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Table Of Integrals Series And Products

Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Matrix Factorization Techniques for Recommender Systems

/pdf/a-break-in-the-clouds-towards-a-cloud-definition-svovsw1r5a.pdf

A Break in the Clouds: Towards a Cloud Definition

This paper considers an energy-limited cognitive relay network, where a secondary transmitter (ST) assists to forward the traffic from a primary transmitter (PT) to a primary receiver (PR), in exchange for serving its own secondary receiver (SR) in the same frequency. The multiple-antenna ST is assumed to be energy-constrained and powered by both information flow from source (PT) and dedicated energy streams from destinations (PR and SR), which is called a destination-aided wireless power transfer (DWPT) scheme. Then, the relay processing matrix, cognitive beamforming vector, and power splitter are jointly designed to maximize the rate of secondary users under the energy causality constraint and the constraint that the demanded rate of primary users is satisfied. For the perfect channel state information (CSI) case, by adopting the semi-definite relax technique and the Charnes–Cooper transformation, the global optimal solution is given. To reduce the complexity, matrix decomposition, zero forcing scheme, and dual method are jointly employed to derive a suboptimal solution. For the imperfect CSI case, the S-procedure is used to transform the worst case robust problem into a tractable semi-definite program. Simulation results reveal that our proposed DWPT scheme is greatly preferred for both perfect and imperfect CSI cases when ST is close to PR/SR.

Destination-Aided Wireless Power Transfer in Energy-Limited Cognitive Relay Systems

This paper addresses the filter design and user selection issues for the downlink of a multi-user MIMO-relay system. To eliminate interuser interference, the filter design is based on the singular value decomposition (SVD) of the first hop link and block-diagonalization (BD) for the second hop link. Then the problem is converted to the power allocation problem at the relay station (RS). It can be determined in a closed- form by the water-filling policy. In a practical system with a large number of users, the RS need to select a subset of best users to serve. The exhaustive search for the optimal userset is, however, computationally prohibitive. Therefore, we propose a low-complexity algorithm that is based on the MIMO-relay channel capacity. Simulation results show that the proposed linear filter design scheme achieves significant system performance improvement compared with the equal power allocation scheme and the user selection scheme allows for a reasonable tradeoff between the complexity and performance.

Linear Filter Design for Multi-User MIMO-Relay Downlink Systems with User Selection

Abstract Nicotine, a toxic and addictive alkaloid from tobacco, is an environmental pollutant. However, nicotine-degrading bacteria (NDB) and their function in tobacco planting soil are not fully understood. First, 52 NDB strains belonging to seven genera were isolated from tobacco soil. The most dominant genera were Flavobacterium (36.5%), Pseudomonas (30.8%), and Arthrobacter (15.4%), and Chitinophaga and Flavobacterium have not been previously reported. Then, two efficient NDB strains, Arthrobacter nitrophenolicus ND6 and Stenotrophomonas geniculata ND16, were screened and inoculated in the compost fertilizer from tobacco waste. The nicotine concentrations were reduced from 1.5 mg/g (DW) to below the safety threshold of 0.5 mg/g. Furthermore, strain ND6 followed the pyridine pathway of nicotine degradation, but the degrading pathway in strain ND16 could not be determined according to genomic analysis and color change. Finally, the abundance of nicotine-degrading genes in tobacco rhizosphere soil was investigated via metagenomic analysis. Five key genes, ndhA , nctB , kdhL , nboR , and dhponh , represent the whole process of nicotine degradation, and their abundance positively correlated with soil nicotine concentrations ( p &lt; 0.05). In conclusion, various NDB including unknown species live in tobacco soil and degrade nicotine efficiently. Some key nicotine-degrading genes could be used in monitoring nicotine degradation in the environment. The fermentation of compost from tobacco waste is a promising application of efficient NDB. Graphical Abstract 

/pdf/cultivation-and-application-of-nicotine-degrading-bacteria-14hrt0aq.pdf

Cultivation and application of nicotine-degrading bacteria and environmental functioning in tobacco planting soil

Distributed mobile cloud computing is a new paradigm to enhance the edge cloud computing capacity and reduce the energy of application processing. In this paper, we establish a distributed cloudlet system which consists of several cloudlets and a computation-intensive application. The application can be divided into multiple related tasks. Each task selects mobile device or the appropriate offloading cloudlet to optimize utility. Besides energy consumption, the utility includes user mobility predictive probability, channel availability and cloudlet availability. Considering these factors can overcome the problem resulting from the user mobility and reduce the probability of connection failure while ensuring processing efficiency. We formulated this dynamic offloading problem as a transferable coalition game because each task is a sensible player to maximize overall utility. Simulation results demonstrate that the dynamic offloading decision scheme we proposed can get a better offloading decision with low complexity.

Multi-factor based Dynamic Offloading with Coalitional Game in Mobile Cloud Computing

Cloud radio access network (C-RAN) is a promising solution for future wireless network due to easy cooperation among remote radio heads (RRHs) and concentrated management in baseband unit (BBU) pool. Physical servers in the BBU provides computation ability in the form of virtual machines(VMs) to manage data of different users. In this paper, we focus on a scenario where each server dynamically provides computation capability according to users'(UE) quality of service (QoS) requirement, which is more practical. By jointly optimizing joint beamforming, RRH selection and dynamic computation allocation under the constraint of limited fronthaul and computation capacity, we minimize the network power consumption (NPC) in both RRHs and BBU pool. The formulated problem is non-convex and difficult to solve in general. We propose a simple two-step iterative algorithm to solve the problem. Firstly, we solve the common wireless optimization problem without considering computation allocation. Then by fixing the transmitting beamforming, we solve the computation resource allocation problem, which is a 0-1 multiple knapsack problem (MKP). Simulation results suggests that our proposed dynamic resource allocation algorithm can improve the system performance and save energy.

Ying Wang

Papers

Destination-Aided Wireless Power Transfer in Energy-Limited Cognitive Relay Systems

Linear Filter Design for Multi-User MIMO-Relay Downlink Systems with User Selection

Cultivation and application of nicotine-degrading bacteria and environmental functioning in tobacco planting soil

Multi-factor based Dynamic Offloading with Coalitional Game in Mobile Cloud Computing

Dynamic Computation and Radio Resource Allocation in Downlink Green C-RAN Systems