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The study of Shannon differential entropy function and its associated measures using quantile function are of recent interest among researchers. However, a bivariate extension of the same have not been considered so far. Recently, a new method of deriving bivariate quantile function and their properties in the context of reliability modeling is available in literature. Motivated by this, the present paper introduces and obtain some properties of quantile-based entropy function in the bivariate case. We also examine various properties of bivariate quantile entropy function for residual random variables. Finally, we illustrate the bivariate quantile-based residual entropy function using a suitable lifetime data. [ABSTRACT FROM AUTHOR]

Every nonlinear system grows by increments, and the final probability distributions for components of that system emerge from an amalgamation of these increments. The resulting probability distribution depends on the constraints imposed on each increment by the physical and chemical processes that produce the system. Hence there is the potential that the observed probability distribution can reveal information on these processes. Complex systems that grow by competition between the supply and consumption of energy and mass have growth laws that are cumulative probability distributions for their component parts that reflect such competition. We show that the type of probability distribution is characteristic of the endowment of orogenic gold deposits with the sequence: Weibull → Fréchet → gamma → log normal representative of increasing endowment. Further, the differential entropy of the probability distribution is indicative of the quality of the deposit, with low-quality deposits represented by high entropy and high-quality deposits represented by low or negative entropy. The type of probability distribution gives an indication of the processes that operated to produce the deposit. These conclusions hold for mineralisation as well as for the associated alteration assemblages. We suggest that the probability distribution for the mineralisation or the alteration assemblage gives a good indication of the endowment and quality of a deposit from a single drill hole. A single drill hole from a deposit can provide information on endowment and organisation. Weibull → Fréchet → gamma → log normal probability distributions are representative of increasing gold endowment. The differential entropies of these distributions characterise the organisation of the system. [ABSTRACT FROM AUTHOR]

In this article, we propose three nonparametric estimators for quantile-based Shannon differential entropy function for complete samples. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study are carried out to compare the performance of the proposed estimators and with other important entropy estimators. The usefulness of the new estimators are also illustrated using real data sets. [ABSTRACT FROM AUTHOR]

The state of charge (SOC) is critical for the safety and reliable utilization of the battery. However, SOC estimation accuracy of lithium iron phosphate (LiFePO4) battery is a challenging task because of its flat voltage plateau and its performance is affected greatly by temperature. An improved open circuit voltage (OCV) combined with coulomb counting (CC) method based on the dual input model of ambient temperature and OCV is proposed. This approach is employed to obtain the initial value of SOC based on the dual input model over a wide range of temperature, and to establish SOC estimation model of modified CC with Simulink. The temperature entropy coefficient and differential analysis has been analyzed under different SOC conditions. The SOC maximum errors predicted by the proposed OCV-CC method maintain within 3.10%, while the maximum errors of the traditional OCV-CC increase from 4.78% to 23.64% under the temperature of 35°C ~−15°C. The results show the estimation accuracy of SOC using the proposed OCV-CC method is improved obviously, especially under low temperature. [ABSTRACT FROM AUTHOR]

In this paper, we propose nonparametric kernel estimators for Shannon differential entropy function under length-biased sampling. Asymptotic properties of the estimators are established under suitable regularity conditions. A simulation study is accomplished to compare the performance of proposed estimators. The usefulness of the estimators are also examined using a real data. [ABSTRACT FROM AUTHOR]

The entropy power inequality (EPI) for convolution of two independent random variables was first proposed by Shannon, C. E., 1948. However, in practice, there are many situations in which the involved random variables are not independent. In this article, considering additive noise channels, it is shown that, under some conditions, EPI holds for the case when the involved random variables are dependent. In order to achieve our main result, meanwhile a lower bound for the Fisher information of the output signal is obtained which is useful on its own. An example is also provided to illustrate our result. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) allows us to draw inference about the population parameters more efficiently as compared with that in simple random sampling. Recent publication has shown that using the concomitant information can lead to improved estimation of the cumulative distribution function (CDF) under RSS set up. In this article, new estimators for both in-stratum and overall CDF are proposed. The proposed estimators are then used for estimating the differential entropy, Bohn and Wolfe model and fraction-of-random model. Three new simple tests for the assumption of perfect ranking are also produced. Our simulation results show that the suggested estimators as well as the perfectness tests provide higher efficiency against their competitors. For illustrative purposes, the proposed procedures are applied on empirical data set in the medical field. [ABSTRACT FROM AUTHOR]

