RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS

We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity.we also investigate the relations among these.Second,we introduce the notion of a relative dimension set.Moreover,using the method,we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions,which says that if the relative dimension sets of two extensions are different,then the extensions are disjoint.

Coherence measures based on sandwiched Rényi relative entropy

Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory.Baumgratz,Cramer and Plenio established a rigorous framework(BCP framework)for quantifying coherence[Baumgratz T,Cramer M and Plenio M B Phys.Rev.Lett.113140401(2014)].In the present paper,under the BCP framework we provide two classes of coherence measures based on the sandwiched Rényi relative entropy.We also prove that we cannot get a new coherence measure f(C(·))by a function f acting on a given coherence measure C.

Relative Entropy and Mean Li-Yorke Chaos Along Some Good Sequences

In this article,we showed that positive relative entropy implies mean Li-Yorke chaos along some good sequences in the fiber.Our result extended Li and Qiao’s result in[Monatsh.Math.,186(2018),153-173].

Maximum relative entropy of coherence for quantum channels

Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of subsuperchannels and sub-superchannel discrimination. For any quantum channels, we show that the advantage of quantum channels in sub-superchannel discrimination can be exactly characterized by the maximum relative entropy of coherence for quantum channels. Similar to the maximum relative entropy of coherence for channels, the robustness of coherence for quantum channels has also been investigated. We show that the maximum relative entropy of coherence for channels provides new operational interpretations of robustness of coherence for quantum channels and illustrates the equivalence of the dephasing-covariant superchannels,incoherent superchannels, and strictly incoherent superchannels in these two operational tasks.

User selection based on user-union and relative entropy in mobile crowdsensing

A critical issue in mobile crowdsensing(MCS) involves selecting appropriate users from a number of participants to guarantee the completion of a sensing task. Users may upload unnecessary data to the sensing platform, leading to redundancy and low user selection efficiency. Furthermore, using exact values to evaluate the quality of the user-union will further reduce selection accuracy when users form a union. This paper proposes a user selection method based on user-union and relative entropy in MCS. More specifically, a user-union matching scheme based on similarity calculation is constructed to achieve user-union and reduce data redundancy effectively. Then, considering the interval-valued influence, a user-union selection strategy with the lowest relative entropy is proposed. Extensive testing was conducted to investigate the impact of various parameters on user selection. The results obtained are encouraging and provide essential insights into the different aspects impacting the data redundancy and interval-valued estimation of MCS user selection.

Experimental Study on Entropy Features in Machining Vibrations of A Thin-Walled Tubular Workpiece

In machining processes,chatter vibrations are always regarded as one of the major limitations for production quality and efficiency.Accurate and timely monitoring of chatter is helpful to maintain stable machining operations.At present,most chatter monitoring methods are based on the energy level at specified chatter frequencies or frequency bands.However,the spectral features of chatter could change during machining operations due to complexity and time-varying dynamics of the physical machining process.The purpose of this paper is to investigate the time-varying chatter features in turning of thin-walled tubular workpieces from the perspective of entropy.The airborne acoustics was selected as the source of information for machining condition monitoring.First,corresponding to the distinguishing surface topographies relevant to machining conditions,the features of the sound signal emitted during turning of the thin-walled cylindrical workpieces were extracted using the spectral analysis and wavelet packet transform,respectively.It was shown that the dominant vibration frequency as well as the energy distribution could shift with the transition of the machining status.After that,two relative entropy indicators based on the spectrum and the wavelet packet energy were constructed to identify chattering events in turning of the thin-walled tubes.The experimental results demonstrate that the proposed indicators could accurately reflect the transition of machining conditions with high sensitivity and robustness in comparison with the traditional FFT-based methods.The achievement of this study lays the foundations of the online chatter monitoring and control technique for turning of the thin-walled tubular workpieces.

Bounds on positive operator-valued measure based coherence of superposition

Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.

