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A model predictive Stackelberg solution to orbital pursuit-evasion game
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作者 Yuchen LIU Chaoyong LI +1 位作者 Jun JIANG Yonghe ZHANG 《Chinese Journal of Aeronautics》 2025年第2期244-255,共12页
In this paper,we investigate analytical numerical iterative strategies for the pursuit-evasion game involving spacecraft with leader–follower information.In the proposed problem,the interplay between two spacecraft g... In this paper,we investigate analytical numerical iterative strategies for the pursuit-evasion game involving spacecraft with leader–follower information.In the proposed problem,the interplay between two spacecraft gives rise to a dynamic and real-time game,complicated further by the presence of perturbation.The primary challenge lies in crafting control strategies that are both efficient and applicable to real-time game problems within a nonlinear system.To overcome this challenge,we introduce the model prediction and iterative correction technique proposed in model predictive static programming,enabling the generation of strategies in analytical iterative form for nonlinear systems.Subsequently,we proceed by integrating this model predictive framework into a simplified Stackelberg equilibrium formulation,tailored to address the practical complexities of leader–follower pursuit-evasion scenarios.Simulation results validate the effectiveness and exceptional efficiency of the proposed solution within a receding horizon framework. 展开更多
关键词 model predictive control Pursuit-evasion problem Leader-follower game Stackelberg game Orbital game
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Measuring the NBA Teams’ Cross-Efficiency by DEA Game 被引量:1
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作者 Luiz Aizemberg Marcos Costa Roboredo +3 位作者 Thiago Graca Ramos Joao Carlos C.B.Soares de Mello Lidia Angulo Meza Alessandro Martins Alves 《American Journal of Operations Research》 2014年第3期101-112,共12页
In this paper, we use DEA to measure the NBA basketball teams’ efficiency in seasons 2006-2007, 2007-2008, 2008-2009 and 2009-2010. In this context, each team is a DMU;we select the payroll and the average attendance... In this paper, we use DEA to measure the NBA basketball teams’ efficiency in seasons 2006-2007, 2007-2008, 2008-2009 and 2009-2010. In this context, each team is a DMU;we select the payroll and the average attendance to be the inputs while the wins and the average points per game to be the outputs. First, in order to obtain benchmarks, we measure the DMUs efficiency through classic DEA BCC model with an assurance region for each one of the four seasons individually and together. When we consider the four seasons together, we may analyse whether the performance of each team increases or decreases over time. Next, we evaluate the teams cross efficiency by DEA game to consider that there is no cooperation among DMUs. This approach also improves the efficiencies discrimination. 展开更多
关键词 Data Envelopment Analysis DEA game cross-efficiency
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A Critical Model Construction of Knowledge Sharing Mechanism in Virtual Organization Based on Game Theoretic Perspective 被引量:9
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作者 LU Jinrong 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2015年第6期465-470,共6页
Virtual organization uses information technology to achieve a closer integration and better management of business relationships between internal and external parties. There are many emerging issues in virtual organiz... Virtual organization uses information technology to achieve a closer integration and better management of business relationships between internal and external parties. There are many emerging issues in virtual organization and one of them is knowl- edge sharing. Knowledge sharing that is the core of knowledge management plays a key role in virtual organization. However, game theoretic exploration about knowledge sharing mechanism based on virtual organization is seldom published, In this study, knowledge sharing mechanism in virtual organization enterprise is explored using game theories from two aspects based on the features of knowledge sharing in virtual organization enterprise. Fi- nally, the critical model of knowledge sharing mechanism in virtual organization also is presented based on the perspective of game analysis. 展开更多
关键词 game theoretic analysis knowledge sharing virtual organization critical model
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Modelling of a Human Driver’s Interaction with Vehicle Automated Steering Using Cooperative Game Theory 被引量:12
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作者 Xiaoxiang Na David J.Cole 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2019年第5期1095-1107,共13页
