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Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

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Chinese Physics Letters 2024年第1期41卷 68-76页

作者：刘通夏旭 Department of Applied Physics School of ScienceNanjing University of Posts and TelecommunicationsNanjing 210003China Academy of mathematics and system sciences Chinese Academy of SciencesBeijing 100190China

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research ***,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical *** propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier *** this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical ***,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical *** to computational complexity,calculations are not performed for higher dimensional ***,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be ***,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

关键词： state exponent critical

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New black-to-white hole solutions with improved geometry and energy conditions

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Science China(Physics,Mechanics & Astronomy) 2024年第7期67卷 30-43页

作者： Zhongwen Feng Yi Ling Xiaoning Wu Qingquan Jiang school of Physics and Astronomy China West Normal UniversityNanchong 637009China Institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China school of Physics University of Chinese Academy of SciencesBeijing 100049China Institute of mathematics Academy of Mathematics and System Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100190China

We construct new black-to-white hole solutions which connect the geometry of spacetime at some gluing surface inside the *** continuity of the metric can be guaranteed up to the arbitrary order which is controlled by the power factor *** sort of black-to-white holes is characterized by the sub-Planckian scalar curvature,independent of the mass of black-to-white *** importantly,we show that the energy condition is only violated within a small region near the gluing *** geodesics of particles within the region from black hole to white hole is also *** turns out that the matter falling into the black hole may pass through the center without singularity and come out from the white *** scenario provides novel ideas for understanding the information loss paradox in traditional black hole physics.

关键词： regular black hole energy condition singularity quantum gravity

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Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

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Science China mathematics 2024年第11期67卷 2433-2452页

作者： Feng Shao Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences

Let X be an irreducible Hermitian symmetric space of compact type(IHSS for short).In this paper,we give the irreducible decomposition of *** a by-product,we give a cohomological characterization of the rank of ***,we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

关键词： tangent bundle pseudoeffective threshold irreducible Hermitian symmetric space of compact type (IHSS) multiplicity free action

Design of zero-determinant strategies and its application to networked repeated games

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Science China(Information sciences) 2024年第10期67卷 227-243页

作者： Daizhan CHENG Changxi LI Key Laboratory of systems and Control Academy of Mathematics and Systems SciencesChinese Academy of Sciences school of mathematics Shandong University

Using the semi-tensor product（STP） of matrices, the profile evolutionary equation（PEE） for repeated finite games is obtained. By PEE, the zero-determinant（ZD） strategies are developed for general finite games. A formula is then obtained to design ZD strategies for general finite games with multiple players and asymmetric strategies. A necessary and sufficient condition is obtained to ensure the availability of the designed ZD strategies. It follows that player i can unilaterally design ki-1（one less than the number of its strategies） dominating linear relations about the expected payoffs of all players. Finally, the fictitious opponent player is proposed for networked repeated games（NRGs）. A technique is proposed to simplify the model by reducing the number of frontier strategies.

关键词： finite repeated game profile evolutionary equation ZD strategy networked repeated games semi-tensor product of matrices

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of systems Science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu school of mathematics Statistics and Mechanics Beijing University of Technology Academy of mathematics and systems Science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

On the Security of Homomorphic Encryption Schemes with Restricted Decryption Oracles

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Journal of systems Science & Complexity 2024年第5期37卷 2240-2261页

作者： MA Guangsheng LI Hongbo school of mathematics and Physics North China Electric Power University Academy of mathematics and systems Science Chinese Academy of Sciences University of Chinese Academy of sciences

Fully homomorphic encryption（FHE） can be used for privacy-preserving aggregation of medical data. In this typical application, the security against passive attacks has been well studied by Li and Micciancio（2021）. In this paper, the authors further consider a “nearly passive” kind of attack, where the attacker may behave like a passive attacker in the view of the third-party *** capture the security against this hard-to-detect attack, the authors propose a new notion of IND-CPArDsecurity. The authors show that the standard LWE encryption and its related FHE schemes can not defend against IND-CPArDattack, even under a stricter rule limiting the content and number of queries made by the attacker. To make the application of FHE schemes more secure, the authors discuss some possible modifications that may serve as countermeasures to IND-CPArDattack.

关键词： Homomorphic encryption privacy secure cloud computing security

2-local unstable homotopy groups of indecomposable A3～2-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A3～*** main technique used is analysing the homotopy property of J（A,X）,defined by Gray（1973） for a CW-pair（X,A）,which is homoto... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Critical observability of partially observed discrete event systems under cyber attacks

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Science China(Information sciences) 2024年第2期67卷 333-334页

作者： Liyun TONG Jinling LIANG Yang LIU Department of mathematics School of SciencesHangzhou Dianzi University school of mathematics Southeast University College of mathematics and Computer Science Zhejiang Normal University

The discrete event system(DES) is a dynamic system driven by asynchronous/sudden events and has been widely used in many critical infrastructures, such as electric transportation networks and intelligent transportatio...

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2-Independent Domination in Trees

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Journal of the Operations Research Society of China 2024年第2期12卷 485-494页

作者： Gang Zhang Baoyindureng Wu College of mathematics and system sciences Xinjiang UniversityUrumqi830046XinjiangChina

A subset D■V(G)in a graph G is a dominating set if every vertex in V(G)I D is adjacent to at least one vertex of S.A subset S■V(G)in a graph G is a 2-independent set if△(G[S])<*** 2-independence numberα2(G)is the order of a largest 2-independent set in ***,a subset D■V(G)in a graph G is a 2-independent dominating set if D is both dominating and *** 2-independent domination number i^(2)(G)is the order of a smallest 2-independent dominating set in *** this paper,we characterize all trees T of order n with i^(2)(T)=n/***,we prove that for any tree T of order n≥2,i^(2)(T)≤2/3α2(T),and this bound is sharp.

关键词： Domination Independent domination 2-Independent domination 2-Independence Trees