The aim of several combustion experiments is the determination of the rate coefficients of important elementary reactions. The experimental conditions are usually selected on the basis of local sensitivity analysis. Shock tube and tubular flow reactor experiments are often designed in such a way that only one reaction step is important at the investigated conditions. Sheen and Manion (J. Phys. Chem. A, 118 (2014) 4929–4941) suggested a method for the design of shock tube experiments based on differential entropy. Their method was modified and extended in this work. In the extended method, both the experimental and residual errors of the measurements are considered at the calculation of the posterior uncertainty of the determined rate parameters, the differential entropy matrix is calculated in an analytical way and the net information flux value is calculated for each suggested experimental point. In an iterative procedure, all investigated experimental points with negative net information flux values are discarded and the remaining experimental conditions are recommended for the measurements. The most valuable candidate experimental points can be determined based on the net information flux values. The method was used for the selection of experimental conditions for the determination of the rate coefficient of reaction NO2 + H = NO + OH at conditions similar to the tubular flow reactor experiments of Alzueta et al. (Energy Fuels, 15 (2001) 724–729). In these experiments, the oxidation of methanol was investigated with and without NO addition. Our method suggested a range of temperature, equivalence ratio and initial NO concentration, where the experimental data carry the most information on the rate coefficient of this elementary reaction. [ABSTRACT FROM AUTHOR]

Centella asiatica L. (CAL) powder contains many medicinal properties that could be subjected to rapid deterioration due to presence of water. Moisture sorption isotherm has been widely used to predict shelf-life and storage stability as well as understanding the sorption mechanism between a material and water molecules. Aims of this study were to analyze the moisture sorption isotherm of CAL powder and its thermodynamic properties (net isosteric heat of sorption, differential entropy, and enthalpy-entropy compensation theory). A study was conducted at three different temperatures (30, 40, and 50 °C) with a range of water activities (0.06–0.92) using static gravimetric method. Results showed that CAL powder demonstrated Type-III moisture sorption isotherm behavior. Peleg isotherms relationship was found to be the most suitable model to describe the sorption isotherm curves followed by BET and Halsey. Furthermore, the net isosteric heat of sorption was determined using Peleg's sorption isotherm model and the results showed exponentially increased as the equilibrium moisture content decreased. Enthalpy-entropy compensation theory was satisfied based on a linear relationship between differential enthalpy and entropy data obtained. Ccompensation theory also indicated that the process is an enthalpy-driven and undergoes a non-spontaneous reaction. [ABSTRACT FROM AUTHOR]

The moisture adsorption isotherms of high-power short time microwave dried paprika (Capsicum annuum L., a pulverized product of dried red pepper) were determined for thermodynamic analysis and assessment of its stability at elevated temperatures. The thermal stability of paprika was evaluated based on alterations in quality characteristics due to the interaction of water molecules with sorption sites during the adsorption process. The GAB model constants revealed the physical significance and the exothermic interaction of the water molecules with the sorption sites on the surfaces of the paprika. The differential enthalpy was found to decrease with increasing water activity due to the existence of highly active polar sites on the surface of paprika at low water activity. The differential entropy decreases due to a rise in water activity as molecular water movement was highly restricted at an elevated water activity. The safe water activity levels corresponding to monolayer moisture content (Mo) of paprika at 30°, 40°, 50°, and 60 °C were found to be 0.58, 0.49, 0.43, and 0.30, respectively. Moreover, the acceleration in quality degradation of paprika was found to increase beyond Mo at the respective adsorption temperature. [ABSTRACT FROM AUTHOR]

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions. [ABSTRACT FROM AUTHOR]

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity. [ABSTRACT FROM AUTHOR]