The introduction of automated driving systems raised questions about how the human driver interacts with the automated system. Non-cooperative game theory is increasingly used for modelling and understanding such inte... The introduction of automated driving systems raised questions about how the human driver interacts with the automated system. Non-cooperative game theory is increasingly used for modelling and understanding such interaction, while its counterpart, cooperative game theory is rarely discussed for similar applications despite it may be potentially more suitable. This paper describes the modelling of a human driver’s steering interaction with an automated steering system using cooperative game theory. The distributed Model Predictive Control approach is adopted to derive the driver’s and the automated steering system’s strategies in a Pareto equilibrium sense, namely their cooperative Pareto steering strategies. Two separate numerical studies are carried out to study the influence of strategy parameters, and the influence of strategy types on the driver’s and the automated system’s steering performance. It is found that when a driver interacts with an automated steering system using a cooperative Pareto steering strategy, the driver can improve his/her performance in following a target path through increasing his/her effort in pursuing his/her own interest under the driver-automation cooperative control goal. It is also found that a driver’s adoption of cooperative Pareto steering strategy leads to a reinforcement in the driver’s steering angle control, compared to the driver’s adoption of non-cooperative Nash strategy. This in turn enables the vehicle to return from a lane-change maneuver to straight-line driving swifter. 展开更多
关键词 AUTOMATED driving system cooperative game theory DRIVER modelLING
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Chaos game representation walk model for the protein sequences 被引量:3
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作者 高洁 蒋丽丽 徐振源 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第10期4571-4579,共9页
A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic (HP) model has been proposed by Yu et al (Physica A 337(2004) 171). A CGR-walk model is proposed based on the ne... A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic (HP) model has been proposed by Yu et al (Physica A 337(2004) 171). A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA(p, d, q) model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA(p, d, q) model. 展开更多
关键词 chaos game representation CGR-walk model protein sequence long-memory ARFIMA(p d q) model autocorrelation function
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Strategic games on a hierarchical network model 被引量:2
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作者 Yi-xiao LI Xiao-gang JIN +1 位作者 Fan-sheng KONG Hui-lan LUO 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第2期271-278,共8页
Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree... Among complex network models,the hierarchical network model is the one most close to such real networks as world trade web,metabolic network,WWW,actor network,and so on.It has not only the property of power-law degree distribution,but also the scaling clustering coefficient property which Barabási-Albert(BA)model does not have.BA model is a model of network growth based on growth and preferential attachment,showing the scale-free degree distribution property.In this paper,we study the evolution of cooperation on a hierarchical network model,adopting the prisoner's dilemma(PD)game and snowdrift game(SG)as metaphors of the interplay between connected nodes.BA model provides a unifying framework for the emergence of cooperation.But interestingly,we found that on hierarchical model,there is no sign of cooperation for PD game,while the fre-quency of cooperation decreases as the common benefit decreases for SG.By comparing the scaling clustering coefficient prop-erties of the hierarchical network model with that of BA model,we found that the former amplifies the effect of hubs.Considering different performances of PD game and SG on complex network,we also found that common benefit leads to cooperation in the evolution.Thus our study may shed light on the emergence of cooperation in both natural and social environments. 展开更多
关键词 Complex network Hierarchical network model Barabási-Albert (BA) model Prisoner's dilemma (PD) game Snowdrift game (SG)
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Multi-Modal Data Analysis Based Game Player Experience Modeling Using LSTM-DNN 被引量:1
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作者 Sehar Shahzad Farooq Mustansar Fiaz +4 位作者 Irfan Mehmood Ali Kashif Bashir Raheel Nawaz KyungJoong Kim Soon Ki Jung 《Computers, Materials & Continua》 SCIE EI 2021年第9期4087-4108,共22页
