Generalized Residual Entropy and Upper Record Values

<abstract><p>This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of $ k $-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of $ k $-records, focusing on the aging properties of the component lifetimes. We also expressed the residual $ n $th upper $ k $-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the $ n $th upper $ k $-records. The estimation was performed using both real COVID-19 data and simulated data.</p></abstract>

Entropy as a measure of information and uncertainty can be calculated in a pixel basis through the use of a spatial/spatial-frequency distribution. A normalized windowed pseudo-Wigner distribution (PWD) and the generalized Renyi entropy have been selected to define locally pixel-wise entropy. The PWD has been calculated in a 1-D window basis, adding directionality to the analysis and allowing in such way an anisotropic image evaluation. By means of this, a value of entropy can be assigned to each pixel of the image and therefore a histogram of these entropy values can be obtained. Statistical parameters of such entropy distribution have been derived to define a new image quality metric that can be interpreted as measure associated to the anisotropy of images. The purpose of this paper is to show how such metric constitutes a useful tool to assess both the fidelity and quality of images. Experimental results have been presented for assessing different noisy and blurred images and for the quality evaluation of resolution enhanced images.

The main purpose of this paper is to carry out numerical simulation of the hydrogen storage on exothermic reaction of metal hydride LaNi5 alloy container. In addition to accelerating the reaction speed of the internal metal hydride by internal control tube water-cooled mode, analyze via the application of second law of thermodynamics the principle of entropy generation. Use COMSOL Mutilphysics 4.3 a to engage in finite element method value simulation on two-dimensional axisymmetric model. Also on the premise that the internal control tube parameters the radius ri, the flow rate U meet the metal hydride saturation time, observe the reaction process of two parameters on the tank, entropy distribution and the results of the accumulated entropy. And try to find the internal tube parameter values of the minimum entropy, whose purpose is to be able to identify the reaction process and the reaction results of internal tank's optimum energy conservation.

In the literature, there are well-developed estimation techniques that can be used to measure the reliability in multicomponent stress-strength models when the information about all experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this article, assuming that the components of the system follow generalized Rayleigh distribution, we investigate classical and Bayesian estimation of the reliability of a multicomponent stress-strength model when the available data are reported in terms of record values. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Moreover, two confidence intervals based on the parametric bootstrap methods are presented. The Bayes estimate of the reliability parameter is derived using different loss functions. Because there is no closed form for the Bayes estimate, we use the Markov chain Monte Carlo method to obtain an approximate Bayes estimate and the highest posterior density credible interval of the reliability. To evaluate the performances of different procedures, simulation studies are conducted, and an example of real data sets is provided.

Statistical models involving bivariate data are among the most important areas of statistical theory. Concomitants of $ k $-record values (CKR) are key topics in statistical theory that have not been extensively studied by researchers. In this paper, we derived the marginal distribution of CKR based on the Huang-Kotz Farlie-Gumbel-Morgenstern type Ⅱ (HK–FGM2) family of bivariate distributions. Additionally, we obtained an expression for past extropy associated with the CKR within the HK–FGM2 family. Three related uncertainty measures (the cumulative residual extropy (CREX), cumulative extropy (CEX), and the negative cumulative extropy (NCEX)), were formulated for CKR based on this family. Furthermore, estimation techniques for CREX and NCEX were explored by employing empirical estimators tailored to CKR using the HK–FGM2 family. Finally, we analyzed a computer series system dataset for illustration purposes, providing significant insights into the behavior of CKR uncertainty measures.

We suggest that elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may have a specific entropy. We use the Sersic law to describe the light profile. The specific entropy (the Boltzmann–Gibbs definition) is then calculated assuming that the galaxy behaves as a spherical, isotropic, one-component system. We predict a relation between the three parameters of the Sersic law linked to the specific entropy, defining a surface in the parameter space, an ‘entropic plane’. We have analysed a sample of simulated merging elliptical galaxies (virtual) and a sample of galaxies belonging to the Coma Cluster (real). Both virtual and realgalaxies are: 1) located in their own ‘entropic plane‘ and 2) in this plane, they are located on a straight line, indicating constant entropy: another physical property A careful examination of the value of the specific entropy indicates a very small increase in the specific entropy with the generation after merging (virtual sample). Although one cannot distinguish between various generations for real galaxies, the distribution of specific entropy in this sample is very similar to that in the virtual sample.

We propose a novel approach to identify the difficulty of visual questions for Visual Question Answering (VQA) without direct supervision or annotations to the difficulty. Prior works have considered the diversity of ground-truth answers of human annotators. In contrast, we analyze the difficulty of visual questions based on the behavior of multiple different VQA models. We propose to cluster the entropy values of the predicted answer distributions obtained by three different models: a baseline method that takes as input images and questions, and two variants that take as input images only and questions only. We use a simple k-means to cluster the visual questions of the VQA v2 validation set. Then we use state-of-the-art methods to determine the accuracy and the entropy of the answer distributions for each cluster. A benefit of the proposed method is that no annotation of the difficulty is required, because the accuracy of each cluster reflects the difficulty of visual questions that belong to it. Our approach can identify clusters of difficult visual questions that are not answered correctly by state-of-the-art methods. Detailed analysis on the VQA v2 dataset reveals that 1) all methods show poor performances on the most difficult cluster (about 10% accuracy), 2) as the cluster difficulty increases, the answers predicted by the different methods begin to differ, and 3) the values of cluster entropy are highly correlated with the cluster accuracy. We show that our approach has the advantage of being able to assess the difficulty of visual questions without ground-truth (i.e., the test set of VQA v2) by assigning them to one of the clusters. We expect that this can stimulate the development of novel directions of research and new algorithms.

