RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.

Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.

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 COMPRESSIBLE POTENTIAL FLOW

Compressible （full） potential flow is expressed as an equivalent first-order system of conservation laws for density ρ and velocity v. Energy E is shown to be the only nontrivial entropy for that system in multiple space dimensions, and it is strictly convex in ρ, v if and only if ｜v｜ 〈 c. For motivation some simple variations on the relative entropy theme of Dafer- mos/DiPerna are given, for example that smooth regions of weak entropy solutions shrink at finite speed, and that smooth solutions force solutions of singular entropy-compatible per- turbations to converge to them. We conjecture that entropy weak solutions of compressible potential flow are unique, in contrast to the known counterexamples for the Euler equations.

Relative entropy entanglement for as a measure of Gaussian states

In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example, the relative entanglement for a two-mode squeezed thermal state has been obtained.

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.

Relative entropy of entanglement of two-qubit 'X' states

Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit ＇X＇ state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ＇X＇ state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.

New Retrieval Method Based on Relative Entropy for LanguageModeling with Different Smoothing Methods

A language model for information retrieval is built by using a query language model to generate queries and a document language model to generate documents. The documents are ranked according to the relative entropies of estimated document language models with respect to the estimated query language model. Two popular and relatively efficient smoothing methods, the Jelinek- Mercer method and the absolute discounting method, are used to smooth the document language model in estimation of the document language, A combined model composed of the feedback document language model and the collection language model is used to estimate the query model. A performacne comparison between the new retrieval method and the existing method with feedback is made, and the retrieval performances of the proposed method with the two different smoothing techniques are evaluated on three Text Retrieval Conference （TREC） data sets. Experimental results show that the method is effective and performs better than the basic language modeling approach; moreover, the method using the Jelinek-Mercer technique performs better than that using the absolute discounting technique, and the perfomance is sensitive to the smoothing peramters.

Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap

With the help of relative entropy theory,norm theory,and bootstrap methodology,a new hypothesis testing method is proposed to verify reliability with a three-parameter Weibull distribution.Based on the relative difference information of the experimental value vector to the theoretical value vector of reliability,six criteria of the minimum weighted relative entropy norm are established to extract the optimal information vector of the Weibull parameters in the reliability experiment of product lifetime.The rejection region used in the hypothesis testing is deduced via the area of intersection set of the estimated truth-value function and its confidence interval function of the three-parameter Weibull distribution.The case studies of simulation lifetime,helicopter component failure,and ceramic material failure indicate that the proposed method is able to reflect the practical situation of the reliability experiment.

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.

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].

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.

Quantum entanglement between the two-mode fields and atomic entropy squeezing in the system of a moving atom interacting with two-mode entangled coherent field

This paper investigates the entropy squeezing of a moving two-level atom interacting with the two-mode entangled coherent field via two-photon transition by using an entropic uncertainty relation and the degree of entanglement between the two-mode fields by using quantum relative entropy.The results obtained from numerical calculation indicate that the squeezed period,the duration of entropy squeezing and the maximal squeezing can be controlled by appropriately choosing the intensity of the light field,the atomic motion and the field-mode structure.The atomic motion leads to the periodic recovery of the initial maximal degree of entanglement between the two-mode fields.Moreover,there exists a corresponding relation between the time evolution properties of the atomic entropy squeezing and those of the entanglement between the two-mode fields.

Risk Assessment of Diary Cattle Brucellosis Based on Systematic Multilevel Grey Relation Entropy Method

[Objective] The study was to explore the major factors affecting diary cattle brucellosis risk assessment,as well as their strong-to-weak sequence,so as to provide theoretical basis for assessing diary cattle brucellosis risk level in different regions.[Method] From 4 dimensions of feeding and importing,breeding,housing and polyculture situation,an evaluation index system was set up,and diary cattle brucellosis risk survey was conducted in 3 typical regions.Finally,systematic multilevel grey relation entropy method was applied to perform data analysis.[Result] The strong-to-weak sequence of Level 1 impact factor of diary cattle brucellosis was as follows：feeding and importinghousingpolyculture situationbreeding;the sequence of Level 2 impact factor was U32〉U12〉U11〉U31〉U21〉U42〉U43〉U23〉U22〉U41;the risk level sequence of 3 typical regions was Province A（County A1,A2,A3）Province B（County B1,B2,B3）Province C（County C1,C2,C3）.[Conclusion] According to the weight of Level 1 index strata,administrative departments at all levels and dairy cattle farmers should lay emphasis on the aspects of feeding,importing and housing;viewed from the perspective of Level 2 index strata,dairy cattle farmers should value the siting of cattle field,the brucellosis surveillance before importing and milking modes most.According to the diary cattle brucellosis risk level of 3 typical regions,if administrative departments at all levels strengthen peoples＇ awareness of their personal health and increase investment in this area,with new healthy cultured atmosphere built,the risk level of diary cattle brucellosis will surly decline.

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.

Information Entropy Squeezing for a Atom in Mode-Mode Competition System

The entropy squeezing properties for a two-level atom interacting with a two-mode field via two differentcompeting transitions are investigated from a quantum information point of view.The influences of the initial state of thesystem and the relative coupling strength between the atom and the field on the atomic information entropy squeezingare discussed.Our results show that the squeezed direction and the frequency of the information entropy squeezing canbe controlled by choosing the phase of the atom dipole and the relative competing strength of atom-field,respectively.We find that,under the same condition,no atomic variance squeezing is predicted from the HUR while optimal entropysqueezing is obtained from the EUR,so the quantum information entropy is a remarkable precision measure for theatomic squeezing in the considered system.

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic ＂Landau＂ potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.

Expanded Relative Operator Entropies and Operator Valued α-Divergence

For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 Since A #0,r B = A and A #l,r B = B, weregard A#t,rB as apath combining A and B.Our aim is to show the essential properties of St,r （AIB）. The Tsallis relative operator entropy by Yanagi, Kuriyama and Furuichi can also be expanded, and by using this, we can give an expanded operator valued a-divergence and obtain its properties.

Measures of Variability for Qualitative Variables Using the R Software

Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.