共查询到20条相似文献,搜索用时 218 毫秒
1.
Muhammed Rasheed Irshad Radhakumari Maya Francesco Buono Maria Longobardi 《Entropy (Basel, Switzerland)》2022,24(1)
Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an -mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out. 相似文献
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Recently, Savaré-Toscani proved that the Rényi entropy power of general probability densities solving the p-nonlinear heat equation in is a concave function of time under certain conditions of three parameters , which extends Costa’s concavity inequality for Shannon’s entropy power to the Rényi entropy power. In this paper, we give a condition of under which the concavity of the Rényi entropy power is valid. The condition contains Savaré-Toscani’s condition as a special case and much more cases. Precisely, the points satisfying Savaré-Toscani’s condition consist of a two-dimensional subset of , and the points satisfying the condition consist a three-dimensional subset of . Furthermore, gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach. 相似文献
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The aim of this paper is to show that -limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on . On the basis of provided examples, we also present how the performed study on the structure of -limit sets is closely connected with the calculation of the topological entropy. 相似文献
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The family of cumulative paired -entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s , with the weights being related to the actual choice of . Again, the asymptotic distribution of the corresponding sample is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel -entropy-related measures are applied to an ordinal time series on the daily level of air quality. 相似文献
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Kornelia M. Batko Izabella
lzak-Prochazka Andrzej
lzak Wioletta M. Bajdur Radomir
urek 《Entropy (Basel, Switzerland)》2022,24(1)
Based on Kedem–Katchalsky formalism, the model equation of the membrane potential () generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ( at the membrane/concentration boundary layers. We present the calculation procedure ( based on novel equations derived in the paper containing the transport parameters of the membrane (, , and ), solutions (, ), concentration boundary layer thicknesses (, ), concentration Raileigh number (), concentration polarization factor (), volume flux (), mechanical pressure difference (), and ratio of known solution concentrations (). From the resulting equation, was calculated for various combinations of the solution concentration ratio (), the Rayleigh concentration number (), the concentration polarization coefficient (), and the hydrostatic pressure difference ). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 () was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m−3 (). It is shown that () depends on the value of one of the factors (i.e., , , and ) at a fixed value of the other three. 相似文献
6.
Pedro Carpena Manuel Gmez-Extremera Pedro A. Bernaola-Galvn 《Entropy (Basel, Switzerland)》2022,24(1)
Detrended Fluctuation Analysis (DFA) has become a standard method to quantify the correlations and scaling properties of real-world complex time series. For a given scale ℓ of observation, DFA provides the function , which quantifies the fluctuations of the time series around the local trend, which is substracted (detrended). If the time series exhibits scaling properties, then asymptotically, and the scaling exponent is typically estimated as the slope of a linear fitting in the vs. plot. In this way, measures the strength of the correlations and characterizes the underlying dynamical system. However, in many cases, and especially in a physiological time series, the scaling behavior is different at short and long scales, resulting in vs. plots with two different slopes, at short scales and at large scales of observation. These two exponents are usually associated with the existence of different mechanisms that work at distinct time scales acting on the underlying dynamical system. Here, however, and since the power-law behavior of is asymptotic, we question the use of to characterize the correlations at short scales. To this end, we show first that, even for artificial time series with perfect scaling, i.e., with a single exponent valid for all scales, DFA provides an value that systematically overestimates the true exponent . In addition, second, when artificial time series with two different scaling exponents at short and large scales are considered, the value provided by DFA not only can severely underestimate or overestimate the true short-scale exponent, but also depends on the value of the large scale exponent. This behavior should prevent the use of to describe the scaling properties at short scales: if DFA is used in two time series with the same scaling behavior at short scales but very different scaling properties at large scales, very different values of will be obtained, although the short scale properties are identical. These artifacts may lead to wrong interpretations when analyzing real-world time series: on the one hand, for time series with truly perfect scaling, the spurious value of could lead to wrongly thinking that there exists some specific mechanism acting only at short time scales in the dynamical system. On the other hand, for time series with true different scaling at short and large scales, the incorrect value would not characterize properly the short scale behavior of the dynamical system. 相似文献
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Ryan Furlong Mirvana Hilal Vincent OBrien Anne Humeau-Heurtier 《Entropy (Basel, Switzerland)》2021,23(10)
Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions ( and , respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both and approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, results in a better classification performance than that extracted by as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis. 相似文献
10.