Translations of summary Theories and classifications of defence mechanisms are not unified. This study addresses the psychological system as a dissipative structure which exchanges information with the external and internal world. When using defence mechanisms, the cognitive-affective schema of an individual could remain stable and ordered by excluding psychological entropy, obtaining psychological negentropy or by dissipating the energy of self-presentation. From this perspective, defences can be classified into three basic types: isolation, compensation and self-dissipation. However, not every kind of defence mechanisms can actually help the individual. Non-adaptive defences are just functioning as an effective strategy in the short run but can be a harmful approach in the long run, while adaptive defences could instead help the individual as a long-term mechanism. Thus, we would like to suggest that it is more useful for the individual to use more adaptive defence mechanisms and seek out social or interpersonal support when undergoing psychic difficulties. As this model of defences is theoretical at present, we therefore aim to support and enrich this viewpoint with empirical evidence. [ABSTRACT FROM AUTHOR]

This paper studies the stabilisability and the performance of stochastic disturbance attenuation of a Markov jump linear system whose feedback channel is subject to an additive white Gaussian noise. First an inequality of differential entropy of random vectors under Markov switching is presented. Then by the concept of entropy power and the theory of information, a necessary condition to stabilise the system is obtained. This requires that the signal-to-noise ratio in the feedback channel is bigger than a specified value. Furthermore, to evaluate the performance of disturbance attenuation, a lower bound of the maximum fluctuation of the system state is presented. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm to achieve both global and local contrast enhancement using a new definition of residual spatial entropy of gray levels of an image. Residual spatial entropy is utilized to assign a weight to each gray level which is further used in mapping of input gray levels to output gray levels to achieve global contrast enhancement. A non-linear mapping is applied on transform-domain coefficients of image enhanced globally to perform local contrast enhancement. The algorithm allows to control levels of perceived global and local contrast. New definitions of full-reference relative contrast measures are also introduced. Experimental results show that proposed algorithm produces better or comparable contrast-enhanced images than several state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new class of lifetime distributions. This new class includes several previously known distributions such as those of Chahkandi and Ganjali (2009), Mahmoudi and Jafari (2012), and Nadarajah et al. (2012). This new class of four-parameter distributions allows for flexible failure rate behavior. Indeed, the failure rate function here can be increasing, decreasing, bathtub-shaped or upside-down bathtub-shaped. Several distributional properties of the new class including moments, quantiles and order statistics are studied. An EM algorithm for computing the estimates of the parameters involved is proposed and some maximum entropy characterizations are discussed. Finally, to show the flexibility and potential of the new class of distributions, applications to two real data sets are provided. [ABSTRACT FROM PUBLISHER]

We consider an Anosov diffeomorphismof a Riemannian manifoldand characterize the deformation of the boundary of a small ballinunder the action ofin terms of the volume of a small neighbourhood ofdivided by the volume of. We prove that the logarithm of this ratio divided bytends to the sum of the positive Lyapunov exponents of an arbitrary-invariant ergodic probability measure a.e. with respect to this measure, provided thatincreases not too fast. A statement concerning the measure-theoretic entropy ofis stated as a corollary. [ABSTRACT FROM AUTHOR]

A general global existence result for one-dimensional pressureless Euler/Euler-Poisson systems with or without viscosity is obtained by employing the “sticky particles” model. We first construct entropy solutions for some appropriate scalar conservation laws, then we show that these solutions encode all the information necessary to obtain solutions for the pressureless systems. Another novel contribution is the stability and uniqueness of solutions, which is obtained via a contraction principle in the Wasserstein metric. [ABSTRACT FROM PUBLISHER]

This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the cross diffusions is convex, while the other one is concave. The treatment of such cases involves a general study of the structure of Lyapunov functionals for cross diffusion systems, and the introduction of a new scheme of approximation, which provides simplified proofs of existence. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to define a new approach for the analysis of data collected by means of SERVQUAL questionnaires which is based on the generalized cross entropy (GCE) approach. In this respect, we firstly give a short review about the important role that SERVQUAL plays in the analysis of service quality as well as in the assessment of the competitiveness of public and private organizations. Secondly, we provide a formal definition of GCE approach together with a brief discussion about its features and usefulness. Finally, we show the application of GCE for a SERVQUAL model, based on a patients’ satisfaction case study and we discuss the results obtained by using the proposed GCE-SERVQUAL methodology. [ABSTRACT FROM AUTHOR]