Game player modeling is a paradigm of computational models to exploit players’behavior and experience using game and player analytics.Player modeling refers to descriptions of players based on frameworks of data deri... Game player modeling is a paradigm of computational models to exploit players’behavior and experience using game and player analytics.Player modeling refers to descriptions of players based on frameworks of data derived from the interaction of a player’s behavior within the game as well as the player’s experience with the game.Player behavior focuses on dynamic and static information gathered at the time of gameplay.Player experience concerns the association of the human player during gameplay,which is based on cognitive and affective physiological measurements collected from sensors mounted on the player’s body or in the player’s surroundings.In this paper,player experience modeling is studied based on the board puzzle game“Candy Crush Saga”using cognitive data of players accessed by physiological and peripheral devices.Long Short-Term Memory-based Deep Neural Network(LSTM-DNN)is used to predict players’effective states in terms of valence,arousal,dominance,and liking by employing the concept of transfer learning.Transfer learning focuses on gaining knowledge while solving one problem and using the same knowledge to solve different but related problems.The homogeneous transfer learning approach has not been implemented in the game domain before,and this novel study opens a new research area for the game industry where the main challenge is predicting the significance of innovative games for entertainment and players’engagement.Relevant not only from a player’s point of view,it is also a benchmark study for game developers who have been facing problems of“cold start”for innovative games that strengthen the game industrial economy. 展开更多
关键词 game player modeling experience modeling player analytics deep learning LSTM game play data Candy Crush Saga
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Case Study on the Forestry Cooperation Model from Game Structure Perspective 被引量:1
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作者 Hao ZHANG Zhijian CAI Yu XIE 《Asian Agricultural Research》 2014年第7期49-51,62,共4页
Take Chinese yew cooperative organization for example,different game structures of forestry cooperation model were analyzed,the elative merit and applicable occasion was discussed combined with empirical investigation... Take Chinese yew cooperative organization for example,different game structures of forestry cooperation model were analyzed,the elative merit and applicable occasion was discussed combined with empirical investigation,and some suggestions were given also.The results showed that depending entirely on normal forest farmers cooperate spontaneously is difficult.Policies should be designed from the perspective of promoted village cadres and influential family salons to cooperation.When market factors become the main obstacle,it is necessary to introduce companies,relax constraints of forest management and build the right market atmosphere.According to unequal status of company and forest farmers,develop the cooperation model of " company + cooperation organization + farmers".In certain circumstances,especially there are several companies vicious competition,the intervention of association can play a coordinating role. 展开更多
关键词 FORESTRY COOPERATION COOPERATION model game struct
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Exploring the dynamic evolutionary mechanism of game model on the protection of traditional villages 被引量:1
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作者 LI Jiaqi JIN Tao +1 位作者 XIANG Wei HUANG Qinzhen 《Regional Sustainability》 2022年第3期188-207,共20页
With the rapid improvement of urbanization and industrialization in countries around the world,how to effectively solve the rapid demise of traditional villages is a social dilemma faced by all countries,which is why ... With the rapid improvement of urbanization and industrialization in countries around the world,how to effectively solve the rapid demise of traditional villages is a social dilemma faced by all countries,which is why a series of relevant protection regulations have been promulgated in different historical periods.However,the formulation of relevant policies is still not scientific,universal,and long-term.In this study,we constructed an evolutionary game model of local governments and residents based on the evolutionary game theory(EGT),which is used to explore the evolutionary stability strategy(ESS)and stability conditions of stakeholders under the premise of mutual influence and restriction.Besides,the study also included the analysis about the impacts of different influence factors on the evolution tendency of the game model.At the same time,numerical simulation examples were used to verify the theoretical results and three crucial conclusions have been drawn.Firstly,the strategic evolution of stakeholders is a dynamic process of continuous adjustment and optimization,and its results and speed show consistent interdependence.Secondly,the decision-making of stakeholders mainly depends on the basic cost,and the high cost of investment is not conducive to the protection of traditional villages.Thirdly,the dynamic evolutionary mechanism composed of different influence factors will have an impact on the direction and speed of decision-making of stakeholders,which provides the basis for them to effectively restrict the decision-making of each other.This study eliminates the weaknesses of existing research approaches and provides scientific and novel ideas for the protection of traditional villages,which can contribute to the formulation and improvement of the relevant laws and regulations. 展开更多