Iulia-Elena Hirica Cristina-Liliana Pripoae Gabriel-Teodor Pripoae Vasile Preda 《Entropy (Basel, Switzerland)》2022,24(1)
A large family of new -weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result of the paper establishes a link between such a metric and a canonical one. A sufficient condition is found, in order that the two metrics be conformal (or homothetic). In particular, we recover a recent result, established for and for non-weighted relative group entropies. Our conformality condition is “universal”, in the sense that it does not depend on the group exponential. 相似文献
11.
Zehba A. S. Raizah Ammar I. Alsabery Abdelraheem M. Aly Ishak Hashim 《Entropy (Basel, Switzerland)》2021,23(10)
The flow and heat transfer fields from a nanofluid within a horizontal annulus partly saturated with a porous region are examined by the Galerkin weighted residual finite element technique scheme. The inner and the outer circular boundaries have hot and cold temperatures, respectively. Impacts of the wide ranges of the Darcy number, porosity, dimensionless length of the porous layer, and nanoparticle volume fractions on the streamlines, isotherms, and isentropic distributions are investigated. The primary outcomes revealed that the stream function value is powered by increasing the Darcy parameter and porosity and reduced by growing the porous region’s area. The Bejan number and the average temperature are reduced by the increase in , porosity , and nanoparticles volume fractions . The heat transfer through the nanofluid-porous layer was determined to be the best toward high rates of Darcy number, porosity, and volume fraction of nanofluid. Further, the local velocity and local temperature in the interface surface between nanofluid-porous layers obtain high values at the smallest area from the porous region (), and in contrast, the local heat transfer takes the lower value. 相似文献
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Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for . Its relationship to Kolmogorov–Sinai entropy and, for , to the recently introduced symbolic correlation integral are touched. 相似文献
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Humaira Kalsoom Miguel Vivas-Cortez Muhammad Idrees Praveen Agarwal 《Entropy (Basel, Switzerland)》2021,23(11)
In this work, first, we consider novel parameterized identities for the left and right part of the -analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized -trapezoid and parameterized -midpoint type integral inequalities via -quasiconvex function. By changing values of parameter , some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the -quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained. 相似文献
14.
Carlos Granero-Belinchn Stphane G. Roux Nicolas B. Garnier 《Entropy (Basel, Switzerland)》2021,23(12)
We introduce an index based on information theory to quantify the stationarity of a stochastic process. The index compares on the one hand the information contained in the increment at the time scale of the process at time t with, on the other hand, the extra information in the variable at time t that is not present at time . By varying the scale , the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale. Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is. We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements. 相似文献
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Muhammad Waqas Huai-Min Chen Guang-Xiong Peng Abd Al Karim Haj Ismail Muhammad Ajaz Zafar Wazir Ramoona Shehzadi Sabiha Jamal Atef AbdelKader 《Entropy (Basel, Switzerland)》2021,23(10)
We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were , , , , and . We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease. 相似文献
16.
We study the viable Starobinsky dark energy model in spatially non-flat FLRW backgrounds, where with and representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky gravity and the density parameter of curvature . In particular, we find the model and density parameters to be at 68% C.L. and at 95% C.L., respectively. The best fitting result shows that , indicating that the viable gravity model is consistent with CDM when is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of and CDM models in the non-flat universe. 相似文献
17.
Yinnian He 《Entropy (Basel, Switzerland)》2021,23(12)
In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair . The method consists of transmitting the finite element solution of the 3D steady Navier–Stokes equations into the finite element solution pairs based on the finite element space pair of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair satisfies the discrete inf-sup condition in a 3D domain . Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to of the FE solution to the exact solution of the 3D steady Navier–Stokes equations in the norm. Finally, we also give the convergence order with respect to of the FE velocity to the exact velocity u of the 3D steady Navier–Stokes equations in the norm. 相似文献
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The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space involving internal variables as additional state variables. The IEQ macrostates are unique in and have no memory just as EQ macrostates are in the EQ state space . The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature T of a system, thus fulfilling Planck’s dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheatflows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat converts the Clausius inequality for a system in a medium at temperature into the Clausius equality, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc. 相似文献
20.
Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA . Then, and are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive. 相似文献