The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because o...The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.展开更多
A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)...A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.展开更多
The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,tr...The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.展开更多
In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive a...In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive approach for handling and modeling uncertainty,capable of representing both quantitative and qualitative information.First,the motivation for proposing the layer-2 transferable belief model and its information processing principles are explored from the perspective of weak propensity.Then,based on these principles,the corresponding information processing methods for the credal and pignistic levels are developed.Finally,the advantages of this model are validated through a classifier that leverages attribute fusion to enhance performance and decision-making accuracy.展开更多
Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar ...Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.展开更多
Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize...Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize the permutational property of rational functions onμq+1,we construct a class of permutation quadrinomials with the form f_(r,a,b,c,s,t,u)(x)=x^(r)(1+ax^(s(q-1))+bx^(t(q-1))+cxu(q-1))of F_(q^(2)).展开更多
Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extrac...Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.展开更多
In the manufacturing industry,reasonable scheduling can greatly improve production efficiency,while excessive resource consumption highlights the growing significance of energy conservation in production.This paper st...In the manufacturing industry,reasonable scheduling can greatly improve production efficiency,while excessive resource consumption highlights the growing significance of energy conservation in production.This paper studies the problem of energy-efficient distributed heterogeneous permutation flowshop problem with variable processing speed(DHPFSP-VPS),considering both the minimum makespan and total energy consumption(TEC)as objectives.A discrete multi-objective squirrel search algorithm(DMSSA)is proposed to solve the DHPFSPVPS.DMSSA makes four improvements based on the squirrel search algorithm.Firstly,in terms of the population initialization strategy,four hybrid initialization methods targeting different objectives are proposed to enhance the quality of initial solutions.Secondly,enhancements are made to the population hierarchy system and position updating methods of the squirrel search algorithm,making it more suitable for discrete scheduling problems.Additionally,regarding the search strategy,six local searches are designed based on problem characteristics to enhance search capability.Moreover,a dynamic predator strategy based on Q-learning is devised to effectively balance DMSSA’s capability for global exploration and local exploitation.Finally,two speed control energy-efficient strategies are designed to reduce TEC.Extensive comparative experiments are conducted in this paper to validate the effectiveness of the proposed strategies.The results of comparing DMSSA with other algorithms demonstrate its superior performance and its potential for efficient solving of the DHPFSP-VPS problem.展开更多
Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishbur...Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simultaneously.The classes of our interest are(321,312)-avoiding and(321,4123)-avoiding Fishburn permutations.The statistics of our interest are ascents,descents,inversions,right-to-left maxima,right-to-left minima,left-to-right maxima and left-to-right minima.Our results generalize a result by Egge.展开更多
We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and o...We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.展开更多
In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a graded algebra.
The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are stu...The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation Sn is proved to be generated by a n-cycle 9 and a permutation τ= （ij,ik） together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit. Based on the above theory, a cascade algorithm for reversible logic gate networks is proposed. A reversible example of logic gate network cascade is given to show the correctness of the algorithm.展开更多
The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV...The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security.展开更多
A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship amon...A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.展开更多
Permutation polynomials is a hot topic in finite fields,they have many applications in different areas.Permutation binomials and trinomials over finite fields were studied recently.In thispaper,by using a powerful lem...Permutation polynomials is a hot topic in finite fields,they have many applications in different areas.Permutation binomials and trinomials over finite fields were studied recently.In thispaper,by using a powerful lemma given by Zieve and some degree 5 and 6 permutation polynomials over Fq,we construct somepermutation binomials over Fqm.展开更多
Representation theory is concerned with the ways of explaining or visualizing a group as a group of matrices. In this paper, we extend the permutation pattern of to a two-line notation. We consider the representations...Representation theory is concerned with the ways of explaining or visualizing a group as a group of matrices. In this paper, we extend the permutation pattern of to a two-line notation. We consider the representations of this non-deranged permutation group(p ≥ 5 and p a prime). Also we reveal some interesting properties and results of the character of where .展开更多
Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the ef...Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.展开更多
Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalize...Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.展开更多
基金supported in part by the National Key Research and Development Program of China under Grant No.2021YFF0901300in part by the National Natural Science Foundation of China under Grant Nos.62173076 and 72271048.
文摘The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.
基金Supported by the National Natural Science Foundation of China(Grant No.12061030)the Natural Science Foundation of Hainan Province(Grant No.122RC652)2023 Excellent Science and Technology Innovation Team of Jiangsu Province Universities(Real-Time Industrial Internet of Things).
文摘A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.
文摘The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.
文摘In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive approach for handling and modeling uncertainty,capable of representing both quantitative and qualitative information.First,the motivation for proposing the layer-2 transferable belief model and its information processing principles are explored from the perspective of weak propensity.Then,based on these principles,the corresponding information processing methods for the credal and pignistic levels are developed.Finally,the advantages of this model are validated through a classifier that leverages attribute fusion to enhance performance and decision-making accuracy.