关键词 Traditional villages Evolutionary game theory(EGT) Evolutionary stability strategy(ESS) Dynamic evolutionary mechanism Evolutionary game model Local governments and residents
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Reverse Engineering, Some Board Games as a Key to the Development of Artificial Intelligence and Construction of Economic Models 被引量:1
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作者 Ewa Drabik 《Economics World》 2018年第2期121-132,共12页
Reverse engineering, also called back engineering, is the process of extracting knowledge or designing information from anything: mechanical device electronic components, computer programs, or biological, chemical ma... Reverse engineering, also called back engineering, is the process of extracting knowledge or designing information from anything: mechanical device electronic components, computer programs, or biological, chemical matters, and--subsequently--analyzing its components. Reverse engineering can be applied for the sake of creating artificial intelligence, e.g. when the used methods are based on very old games, such as Go and chess. Many generations of computers are able to play at the same level as human grandmasters. A computers' arrival at that level is due to imitation of human Go or chess play. A particular emphasis shall be placed upon the Go game, known for 5,500 years. Invented in China, it may be classified as the oldest board game, having its ardent enthusiasts until present times. Old physical issues can be easily projected upon the modeling of new economic phenomena and quantum games. The aim of this paper is to discuss the applications of reverse engineering, traditional social games and other domains, such as quantum physics, to the analysis of utterly new social as well as economic phenomena. 展开更多
关键词 reverse engineering category theory quantum games social games modelling of economic phenomena
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Research on Financing Game Model of Small and Medium-sized Enterprises based on Different Risk Categories 被引量:1
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作者 Tian Tang 《International Journal of Technology Management》 2016年第9期61-63,共3页
With the development of market economy and the deepening of economic system reform, some of the Small and medium-sized(SME) enterprises have become the most dynamic economic growth point in the national economy. Nev... With the development of market economy and the deepening of economic system reform, some of the Small and medium-sized(SME) enterprises have become the most dynamic economic growth point in the national economy. Nevertheless, SMEs are facing a lot of problems in the market competition, such as technical backwardness, information lag, lack of talents, etc.. The healthy development of SMEs is very important, whereas, SMEs’ financing is a worldwide problem, and the result of financing game between banks and enterprises depends on a variety of decision-making factors. In this paper, from the point of view of bank, we analyze the diffi culties of external financing of SMEs, and establish a financing game model based on different risk categories, in order to better solve the problems that remain in the process of financing and promote the healthy and sustainable development of SMEs. 展开更多
关键词 Financing game model Small and Medium-sized Enterprises Risk Categories Risk Management
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System dynamics of behaviour-evolutionary mix-game models
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作者 苟成玲 高洁萍 陈芳 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第11期224-229,共6页
In real financial markets there are two kinds of traders: one is fundamentalist, and the other is a trend-follower. The mix-game model is proposed to mimic such phenomena. In a mix-game model there are two groups of ... In real financial markets there are two kinds of traders: one is fundamentalist, and the other is a trend-follower. The mix-game model is proposed to mimic such phenomena. In a mix-game model there are two groups of agents: Group 1 plays the majority game and Group 2 plays the minority game. In this paper, we investigate such a case that some traders in real financial markets could change their investment behaviours by assigning the evolutionary abilities to agents: if the winning rates of agents are smaller than a threshold, they will join the other group; and agents will repeat such an evolution at certain time intervals. Through the simulations, we obtain the following findings: (i) the volatilities of systems increase with the increase of the number of agents in Group 1 and the times of behavioural changes of all agents; (ii) the performances of agents in both groups and the stabilities of systems become better if all agents take more time to observe their new investment behaviours; (iii) there are two-phase zones of market and non-market and two-phase zones of evolution and non-evolution; (iv) parameter configurations located within the cross areas between the zones of markets and the zones of evolution are suited for simulating the financial markets. 展开更多