RIGHT MEAN FOR THEα-z BURES-WASSERSTEIN QUANTUM DIVERGENCE

The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean,which provides a new non-commutative version of generalized mean(H?lder mean).We investigate its fundamental properties,and give many interesting operator inequalities with the matrix power mean including the Cartan mean.Moreover,we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.

Tsallis relativeαentropy of coherence dynamics in Grover′s search algorithm

Quantum coherence plays a central role in Grover’s search algorithm.We study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search algorithm.We prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success probability.We show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target states.Moreover,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.

AMENDATORY DEFINITION OF SECURITY FOR STEGANOGRAPHIC SYSTEM

The security of steganographic system is significant in this research field. The security defined by relative entropy D (P C || PS )is widely cited to measure the security of different steg-anographic systems. However,two examples are presented to show that some limitations exist in Cachin’s definition. Based on the analysis of a basal hypothesis testing problem,a very useful con-clusion can be drawn to define the security of steganographic system. According to the above illation,an amendatory definition is presented based on the probability of the empirical probability distribution. With the help of new definition,the relationship between security and capacity can be interpreted clearly,and truly secure steganographic method could be designed.

L^(2)-CONVERGENCE TO NONLINEAR DIFFUSION WAVES FOR EULER EQUATIONS WITH TIME-DEPENDENT DAMPING

In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.

Quantifying coherence with dynamical discord

Quantum coherence and discord are two kinds of manifestations of nonclassicality.By calculating the coherence and discord in the specific bipartite quantum systems,we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations.We show that the coherence bounds the dynamical discord,and under particular conditions of the initial quantum states,the coherence of single systems is equal to the dynamical discord.We extend these results to the multipartite quantum systems.

δ-Calculus:A New Approach to Quantifying Location Privacy

With the rapid development of mobile wireless Internet and high-precision localization devices,location-based services(LBS)bring more convenience for people over recent years.In LBS,if the original location data are directly provided,serious privacy problems raise.As a response to these problems,a large number of location-privacy protection mechanisms(LPPMs)(including formal LPPMs,FLPPMs,etc.)and their evaluation metrics have been proposed to prevent personal location information from being leakage and quantify privacy leakage.However,existing schemes independently consider FLPPMs and evaluation metrics,without synergizing them into a unifying framework.In this paper,a unified model is proposed to synergize FLPPMs and evaluation metrics.In detail,the probabilistic process calculus(calledδ-calculus)is proposed to characterize obfuscation schemes(which is a LPPM)and integrateα-entropy toδ-calculus to evaluate its privacy leakage.Further,we use two calculus moving and probabilistic choice to model nodes’mobility and compute its probability distribution of nodes’locations,and a renaming function to model privacy leakage.By formally defining the attacker’s ability and extending relative entropy,an evaluation algorithm is proposed to quantify the leakage of location privacy.Finally,a series of examples are designed to demonstrate the efficiency of our proposed approach.

A Review on Ranking of Z-numbers

There are numerous studies about Z-numbers since its inception in 2011.Because Z-number concept reflects human ability to make rational decisions,Z-number based multi-criteria decision making problems are one of these studies.When the problem is translated from linguistic information into Z-number domain,the important question occurs that which Z-number should be selected.To answer this question,several ranking methods have been proposed.To compare the performances of these methods,benchmark set of fuzzy Z-numbers has been created in time.There are relatively new methods that their performances are not examined yet on this benchmark problem.In this paper,we worked on these studies which are relative entropy based Z-number ranking method and a method for ranking discrete Z-numbers.The authors tried to examine their performances on the benchmark problem and compared the results with the other ranking algorithms.The results are consistent with the literature,mostly.The advantages and the drawbacks of the methods are presented which can be useful for the researchers who are interested in this area.

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.

Entanglement for a two-parameter class of states in a high-dimension bipartite quantum system

The entanglement for a two-parameter class of states in a high-dimension (m n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er.