基金supported by the National Natural Science Foundation of China under Grant Nos.92265209,11174081 and 62305285the Natural Science Foundation of Chongqing under Grant No.CSTB2024NSCQ-MSX0643the Shanghai Municipal Science and Technology Major Project under Grant No.2019SHZDZX01。
文摘Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.
基金Supported by the National Natural Science Foundation of China(11926344)Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202401601)+1 种基金Doctor Talent Program of Chongqing University of Education(2023BSRC003)Undergraduate Science Research Program of Chongqing University of Education(KY20240046)。
文摘Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize the permutational property of rational functions onμq+1,we construct a class of permutation quadrinomials with the form f_(r,a,b,c,s,t,u)(x)=x^(r)(1+ax^(s(q-1))+bx^(t(q-1))+cxu(q-1))of F_(q^(2)).
基金supported financially by FundamentalResearch Program of Shanxi Province(No.202103021223056).
文摘Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.
基金supported by the Key Research and Development Project of Hubei Province(Nos.2020BAB114 and 2023BAB094).
文摘In the manufacturing industry,reasonable scheduling can greatly improve production efficiency,while excessive resource consumption highlights the growing significance of energy conservation in production.This paper studies the problem of energy-efficient distributed heterogeneous permutation flowshop problem with variable processing speed(DHPFSP-VPS),considering both the minimum makespan and total energy consumption(TEC)as objectives.A discrete multi-objective squirrel search algorithm(DMSSA)is proposed to solve the DHPFSPVPS.DMSSA makes four improvements based on the squirrel search algorithm.Firstly,in terms of the population initialization strategy,four hybrid initialization methods targeting different objectives are proposed to enhance the quality of initial solutions.Secondly,enhancements are made to the population hierarchy system and position updating methods of the squirrel search algorithm,making it more suitable for discrete scheduling problems.Additionally,regarding the search strategy,six local searches are designed based on problem characteristics to enhance search capability.Moreover,a dynamic predator strategy based on Q-learning is devised to effectively balance DMSSA’s capability for global exploration and local exploitation.Finally,two speed control energy-efficient strategies are designed to reduce TEC.Extensive comparative experiments are conducted in this paper to validate the effectiveness of the proposed strategies.The results of comparing DMSSA with other algorithms demonstrate its superior performance and its potential for efficient solving of the DHPFSP-VPS problem.
基金National Natural Science Foundation of China(Grant No.12171362)。
文摘Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simultaneously.The classes of our interest are(321,312)-avoiding and(321,4123)-avoiding Fishburn permutations.The statistics of our interest are ascents,descents,inversions,right-to-left maxima,right-to-left minima,left-to-right maxima and left-to-right minima.Our results generalize a result by Egge.
文摘We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.
文摘In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a graded algebra.
基金the National Natural Science Foundation of China(60673127)the National High Technology Research and Development Program of China(863Program)(2007AA01Z404)~~
文摘The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation Sn is proved to be generated by a n-cycle 9 and a permutation τ= （ij,ik） together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit. Based on the above theory, a cascade algorithm for reversible logic gate networks is proposed. A reversible example of logic gate network cascade is given to show the correctness of the algorithm.
基金supported by the National Natural Science Foundation of China (Grant No. 61672124)the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund,China (Grant No. MMJJ20170203)+2 种基金the Liaoning Provincial Science and Technology Innovation Leading Talents Program Project,China (Grant No. XLYC1802013)the Key Research and Development Projects of Liaoning Province,China (Grant No. 2019020105-JH2/103)the Jinan City 20-University Funding Projects for Introducing Innovation Team Program,China (Grant No. 2019GXRC031)。
文摘The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security.
文摘A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.
基金Supported Partially by the National Natural Science Foundation of China(11926344)Science and Technology Research Projects of Chongqing Municipal Education Commission(KJQN201901402,KJQN201900506)Fund Project of Chongqing Normal University(17XWB021)。
文摘Permutation polynomials is a hot topic in finite fields,they have many applications in different areas.Permutation binomials and trinomials over finite fields were studied recently.In thispaper,by using a powerful lemma given by Zieve and some degree 5 and 6 permutation polynomials over Fq,we construct somepermutation binomials over Fqm.
文摘Representation theory is concerned with the ways of explaining or visualizing a group as a group of matrices. In this paper, we extend the permutation pattern of to a two-line notation. We consider the representations of this non-deranged permutation group(p ≥ 5 and p a prime). Also we reveal some interesting properties and results of the character of where .
基金supported by the National Natural Science Foundation of China(No.51904173)Shandong Provincial Natural Science Foundation(No.ZR2018MEE008)the Project of Shandong Province Higher Educational Science and Technology Program(No.J18KA307).
文摘Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) .
文摘Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.
