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The Generalized Stackelberg Equilibrium of the Two-Person Stopping Game

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j.urnal of the Operations Research Society of China 2024年第1期12卷 155-168页

作者： Marek Skarupski Krzysztof j.Szaj.wski Faculty of Pure and Applied Mathematics Wroclaw University of Science and Technology50-370WrocƚawDolonoslaskiePoland

In modeling the bilateral selection of states of the process,Dynkin(Dokl Akad Nauk USSR 185:241–288,1969)proposed a two-person game in which players use stopping moments as *** purpose of this work is to present a model of the game in which the players have different information about the process itself,as well as various laws to stop the process and accept its *** game model uses the stochastic process apparatus,in particular,the ability to create different filters for the same *** sets of stopping moments based on different filters are not identical,which allows us to model different sets of strategies for *** show that the follower,by observing the behavior of a rational leader,can recover information that is lost due to the lack of complete observation of the state of the *** the competition of two opponents for the maximum of the ***,one of whom has access to full information and the other only knows their relative ranks,we found the generalized Stackelberg *** the priority of a player observing the relative ranks is less than 50%,then that player modifies his strategy based on the behavior of the second *** a player with full information,information about the behavior of the player observing the relative ranks is useless.

关键词： No-zero-sum game Optional stopping Equilibrium Filtration

Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

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Applied Mathematics and Mechanics(English Edition) 2024年第5期45卷 819-836页

作者： D.LEE S.CHANG j.LEE Department of Automotive Engineering Hanyang UniversitySeoul 04763Republic of Korea School of Mechanical Engineering Chungnam National UniversityDaejeon 34134Republic of Korea Department of Mechanical Robotics and Energy EngineeringDongguk UniversitySeoul 04620Republic of Korea

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random *** method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data *** the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random *** allows for avoiding repeated computations of invariant substructures while generating the input-output data *** substructuring with static condensation further improves the computational efficiency of the reanalysis without losing ***,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional *** numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

关键词： forward uncertainty quantification(UQ) generalized polynomial chaos expansion(GPCE) static reanalysis method static condensation substructuring

Attitude control of multi-spacecraft systems on SO(3)with stochastic links failure

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Chinese j.urnal of Aeronautics 2024年第3期37卷 320-331页

作者： KANG Zeyu SHEN Qiang WU Shufan Chris j.DAMAREN MU Zhongcheng School of Aeronautics and Astronautics Shanghai Jiao Tong UniversityShanghai 200240China Institute for Aerospace Studies University of TorontoTorontoOntario M3H 5T6Canada

In this paper,for Multi-Spacecraft System(MSS)with a directed communication topology link and a static virtual leader,a controller is proposed to realize attitude consensus and attitude stabilization with stochastic links failure and actuator ***,an MSS attitude error model suitable for a directed topology link and with a static virtual leader based on SO(3)is derived,which considers that the attitude error on SO(3)cannot be defined based on algebraic ***,we design a controller to realize the MSS on SO(3)with attitude consensus and attitude stabilization under stochastic links failure and actuator ***,the simulation results of a multi-spacecraft system with stochastic links failure and a static virtual leader spacecraft are demonstrated to illustrate the efficiency of the attitude controller.

关键词： Multi-spacecraft systems Attitude consensus Attitude stabilization stochastic links failure Super-martingale convergence

Envisioning future deep learning theories: some basic concepts and characteristics

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Science China(Information Sciences) 2024年第10期67卷 373-382页

作者： Weij.e j.SU The Wharton School University of Pennsylvania School of Engineering and Applied Science University of Pennsylvania

To advance deep learning methodologies in the next decade, a theoretical framework for reasoning about modern neural networks is needed. While efforts are increasing toward demystifying why deep learning is so effective, a comprehensive picture remains lacking, suggesting that a better theory is possible. We argue that a future deep learning theory should inherit three characteristics: a hierarchically structured network architecture, parameters iteratively optimized using stochastic gradient-based methods, and information from the data that evolves compressively. As an instantiation, we integrate these characteristics into a graphical model called neurashed. This model effectively explains some common empirical patterns in deep learning. In particular, neurashed enables insights into implicit regularization, information bottleneck, and local ***, we discuss how neurashed can guide the development of deep learning theories.