关键词 minority game model mix-game model behavioural evolution system dynamics
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Discrete-time dynamic graphical games:model-free reinforcement learning solution 被引量:7
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作者 Mohammed I.ABOUHEAF Frank L.LEWIS +1 位作者 Magdi S.MAHMOUD Dariusz G.MIKULSKI 《Control Theory and Technology》 EI CSCD 2015年第1期55-69,共15页
This paper introduces a model-free reinforcement learning technique that is used to solve a class of dynamic games known as dynamic graphical games. The graphical game results from to make all the agents synchronize t... This paper introduces a model-free reinforcement learning technique that is used to solve a class of dynamic games known as dynamic graphical games. The graphical game results from to make all the agents synchronize to the state of a command multi-agent dynamical systems, where pinning control is used generator or a leader agent. Novel coupled Bellman equations and Hamiltonian functions are developed for the dynamic graphical games. The Hamiltonian mechanics are used to derive the necessary conditions for optimality. The solution for the dynamic graphical game is given in terms of the solution to a set of coupled Hamilton-Jacobi-Bellman equations developed herein. Nash equilibrium solution for the graphical game is given in terms of the solution to the underlying coupled Hamilton-Jacobi-Bellman equations. An online model-free policy iteration algorithm is developed to learn the Nash solution for the dynamic graphical game. This algorithm does not require any knowledge of the agents' dynamics. A proof of convergence for this multi-agent learning algorithm is given under mild assumption about the inter-connectivity properties of the graph. A gradient descent technique with critic network structures is used to implement the policy iteration algorithm to solve the graphical game online in real-time. 展开更多
关键词 Dynamic graphical games Nash equilibrium discrete mechanics optimal control model-free reinforcementlearning policy iteration
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Pricing Game Model of Wasted Clothing Recycling and Remanufacturing Based on Government Subsidy
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作者 WANG Mingjing ZHUANG Meiling LIU Jing 《Journal of Donghua University(English Edition)》 EI CAS 2019年第1期46-51,共6页
In the global environment of pursuing resource regeneration and green environmental protection, more and more wasted clothing need to be solved. In order to make full use of the wasted clothing and save land and soil ... In the global environment of pursuing resource regeneration and green environmental protection, more and more wasted clothing need to be solved. In order to make full use of the wasted clothing and save land and soil resources, an idea of wasted clothing's recycling and remanufacturing is put forward. In the new idea a pricing game model is established basing on Stacklberg differential game theory between traditional and remanufactured clothing. In this model, the differences in consumers' willingness to pay and the government's subsidies are considered. Government's optimal subsidy are obtained which ensure not only the interests of manufacturers but also environmental reputation and maximum social benefits. The study is helpful to push the wasted clothing's recycling and remanufacturing plan. It makes some index more precise quantification as government's subsidy, manufacturers and the social benefits. Government and manufactures can make the detailed cooperation plan reference to it. 展开更多
关键词 wasted CLOTHING RECYCLING and REMANUFACTURING PRICING game model government SUBSIDY Stacklberg differential game theory
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Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model
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作者 华达银 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第4期213-217,共5页
We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exp... We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class. 展开更多
关键词 evolutionary game model nonequilibrium phase transition with absorbing state cooperation phenomenon hysteresis behavior
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A CONNECTION ADMISSION CONTROL SCHEME BASED ON GAME THEORETICAL MODEL IN ATM NETWORKS
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作者 Chen Huimin Wang Pu Li Yanda (Department of Automation, Tsinghua University, Beijing 100084) 《Journal of Electronics(China)》 1999年第1期7-15,共9页
In this paper, the main schemes of connection admission control (CAC) in ATM networks are briefly discussed especially the principle of dynamic bandwidth allocation. Then the fair share of the bandwidth among differen... In this paper, the main schemes of connection admission control (CAC) in ATM networks are briefly discussed especially the principle of dynamic bandwidth allocation. Then the fair share of the bandwidth among different traffic sources is analyzed based on cooperative game model. A CAC scheme is proposed using the genetic algorithm (GA) to optimize the bandwidth-delay-product formed utilization function that ensures the fair share and accuracy of accepting/rejecting the incoming calls. Simulation results show that the proposed scheme ensures fairness of the shared bandwidth to different traffic sources. 展开更多
