In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, the...In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, they are weak in suppressing background noises and worse in segmenting targets with non-uniform gray level. The concept of 2D histogram shape modification is proposed, which is realized by target information prior restraint after enhancing target information using plateau histogram equalization. The formula of 2D minimum Renyi entropy is deduced for image segmentation, then the shape-modified 2D histogram is combined wfth four optimal objective functions （i.e., maximum between-class variance, maximum entropy, maximum correlation and minimum Renyi entropy） respectively for the appli- cation of infrared image segmentation. Simultaneously, F-measure is introduced to evaluate the segmentation effects objectively. The experimental results show that F-measure is an effective evaluation index for image segmentation since its value is fully consistent with the subjective evaluation, and after 2D histogram shape modification, the methods of optimal objective functions can overcome their original forms＇ deficiency and their segmentation effects are more or less improvements, where the best one is the maximum entropy method based on 2D histogram shape modification.展开更多
We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the s...We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.展开更多
The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Ha...The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.展开更多
Fault detection is beneficial for chiller routine operation management in building automation systems.Considering the limitations of traditional principal component analysis(PCA)algorithm for chiller fault detection,a...Fault detection is beneficial for chiller routine operation management in building automation systems.Considering the limitations of traditional principal component analysis(PCA)algorithm for chiller fault detection,a so-called kernel entropy component analysis(KECA)method has been developed and the development results are reported in this paper.Unlike traditional PCA,in KECA,the feature extraction or dimensionality reduction is implemented in a new space,called kernel feature space.The new space is nonlinearly related to the input space.The data set in the kernel feature space is projected onto a principal component subspace constructed by the feature space principal axes determined by the maximum Rényi entropy rather than the top eigenvalues.The proposed KECA is more suitable to deal with nonlinear process without Gaussian assumption.Using the available experimental data from ASHRAE RP-1043,seven typical chiller faults were tested by the proposed KECA method,and the results were compared to that of PCA.Two statistics,i.e.T2 and squared prediction error(SPE),were employed for fault detection monitoring.The fault detection results showed that the proposed KECA method had a better performance in terms of a higher detection accuracy in comparison to the traditional PCA.For the seven typical faults,the fault detection ratios were over 55%,even at their corresponding least severity level when using the proposed KECA based chiller fault detection method.展开更多
We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chir...We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.展开更多
We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansio...We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.展开更多
This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the in...This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the information set features from keystroke dynamics for the authentication of users. A new composite fuzzy classifier is also proposed based on Mamta-Hanman entropy function and applied on the Information Set based features. A comparison of the results of the proposed approach with those of Support Vector Machine and Random Forest classifier shows that the new classifier outperforms the other two.展开更多
--This paper presents a novel time delay estimation （TDE） method using the concept of entropy. The relative delay is estimated by minimizing the estimated joint entropy of multiple sensor output signals. When estima...--This paper presents a novel time delay estimation （TDE） method using the concept of entropy. The relative delay is estimated by minimizing the estimated joint entropy of multiple sensor output signals. When estimating the entropy, the information about the prior distribution of the source signal is not required. Instead, the Parzen window estimator is employed to estimate the density function of the source signal from multiple sensor output signals. Meanwhile, based on the Parzen window estimator, the Renyi＇s quadratic entropy （RQE） is incorporated to effectively and efficiently estimate the high-dimensional joint entropy of the multichannel outputs. Furthermore, a modified form of the joint entropy for embedding information about reverberation （multipath reflections） for speech signals is introduced to enhance the estimator＇s robustness against reverberation.展开更多
In this paper we consider a generalize dynamic entropy measure and prove that this mea- sure characterizes the distribution function uniquely. Also we propose cumulative resi- dual R^nyi entropy of order statistics an...In this paper we consider a generalize dynamic entropy measure and prove that this mea- sure characterizes the distribution function uniquely. Also we propose cumulative resi- dual R^nyi entropy of order statistics and prove that it also determines the distribution function uniquely. Applications of entropy concepts to DNA sequence analysis, the ulti- mate support for the biological systems, have been widely explored by researchers. The entropy measures discussed here can be applied for analysis of ordered DNA sequences.展开更多