关键词： deep learning local elasticity information bottleneck implicit regularization phenomenological model

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stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

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Petroleum Science 2024年第2期21卷 918-935页

作者： Fábio j.nior Damasceno Fernandes Leonardo Teixeira Antonio Fernando Menezes Freire Wagner Moreira Lupinacci Exploratory Interpretation and Reservoir Characterization Group(GIECAR) Department of Geology and GeophysicsFederal Fluminense UniversityNiter oiRJ24210-346Brazil Petrobras Rio de JaneiroRJ20231-030Brazil National Institute of Science and Technology of Petroleum Geophysics(INCT-GP/CNPQ) Niter oiRJ24210-346Brazil

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1,reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

关键词： stochastic inversion Bayesian classification Porosity modeling Carbonate reservoirs Igneous rocks

Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 461-478页

作者： Haitao LI Tianyu ZHENG Weiyang QIN Ruilan TIAN Hu DING j.C.j. Liqun CHEN Department of Engineering Mechanics North University of ChinaTaiyuan 030051China Department of Engineering Mechanics Northwestern Polytechnical UniversityXi'an 710072China Department of Engineering Mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechnoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China School of Mechanical and Mechatronic Engineering University of Technology SydneyNew South Wales 2007Australia

In the practical environment,it is very common for the simultaneous occurrence of base excitation and *** the combined energy of vibration and wind with a single energy harvesting structure is *** this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy *** results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well j.mp and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base ***,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed *** experiments are conducted to investigate the validity of the theoretical prediction and numerical *** experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind ***,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

关键词： bi-stability inter-well response galloping band-limited random

stochastic SIS metapopulation models for the spread of disease among species in a fragmented landscape

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International j.urnal of Biomathematics 2016年第4期9卷 97-119页

作者： Amy j. Ekanayake Department of Mathematics Western Illinois University 1 University Circle Maeomb Illinois 61455 USA

Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.

关键词： Epidemic metapopulation Ito stochastic differential equation Markov chain moment closure.

Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of stochastic Climate Model

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Chinese Annals of Mathematics,Series B 2011年第3期32卷 343-368页

作者： Yuan YUAN Andrew j. MAj.A Department of Mathematics Courant Institute New York University 251 Mercer Street New York NY 10012 USA Department of Mathematics and Center for Atmospheric Ocean Sciences Courant Institute New York University 251 Mercer Street New York NY 10012 USA

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability,climate sensitivity,and improved extended range ***,techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency *** was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative(CAM) stochastic *** probability distribution functions(PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a ***,rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic *** Gaussian lower bounds are also established under suitable hypotheses.

关键词： Reduced stochastic climate model Invariant measure Fokker-Planck equation Comparison principle Global estimates of probability density function

Differential introgression suggests candidate beneficial and barrier loci between two parapatric subspecies of Pearson＇s horseshoe bat Rhinolophus pearsoni

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Current Zoology 2016年第4期62卷 405-412页

作者： Xiuguang MAO Shuyi ZHANG Stephen j. ROSSlTER Institute of Estuarine and Coastal Research East China Normal University Shanghai 200062 China School of Biological and Chemical Sciences Queen Mary University of London London E14NS UK

Observations that rates of introgression between taxa can vary across loci are increasingly common. Here, we test for differential locus-wise introgression in 2 parapatric subspecies of Pearson＇s horseshoe bat （Rhinolophus pearsoni chinensis and R. p. pearsoni）. To efficiently identify putative speciation genes and/or beneficial genes in our current system, we used a candidate gene approach by including loci from X chromosome that are suggested to be more likely involved in reproductive isolation in other organisms and loci underlying hearing that have been suggested to spread across the hybrid zone in another congeneric species. Phylogenetic and coalescent analyses were performed at 2 X-linked, 4 hearing genes, as well as 2 other autosomal loci individually. Likelihood ratio tests could not rej.ct the model of zero gene flow at 2 X-linked and 2 autosomal genes. In contrast, gene flow was supported at 3 of 4 hearing genes. While this introgression could be adaptive, we cannot rule out stochastic processes. Our results highlight the utility of the candidate gene approach in searching for speciation genes and/or beneficial genes across the species boundary in natural populations.

关键词： gene flow hybridization hybrid zone reproductive isolation.