The paper summarizes properties of the pattern complexity for the generalized Thue-Morse sequenceTand the sequence entropy of shiftXTgenerated by that sequence. We give the exact value of the pattern complexity and prove that the value of sequence entropyh∞(XT) is always bounded by log 4. In the second part we deal with the special case ofTdefined by the constant sequence and we find an upper bounding on the value ofh∞(XT). The last theorem joins the properties of the shiftXTwith odometers and shows an odometerGswhereXTis at most 4-to-1 extension of. [ABSTRACT FROM PUBLISHER]

In this paper, we study Friedland's entropy for Zk+-actions, which was introduced by Friedland in 1996. Unlike the traditional definition, it is non-zero for actions whose generators have finite entropy as single transformations. We investigate two types of Zk+-actions: (1)Zk+ -actions on finite graphs, and (2) expanding Zk+-actions on closed Riemannian manifolds, and show that their preimage branch entropies, which rely on the preimage structure of the actions, are zero. Hence, the upper bounds of Friedland's entropy for these Zk+-actions are obtained. [ABSTRACT FROM AUTHOR]

Many metrics of design complexity have been proposed in the literature. Of these, the most popular are information theoretic metrics, such as information content based on Suh's axiomatic theory and differential entropy based on Shannon's information theory. In this paper, we show that these metrics do not provide common sense measures of complexity, and they also do not possess proper mathematical properties. At best, they are geared towards measuring a designs goodness-of-fit rather than its complexity. At least in part, the inappropriate use of these metrics can be attributed to misuse of terms such as ‘entropy’ and ‘minimise information content’. [ABSTRACT FROM AUTHOR]

This work describes preparation, characterization, and a moisture uptake study of silver nanoparticle-loaded calcium alginate films. The equilibrium uptake data was interpreted by various isotherm models. In the lower moisture content range of 0.02 to 0.06, the enthalpy of sorption (ΔH) and differential entropy (ΔS) were 25.25 to 4.82 kJ/mol and 0.07521 to 0.01371 kJ/mol/K, respectively. There was fair correlation between ΔH and ΔS values. Finally, the higher value of isokinetic temperature, TB(i.e., 336.77), as compared to the harmonic mean temperature, Tm(i.e., 302.05), indicated that moisture uptake mechanism was enthalpy driven. [ABSTRACT FROM AUTHOR]

Expressions for the entropy, the Kullback-Leibler information, and the Iα-information are established for distributions of progressively Type-II censored order statistics. These results are used to identify minimum and maximum information censoring plans. In particular, we find minimum and maximum entropy plans for DFR, exponential, Pareto, reflected power, and Weibull distributions. The results for Kullback-Leibler and Iα-information hold for any continuous distribution. [ABSTRACT FROM AUTHOR]

The differential entropy is importantly used in many disciplines, where the estimation of entropy is often the main research objective or the first step toward it. To estimate entropy, plug-in estimators, such as histogram based entropy estimators or kernel based entropy estimators, are commonly used. Especially, though the histogram itself performs poorly in estimating density, the histogram based entropy estimator is often employed due to its computational benefit. Many efforts have been made to understand the properties of the histogram based entropy estimator theoretically, but most of such efforts are restricted to the case of independently and identically distributed (IID) samples. In this article, we show that two histogram-based entropy estimators by Gyórfi and van der Meulen (1987) are almost surely consistent when samples are from a φ-mixing process. A limited simulation study is implemented to compare those two estimators and to investigate their performance for varying intensity of dependency. In addition, we discuss the extension of [image omitted]-consistency of the estimators in IID setting by Hall (1990) to the case of dependent samples. [ABSTRACT FROM AUTHOR]