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Understanding Human and Machine Interaction from Decision Perspective: An Empirical Study Based on the Game of Go

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Journal of Systems science & Complexity 2024年第2期37卷 647-667页

作者： ZHAO Ping LI Xuerong WANG Shouyang Academy of Mathematics and Systems science Chinese Academy of SciencesBeijing 100190China school of mathematical sciences University of Chinese Academy of SciencesBeijing 100190China

The authors aim to interpret human and AI interactions from the decision *** authors decompose the interaction analysis into the following main components in the context of interactions:Individual behavior patterns,interaction relationships,and comprehensive *** authors interpret intertemporal decisions from a physical perspective and employ cross-discipline concepts and methodologies to extract the behavior characteristics of players in the empirical case *** the individual behavior patterns,the authors find that human players prefer short-term periods to AI in *** interaction relationship analysis reveals a dynamic relationship between possible short-term co-movement and nearly counter-movement in the long *** authors apply principal component analysis to descriptive indicators and discover a regular decision *** main behavior pattern of players in the game of Go is switching between careful and daring *** differences in the decision hierarchies imply a discrepancy of patience between humans and AI.

关键词： Coherence analysis decision hierarchy machine behaviour multitaper spectral analysis

Cauchy matrix approach for H1a equation in the torqued Adler–Bobenko–Suris lattice list

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Communications in Theoretical Physics 2024年第10期76卷 3-8页

作者： Jing Wang Song-lin Zhao Shoufeng Shen school of mathematical sciences Zhejiang University of Technology

As a torqued version of the lattice potential Korteweg–de Vries equation, the H1ais an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.

关键词： Cauchy matrix scheme exact solutions torqued H1 equation

Multi-scale hash encoding based neural geometry representation

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Computational Visual Media 2024年第3期10卷 453-470页

作者： Zhi Deng Haoyao Xiao Yining Lang Hao Feng Juyong Zhang school of mathematical sciences University of Science and Technology of ChinaHefei 230026China Alibaba Artificial Intelligence Governance Laboratory Alibaba GroupHangzhou 310017China

Recently, neural implicit function-basedrepresentation has attracted more and more attention,and has been widely used to represent surfacesusing differentiable neural networks. However, surfacereconstruction from point clouds or multi-view imagesusing existing neural geometry representations stillsuffer from slow computation and poor accuracy. Toalleviate these issues, we propose a multi-scale hashencoding-based neural geometry representation whicheffectively and efficiently represents the surface asa signed distance field. Our novel neural networkstructure carefully combines low-frequency Fourierposition encoding with multi-scale hash encoding. Theinitialization of the geometry network and geometryfeatures of the rendering module are accordinglyredesigned. Our experiments demonstrate that theproposed representation is at least 10 times faster forreconstructing point clouds with millions of *** also significantly improves speed and accuracyof multi-view reconstruction. Our code and modelsare available at https://***/Dengzhi-USTC/Neural-Geometry-Reconstruction.

关键词： neural geometry representation hash encoding point cloud reconstruction multi-view reconstruction

The real estate time-stamping and registration system based on Ethereum blockchain

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Blockchain(Research and Applications) 2024年第1期5卷 119-132页

作者： Liyuan Zhang Limian Ci Yonghong Wu Benchawan Wiwatanapataphee school of Electrical Engineering Computing&Mathematical ScienceCurtin UniversityKent StreetPerth6102WAAustralia

In recent years,there has been a growing interest in real estate investments that utilize blockchain *** real estate investments usually involve third-party intermediaries for verifying and recording informal real estate *** paper proposes a blockchain-based real estate investment model and presents a detailed description of the real estate register authentication aspect of the *** model uses blockchain technology to create tamper-evident records of real estate transactions and provide secure authentication and verification for informal real estate ***,each real estate transaction is recorded in a block,and all transaction records are kept on the *** means that inventors can access these transaction records and verify their authenticity and *** system can also use smart contracts to automate the process of real estate transactions,which further improves transaction efficiency and reduces ***,the model’s timestamp and authentication mechanism can eliminate third-party intermediaries and ensure the authenticity and validity of real estate transactions through distributed ledgers and verification ***,blockchain-based real estate systems offer advantages of security,transparency,efficiency,and cost *** ongoing blockchain advancements,these systems are expected to play a crucial role in future real estate investment transactions.