Link flooding attack(LFA)is a fresh distributed denial of service attack(DDoS).Attackers can cut off the critical links,making the services in the target area unavailable.LFA manipulates legal lowspeed flow to flood c...Link flooding attack(LFA)is a fresh distributed denial of service attack(DDoS).Attackers can cut off the critical links,making the services in the target area unavailable.LFA manipulates legal lowspeed flow to flood critical links,so traditional technologies are difficult to resist such attack.Meanwhile,LFA is also one of the most important threats to Internet of things(IoT)devices.The introduction of software defined network(SDN)effectively solves the security problem of the IoT.Aiming at the LFA in the software defined Internet of things(SDN-IoT),this paper proposes a new LFA mitigation scheme ReLFA.Renyi entropy is to locate the congested link in the data plane in our scheme,and determines the target links according to the alarm threshold.When LFA is detected on the target links,the control plane uses the method based on deep reinforcement learning(DRL)to carry out traffic engineering.Simulation results show that ReLFA can effectively alleviate the impact of LFA in SDN IoT.In addition,the rerouting time of ReLFA is superior to other latest schemes.展开更多
At this current time,data stream classification plays a key role in big data analytics due to its enormous growth.Most of the existing classification methods used ensemble learning,which is trustworthy but these metho...At this current time,data stream classification plays a key role in big data analytics due to its enormous growth.Most of the existing classification methods used ensemble learning,which is trustworthy but these methods are not effective to face the issues of learning from imbalanced big data,it also supposes that all data are pre-classified.Another weakness of current methods is that it takes a long evaluation time when the target data stream contains a high number of features.The main objective of this research is to develop a new method for incremental learning based on the proposed ant lion fuzzy-generative adversarial network model.The proposed model is implemented in spark architecture.For each data stream,the class output is computed at slave nodes by training a generative adversarial network with the back propagation error based on fuzzy bound computation.This method overcomes the limitations of existing methods as it can classify data streams that are slightly or completely unlabeled data and providing high scalability and efficiency.The results show that the proposed model outperforms stateof-the-art performance in terms of accuracy(0.861)precision(0.9328)and minimal MSE(0.0416).展开更多
For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.
In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimen...In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.展开更多
基金supported by the China Postdoctoral Science Foundation(20100471451)the Science and Technology Foundation of State Key Laboratory of Underwater Measurement&Control Technology(9140C2603051003)
文摘In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, they are weak in suppressing background noises and worse in segmenting targets with non-uniform gray level. The concept of 2D histogram shape modification is proposed, which is realized by target information prior restraint after enhancing target information using plateau histogram equalization. The formula of 2D minimum Renyi entropy is deduced for image segmentation, then the shape-modified 2D histogram is combined wfth four optimal objective functions （i.e., maximum between-class variance, maximum entropy, maximum correlation and minimum Renyi entropy） respectively for the appli- cation of infrared image segmentation. Simultaneously, F-measure is introduced to evaluate the segmentation effects objectively. The experimental results show that F-measure is an effective evaluation index for image segmentation since its value is fully consistent with the subjective evaluation, and after 2D histogram shape modification, the methods of optimal objective functions can overcome their original forms＇ deficiency and their segmentation effects are more or less improvements, where the best one is the maximum entropy method based on 2D histogram shape modification.
文摘We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.
文摘The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
基金The financial supports for the Natural Science Foundation of Zhejiang Province(Project No.LQ19E060007)are gratefully acknowledged.
文摘Fault detection is beneficial for chiller routine operation management in building automation systems.Considering the limitations of traditional principal component analysis(PCA)algorithm for chiller fault detection,a so-called kernel entropy component analysis(KECA)method has been developed and the development results are reported in this paper.Unlike traditional PCA,in KECA,the feature extraction or dimensionality reduction is implemented in a new space,called kernel feature space.The new space is nonlinearly related to the input space.The data set in the kernel feature space is projected onto a principal component subspace constructed by the feature space principal axes determined by the maximum Rényi entropy rather than the top eigenvalues.The proposed KECA is more suitable to deal with nonlinear process without Gaussian assumption.Using the available experimental data from ASHRAE RP-1043,seven typical chiller faults were tested by the proposed KECA method,and the results were compared to that of PCA.Two statistics,i.e.T2 and squared prediction error(SPE),were employed for fault detection monitoring.The fault detection results showed that the proposed KECA method had a better performance in terms of a higher detection accuracy in comparison to the traditional PCA.For the seven typical faults,the fault detection ratios were over 55%,even at their corresponding least severity level when using the proposed KECA based chiller fault detection method.
基金Supported by ERC Starting Grant 637844-HBQFTNCER
文摘We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.