A combination weighting model based on iMOEA/D-DE

This paper proposes a combination weighting(CW)model based on iMOEA/D-DE(i.e.,improved multiobjective evolutionary algorithm based on decomposition with differential evolution)with the aim to accurately compute the weight of evaluation methods.Multi-expert weight considers only subjective weights,leading to poor objectivity.To overcome this shortcoming,a multiobjective optimization model of CW based on improved game theory is proposed while considering the uncertainty of combination coefficients.An improved mutation operator is introduced to improve the convergence speed,and thus better optimization results are obtained.Meanwhile,an adaptive mutation constant and crossover probability constant with self-learning ability are proposed to improve the robustness of MOEA/D-DE.Since the existing weight evaluation approaches cannot evaluate weights separately,a new weight evaluation approach based on relative entropy is presented.Taking the evaluation method of integrated navigation systems as an example,certain experiments are carried out.It is proved that the proposed algorithm is effective and has excellent performance.

Hydrodynamic Limit for Exclusion Processes

The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each site.We mostly discuss the symmetric and reversible case.The weakly asymmetric case recently attracts attention related to KPZ equation;cf.Bertini and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time scaling.From this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,respectively.Section 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the particle.This gives a non-trivial interaction among particles.We study only the case that the jump rate satisfies the so-called gradient condition.The hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock estimates.We also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs principle.Section 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic limit.The difference between these two methods is as follows.Let N^(d)be the volume of the domain on which the system is defined(typically,d-dimensional discrete box with side length N)and denote the(relative)entropy by H.Then,H relative to a global equilibrium behaves as H=O(N^(d))(or entropy per volume is O(1))as N→∞.GPV method rather relies on the fact that the entropy production I,which is the time derivative of H,behaves as O(N^(d−2))so that I per volume is o(1),and this characterizes the limit measures.On the other hand,Yau’s method shows H=o(Nd)for H relative to local equilibria so that the entropy per volume is o(1)and this proves the hydrodynamic limit.In Sect.4,we considerKawasaki dynamics perturbed by relatively largeGlauber effect,which allows creation and annihilation of particles.This leads to the reaction–diffusion equation in the hydrodynamic limit.We discuss especially the equation with reaction term of bistable type and the problem related to the fast reaction limit or the sharp interface limit leading to the motion by mean curvature.We apply the estimate on the relative entropy due to Jara and Menezes(Non-equilibrium fluctuations of interacting particle systems,2017;Symmetric exclusion as a random environment:invariance principle,2018),which is actually obtained as a combination of GPV and Yau’s estimates.This makes possible to study the hydrodynamic limit for microscopic systems with another diverging factors apart from that caused by the space–time scaling.

Optimizing soil dissolved organic matter extraction by grey relational analysis

Dissolved organic matter(DOM)in soil plays an important role in the fate and transport o f contaminants.It is typically composed of many compounds,but the effect of different extraction factors on the abundance of different DOM components is unknown.In this study,DOM was extracted from three soils(paddy field,vegetable field and forest soils)with various extraction time,liquid to solid ratios(LSRs).extractant types,and extractant concentrations.The LSR had a significant effect on DOM content,which increased by 0.5-4.0 times among the three soils when LSR increased from 2:1 to 10:1(P<0.05).Dissolved organic matter content increased by 4%-53%when extraction time increased from 10 to 300 min(P<0.05).Extractant concentration had different effects on DOM content depending on the extractant.Higher concentrations of KC1 promoted DOM extraction,while higher concentrations o f KH2PO4 inhibited DOM extraction.Therefore,grey relational analysis was used to further quantitatively evaluate the effect of extraction time,LSR,and extractant concentration on DOM,using KC1 as an extractant.For the paddy field and forest soils,the impact of these three factors on DOM extraction efficiency was in the following order:KC1 concentration>LSR>extraction time.However,the effect was different for the vegetable field soil:LSR>extraction time>KCI concentration.Taking all these factors into account,1.50 mol L^-1 KC1 and an LSR of 10:1 with a shaking time of 300 min was recommended as the most appropriate method for soil DOM extraction.