关键词： Blockchian technology Smart contract Real estate investment Time-stamping and registration system

Compressed Data Separation via ℓ_(q)-Split Analysis with ℓ_(∞)-Constraint

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1655-1673页

作者： Ming Yang Gu Song Li Jun Hong Lin school of mathematical science Zhejiang UniversityHangzhou310027P.R.China Center for Data science Zhejiang UniversityHangzhou310027P.R.China

In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random *** propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0 详细信息

In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random *** propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0

关键词： Data separation ℓ_(q)-split analysis Dantzig selector frames restricted isometry property compressed sensing

Input-to-State Stability of Impulsive Switched Systems Involving Uncertain Impulse-Switching Moments

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1515-1517页

作者： Chang Liu Wenlu Liu Tengda Wei Xiaodi Li school of mathematical and Statistics Shandong Normal UniversityJinan 250014China

Dear Editor,This letter studies the input-to-state stability(ISS)for a class of impulsive switched systems,where uncertain impulse-switching moments are *** robustness of ISS with respect to the perturbations of the occurrence time of impulse-switching moments is revealed by several less conservative dwell-time conditions for the uncertain impulse-switching moments combined with Lyapunov ***,the Lyapunov conditions have multiple coefficients at discrete time so as to handle the hybrid effect of impulse-switching moments,and the case that time derivative of Lyapunov function is indefinite is also taken into ***,a numerical example is proposed to illustrate the effectiveness of the theoretical results.

关键词： letter conservative derivative

TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION

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Journal of Computational Mathematics 2024年第4期42卷 1124-1144页

作者： Hanzhang Hu Yanping Chen Jianwei Zhou school of Mathematics Jiaying UniversityMeizhou 514015China school of mathematical science South China Normal UniversityGuangzhou 510631China school of Mathematics and Statistics Linyi UniversityLinyi 276005China

A two-grid finite element method with L1 scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger *** finite element solution in the L-norm are proved bounded without any time-step size conditions(dependent on spatial-step size).The classical L1 scheme is considered in the time direction,and the two-grid finite element method is applied in spatial *** optimal order error estimations of the two-grid solution in the LP-norm is proved without any time-step size *** is shown,both theoretically and numerically,that the coarse space can be extremely coarse,with no loss in the order of accuracy.

关键词： Time-fractional nonlinear Schrodinger equation Two-grid finite element me-thod The L1 scheme

On a Flexible Loan Repayment Method Depending on Borrower's Asset with an Early Termination Clause

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 557-567页

作者： Jin LIANG Jia-qi MAO Zhao-ya LIU school of mathematical sciences Tongji UniversityShanghai 200092China

Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability,a loan with a new and flexible repayment method is designed,which depends on the asset value of the *** repayment method can reduce the loan default probability,but it causes the uncertainty of the pay off *** the repayment term is related to the regular repayment amount in this method,a boundary for the regular repayment amount is set up in order to avoid too long repayment *** will balance the benefit of borrowers and lenders and improve the applicability of this *** establishing a mathematical model of the residual value of the loan,this model can be transformed into an initial-boundary problem of a partial differential *** analytic solution and the expected time to pay off the loan are ***,numerical analysis are shown.

关键词： flexible repayment method repayment ratio early termination clause expected pay off time

Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains

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science China Mathematics 2024年第8期67卷 1827-1864页

作者： Xiaoshu Ge Chunping Zhong school of mathematical sciences Xiamen UniversityXiamen 361005China

In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of typesⅠ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio(1994).These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found in the literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed to admit differential geometry *** are,however,not necessarily Hermitian quadratic as the Bergman *** metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of typesⅠ-Ⅳ,respectively,and they are all proved to be complete K?hler-Berwald *** enjoy very similar curvature properties as those of the Bergman metric on the irreducible classical domains,i.e.,their holomorphic sectional curvatures are bounded between two negative constants and their holomorphic bisectional curvatures are always nonpositive and bounded below by negative constants,*** the viewpoint of complex analysis,these metrics are analogs of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the sense of Chern(1996).

关键词： holomorphic invariant metric Kahler-Berwald metric irreducible classical domains