) 1.8, 631.5; P<0.01) for high ApEn of systolic BP as compared to low values. In multivariable regression analysis, ApEn of systolic (P=0.01) and average of diastolic BP (P<0.01) were independent predictors of hypertensive crisis. A combination of these two measures had a positive predictive value of 75%, and a negative predictive value of 91%, respectively. ApEn, combined with other measures of 24-h ABPM, is a potentially powerful predictor of hypertensive crisis. If confirmed in independent samples, these findings have major clinical implications since measures predicting the risk of hypertensive crisis define patients requiring intensive follow-up and intensified therapy.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\'enyi relative entropy formula.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

Entropy, information and doubly stochastic transformations

I analyze two inequalities on entropy and information, one due to von Neumann and a recent one to Schiffer, and show that the relevant quantities in these inequalities are related by special doubly stochastic matrices (DSM). I then use generalization of the first inequality to prove algebraically a generalization of Schiffer's inequality to arbitrary DSM. I also give a second interpretation to the latter inequality, determine its domain of applicability, and illustrate it by using Zeeman splitting. This example shows that symmetric (degenerate) systems have less entropy than the corresponding split systems, if compared at the same average energy. This seemingly counter-intuitive result is explained thermodynamically. © 1991.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Exact Probability Distribution versus Entropy

The problem addressed concerns the determination of the average numberof successive attempts of guessing a word of a certain length consisting of letters withgiven probabilities of occurrence. Both first- and second-order approximations to a naturallanguage are considered. The guessing strategy used is guessing words in decreasing orderof probability. When word and alphabet sizes are large, approximations are necessary inorder to estimate the number of guesses. Several kinds of approximations are discusseddemonstrating moderate requirements regarding both memory and central processing unit(CPU) time. When considering realistic sizes of alphabets and words (100), the numberof guesses can be estimated within minutes with reasonable accuracy (a few percent) andmay therefore constitute an alternative to, e.g., various entropy expressions. For manyprobability distributions, the density of the logarithm of probability products is close to anormal distribution. For those cases, it is possible to derive an analytical expression for theaverage number of guesses. The proportion of guesses needed on average compared to thetotal number decreases almost exponentially with the word length. The leading term in anasymptotic expansion can be used to estimate the number of guesses for large word lengths.Comparisons with analytical lower bounds and entropy expressions are also provided.

Effect of morphodynamics on annual average zonation pattern of benthic macrofauna of exposed sandy beaches in Santa Catarina, Brazil

This study investigated the effect of environmental factors on the annual average zonation pattern of benthic macrofauna of sub-aerial profile of three exposed sandy beaches of Santa Catarina with different morphodynamic characteristics. Sampling was carried out between March 2000 and March 2001, with monthly frequency on reflective and dissipative morphodynamic extremes and bimonthly frequency on the intermediate state. Results showed that macrobenthic zonation presented marked differences across the morphodynamic spectrum. The main differences observed from reflective to dissipative conditions were: a) increase in the number of species in lower zones of the beach; b) expansion of zones characterized by high water content of sediment and c) increase in the overlapping of zones, mainly on lower levels of the beach. Canonical Correspondence Analysis related these differences to distinctive cross-shore gradients in sediment moisture levels, sediment reworking and mean grain size that exist across the morphodynamic spectrum, showing that it is important to analyze these environmental factors in studies conducted to investigate zonation on microtidal exposed sandy beaches.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Genetic analysis of average annual productivity of Nellore breeding cows (COWPROD)

With the aim of estimating the coefficient of heritability of average annual productivity of Nellore cows (COWPROD), a data set from 24,855 animals with known pedigree was analyzed. COWPROD is defined as the amount (in kilograms) of weaned calves produced yearly by one cow during her remaining time in herd ignoring a fixed period of 365 days. COWPROD was calculated regarding three standards: a) based on the post-weaning weight from the calves ignoring any kind of adjustment (COWPROD_NAJ), b) adjusted weight for the fixed effects (COWPROD_AJFIX) and c) adjusted weight for the fixed effects and for the genetic merit of the sire (COWPROD_AJFIN). The obtained heritabilities were 0.15, 0.15 and 0.16 for COWPROD_NAJ, COWPROD_AJFIX and COWPROD_AJFIN, respectively. A complete set composed of 105,158 COWPROD records on 130,740 animals in pedigree was also analyzed for predicting the genetic merit of all animals in the data set and for the calculation of the genetic, phenotypic and residual trends. Ranking correlation was high for the adjusted and non-adjusted data, yet, for some of the animals, the difference among the genetic values was large. This would be an indication that it would be better to work always with the adjusted weaning weights. The genetic trend was positive, but was of small magnitude (0.26% of the trait average) and the residual trend was negative as a consequence of the large intensification of the production system, which has been occurring in the last years in the farms studied. The phenotypic trend was also negative and intermediate between the genetic and the residual ones.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.