关键词 CONNECTION ADMISSION control Cooperative game model GENETIC algorithm Dynamic BANDWIDTH ALLOCATION ATM network
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Science Letters:Human-centered modeling for style-based adaptive games
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作者 Chee-onn WONG Jongin KIM +1 位作者 Eunjung HAN Keechul JUNG 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2009年第4期530-534,共5页
This letter proposes a categorization matrix to analyze the playing style of a computer game player for a shooting game genre. Our aim is to use human-centered modeling as a strategy for adaptive games based on entert... This letter proposes a categorization matrix to analyze the playing style of a computer game player for a shooting game genre. Our aim is to use human-centered modeling as a strategy for adaptive games based on entertainment measure to evaluate the playing experience. We utilized a self-organizing map (SOM) to cluster the player's style with the data obtained while playing the game. We further argued that style-based adaptation contributes to higher enjoyment, and this is reflected in our experiment using a supervised multilayered perceptron (MLP) network. 展开更多
关键词 Player modeling Categorization matrix Adaptive games Human-centered modeling Data clustering
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A Nash Game Approach to Mixed H_2/H_∞ Model Predictive Control: Part 3–Output Feedback Case
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作者 Pakkiriswamy Aadaleesan Prabirkumar Saha 《International Journal of Automation and computing》 EI CSCD 2018年第5期616-624,共9页
In this paper, the state-feedback Nash game based mixed H2/H∞ design^([1, 2])has been extended for output feedback case. The algorithm is applied to control bioreactor system with a Laguerre-Wavelet Network(LWN)^... In this paper, the state-feedback Nash game based mixed H2/H∞ design^([1, 2])has been extended for output feedback case. The algorithm is applied to control bioreactor system with a Laguerre-Wavelet Network(LWN)^([3, 4])model of the bioreactor.This is achieved by using the LWN model as a deviation model and by successively linearising the deviation model along the state trajectory. For reducing the approximation error and to improve the controller performance, symbolic derivation algorithm, viz.,automatic differentiation is employed. A cautionary note is also given on the fragility of the output feedback mixed H2/H∞ model predictive controller^([4, 5])due to its sensitivity to its own parametric changes. 展开更多
关键词 Robust model predictive control mixed H2/H∞ control Nash game output feedback model predictive control (MPC) automatic differentiation fragility of controller.
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Certainty of patient survival with reference to game information dynamic model
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作者 Hiroyuki Iida Takeo Nakagawa Nathan Nossal 《Open Journal of Preventive Medicine》 2012年第4期490-498,共9页
This paper is concerned with Hepato-Cellular Carcinoma (HCC) patients treated naturopathic agents. Patients treated with ≥4 agents survived significantly longer than patients treated with ≤3 agents. The great effect... This paper is concerned with Hepato-Cellular Carcinoma (HCC) patients treated naturopathic agents. Patients treated with ≥4 agents survived significantly longer than patients treated with ≤3 agents. The great effect is seen in patients treated with at least 4 agents that include Cordyceps sinensis. This greater certainty of patient survival without toxic side effects is significant benefit comparing with the conventional therapy. Treatment of HCC with a regimen of ≥4 agents prepared from natural products is associated with greater certainty of patient survival in a substantial portion of patients. The information dynamic model for certainty of patient survival is derived based on fluid mechanics, where a series of approximate solutions of the flow between two parallel flat walls, one of which is at rest, the other is suddenly accelerated from the rest to a constant velocity are used. The kinetic energy of certainty of patient survival decreases with increasing time, while the potential energy increases with increasing time. Total mechanical energy of patients treated with 4 or more agents is smaller than that treated with 3 or fewer agents. The kinetic energy (potential energy) of patients treated with 4 or more agents decreases (increases) more slower than the kinetic energy (potential energy) of patients treated with 3 or fewer agents. 展开更多
关键词 CERTAINTY of Patient Survival game INFORMATION Dynamic model Naturopathic Therapy HERBAL Treatment Natural ANTIOXIDANTS Hepato-Cellular Carcinoma
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