基金supported by National Basic Research Program of China(973 Program)(2011CB707802,2013CB910200)Natural Science Foundation of China Grant(11126180)
文摘We obtain the expansion of Renyi divergence of order α （0 〈 α 〈 1） between the normalized sum of IID continuous random variables and the Caussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm.
文摘This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the information set features from keystroke dynamics for the authentication of users. A new composite fuzzy classifier is also proposed based on Mamta-Hanman entropy function and applied on the Information Set based features. A comparison of the results of the proposed approach with those of Support Vector Machine and Random Forest classifier shows that the new classifier outperforms the other two.
基金supported by the National Natural Science Foundation of China under Grant No.61172140‘985’ Key Projects for Excellent Teaching Team Supporting (postgraduate) under Grant No.A1098522-02
文摘--This paper presents a novel time delay estimation （TDE） method using the concept of entropy. The relative delay is estimated by minimizing the estimated joint entropy of multiple sensor output signals. When estimating the entropy, the information about the prior distribution of the source signal is not required. Instead, the Parzen window estimator is employed to estimate the density function of the source signal from multiple sensor output signals. Meanwhile, based on the Parzen window estimator, the Renyi＇s quadratic entropy （RQE） is incorporated to effectively and efficiently estimate the high-dimensional joint entropy of the multichannel outputs. Furthermore, a modified form of the joint entropy for embedding information about reverberation （multipath reflections） for speech signals is introduced to enhance the estimator＇s robustness against reverberation.
文摘In this paper we consider a generalize dynamic entropy measure and prove that this mea- sure characterizes the distribution function uniquely. Also we propose cumulative resi- dual R^nyi entropy of order statistics and prove that it also determines the distribution function uniquely. Applications of entropy concepts to DNA sequence analysis, the ulti- mate support for the biological systems, have been widely explored by researchers. The entropy measures discussed here can be applied for analysis of ordered DNA sequences.
基金supported by the Fundamental Research Funds under Grant 2021JBZD204ZTE industry-university research cooperation fund project “Research on network identity trusted communication technology architecture”State Key Laboratory of Mobile Network and Mobile Multimedia Technology
文摘Link flooding attack(LFA)is a fresh distributed denial of service attack(DDoS).Attackers can cut off the critical links,making the services in the target area unavailable.LFA manipulates legal lowspeed flow to flood critical links,so traditional technologies are difficult to resist such attack.Meanwhile,LFA is also one of the most important threats to Internet of things(IoT)devices.The introduction of software defined network(SDN)effectively solves the security problem of the IoT.Aiming at the LFA in the software defined Internet of things(SDN-IoT),this paper proposes a new LFA mitigation scheme ReLFA.Renyi entropy is to locate the congested link in the data plane in our scheme,and determines the target links according to the alarm threshold.When LFA is detected on the target links,the control plane uses the method based on deep reinforcement learning(DRL)to carry out traffic engineering.Simulation results show that ReLFA can effectively alleviate the impact of LFA in SDN IoT.In addition,the rerouting time of ReLFA is superior to other latest schemes.
基金Taif University Researchers Supporting Project Number(TURSP-2020/126),Taif University,Taif,Saudi Arabia.
文摘At this current time,data stream classification plays a key role in big data analytics due to its enormous growth.Most of the existing classification methods used ensemble learning,which is trustworthy but these methods are not effective to face the issues of learning from imbalanced big data,it also supposes that all data are pre-classified.Another weakness of current methods is that it takes a long evaluation time when the target data stream contains a high number of features.The main objective of this research is to develop a new method for incremental learning based on the proposed ant lion fuzzy-generative adversarial network model.The proposed model is implemented in spark architecture.For each data stream,the class output is computed at slave nodes by training a generative adversarial network with the back propagation error based on fuzzy bound computation.This method overcomes the limitations of existing methods as it can classify data streams that are slightly or completely unlabeled data and providing high scalability and efficiency.The results show that the proposed model outperforms stateof-the-art performance in terms of accuracy(0.861)precision(0.9328)and minimal MSE(0.0416).
文摘For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.
基金supported by the National Natural Science Foundation of China(Grant Nos.11671244,61373150,and 61602291)the Higher School Doctoral Subject Foundation of Ministry of Education of China(Grant No.20130202110001)the Fundamental Research Funds for the Central Universities(Grant No.2016CBY003)
文摘In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.