Foraging mammals exhibit a familiar yet poorly characterized phenomenon, ‘alternation’, a pause to sniff in the air preceded by the animal rearing on its hind legs or raising its head. Rodents spontaneously alternate in the presence of airflow, suggesting that alternation serves an important role during plume-tracking. To test this hypothesis, we combine fully resolved simulations of turbulent odor transport and Bellman optimization methods for decision-making under partial observability. We show that an agent trained to minimize search time in a realistic odor plume exhibits extensive alternation together with the characteristic cast-and-surge behavior observed in insects. Alternation is linked with casting and occurs more frequently far downwind of the source, where the likelihood of detecting airborne cues is higher relative to ground cues. Casting and alternation emerge as complementary tools for effective exploration with sparse cues. A model based on marginal value theory captures the interplay between casting, surging, and alternation.

In the present work, we discuss the cumulative residual entropy of equilibrium distribution of order n. The work provides a generalization of cumulative residual entropy and its dynamic version and also acts as the entropy of a hierarchy of weighted distributions. We provide a comparison of the new entropy with the corresponding Shannon’s entropy and discuss their properties.

The authors demonstrate that all Ising antiferromagnets with arbitrary many-neighboured interactions and in the maximum critical field, have highly degenerate ground states accompanied with non-zero residual entropies. The residual entropies vanish when the range of interaction tends to infinity. The proof is realised by an explicit calculation in the case of a one-dimensional many-neighboured Ising antiferromagnet, and by establishing bounds for the residual entropy in the case of an Ising system situated on a lattice with arbitrary number of dimensions. They also show that the established bounds may serve as estimates of frequently unknown actual values of the residual entropy.

Worst-case distortion riskmetrics and weighted entropy with partial information

The residual magnetic entropy is calculated for the short-range Edwards-Anderson spin-glass model by the Monte Carlo method. For slow cooling, a finite value of the residual magnetic entropy is obtained, which depends only weakly on the cooling rate. A comparison with available information about the total density of states and the density of metastable states suggests that the residual magnetic entropy is determined by the density of metastable states at the residual energy of the spin glass at zero temperature.

This paper presented a fault diagnosis method for key components of satellite, called Anomaly Monitoring Method (AMM), which is made up of state estimation based on Multivariate State Estimation Techniques (MSET) and anomaly detection based on Sequential Probability Ratio Test (SPRT). On the basis of analysis failure of lithium-ion batteries (LIBs), we divided the failure of LIBs into internal failure, external failure, and thermal runaway and selected electrolyte resistance (Re) and the charge transfer resistance (Rct) as the key parameters of state estimation. Then, through the actual in-orbit telemetry data of the key parameters of LIBs, we obtained the actual residual value (RX) and healthy residual value (RL) of LIBs based on the state estimation of MSET, and then, through the residual values (RX and RL) of LIBs, we detected the anomaly states based on the anomaly detection of SPRT. Lastly, we conducted an example of AMM for LIBs, and, according to the results of AMM, we validated the feasibility and effectiveness of AMM by comparing it with the results of threshold detective method (TDM).

This paper presents residual values of Helmholtz energy (Ar/(RT)), entropy (Sr/R), and internal energy (Ur/(RT)) for a ternary mixture that resembles a distribution natural gas between 223.15 K and 303.15 K up to 20 MPa. The methodology uses isochoric and isothermal density measurements to apply corrections to the residuals for Helmholtz energy (δAr/(RT)), entropy (δSr/R), and internal energy (δUr/(RT)) calculated using an equation of state. The method is demonstrated for three representative equations of state: REFPROP, Peng–Robinson, and Redlich–Kwong. Accurate (p−ρ–T) isochoric and isothermal data provide experimental values of the compression factor (Z) and the derivative of pressure with respect to temperature at constant density (∂p/∂T)ρ which are used to calculate residual entropies and energies. The results obtained by using different equations of state at the same conditions have slight differences in the residual values. It is possible to represent those differences by equivalent changes in temperature for entropy (δTS) and internal energy (δTU) that are ≤ 0.5 K for temperatures above 225 K. For this mixture, the values of δAr/(RT), δSr/R, and δUr/(RT) determined from REFPROP are sufficiently small that no corrections are required. For the Peng–Robinson and Redlich–Kwong equations of state, a global fit describing the residual corrections presents a practical application. The residual deviations of the plots lie within ± 0.0005, ± 0.001, and ± 0.002 in the residuals for δAr/(RT), δSr/(RT), and δUr/(RT), respectively.

The heat capacity of propylene oxide has been determined from 11° to 300°K in an automatic low-temperature adiabatic calorimeter. The melting point of propylene oxide is 161.22°±0.05°K and the heat of melting is 1561.4±1.7 cal/mole. The absolute entropy at 298.15°K is 46.91±0.15 cal/mole·°K) which includes a residual entropy of R ln 2 for the entropy of mixing of the optical isomers. The third-law entropy of gaseous propylene oxide at 298.15°K is determined from the entropy of the liquid plus literature data on the heat of vaporization, vapor pressure, and the critical constants. This entropy value is in good agreement with the value determined from statistical thermodynamics using literature data on the fundamental vibrational assignment, the internal rotational barrier, and the entropy of mixing.