There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Statistics for Spatial Data.

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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

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

In this letter, we investigate the effect of imperfect channel estimation on the performance of distributed space-time block codes (DSTBCs) with amplify-and-forward relaying. Exploiting the orthogonality of the underlying code, we derive a maximum likelihood metric conditioned on the channel estimate acquired through the insertion of pilot symbols. For a large number of pilot symbols, we demonstrate that the proposed decoding rule coincides with the so-called mismatched receiver. On the other hand, as the number of pilot symbols decreases, the proposed decoder converges to a non-coherent detector. Through Monte-Carlo simulations, we further demonstrate that the performance of the proposed scheme lies within 0.8 dB of the genie receiver performance bound.

/pdf/pilot-symbol-assisted-detection-scheme-for-distributed-3d4inj70im.pdf

Pilot-symbol-assisted detection scheme for distributed orthogonal space-time block coding

TG7r1 channel model document for high rate PD communications

We analyze the error rate performance of coded wireless optical links operating over atmospheric channels, where the turbulence-induced fading is modeled by the negative exponential distribution, K distribution and I-K distribution. First, we derive bounds on the pairwise error probability (PEP) for each fading model and then apply the transfer function technique in conjunction with derived PEP bounds to obtain bit error rate performance. Simulation results are also included to confirm the analytical results.

/pdf/error-performance-analysis-of-coded-wireless-optical-links-24jqw4qr01.pdf

Error performance analysis of coded wireless optical links over atmospheric turbulence channels

In this paper, we investigate the information theoretic performance of parallel relaying in free-space optical (FSO) communications over Gamma-Gamma fading channels. We consider an intensity modulation/direct-detection (IM/DD) FSO system with a single relay and a line-of-sight link between the source and the destination. Considering both amplify-and-forward and decode-and-forward relaying, we develop performance characterizations of each relaying mode in terms of outage probability, diversity gain, coding gain, and diversity-multiplexing tradeoff (DMT). Our results demonstrate that parallel relaying improves the performance of FSO systems by bringing diversity advantages. In addition, both relaying modes achieve the same DMT and diversity gain while their coding gains can be different depending on underlying channels' characteristics.

Performance Analysis of Parallel Relaying in Free-Space Optical Systems

Although there has been a growing interest on the study of diversity-multiplexing tradeoff (DMT), the existing works are mostly restricted to the outcomes reported for Rayleigh, Rician, and Nakagami fading channels. In this paper, we investigate the optimal tradeoff in the presence of log-normal fading, which provides an accurate model for indoor wireless, optical wireless, and ultra-wideband channels. We consider a multiple-input multiple-output (MIMO) log-normal channel, derive the outage probability expression, and then present the asymptotical DMT expression. It is shown that the asymptotical maximum diversity gain tends to infinity with logarithm of signal-to-noise ratio (SNR). To have further insight, we normalize the DMT with that of single-input single-output case and express the relative asymptotical DMT of the MIMO log-normal channel as a function of the number of transmit and receive antennas. We further study DMT for finite SNRs and demonstrate convergence to the asymptotical case. Extensive numerical results are provided to corroborate the analytical derivation.

Murat Uysal

Papers

Pilot-symbol-assisted detection scheme for distributed orthogonal space-time block coding

TG7r1 channel model document for high rate PD communications

Error performance analysis of coded wireless optical links over atmospheric turbulence channels

Performance Analysis of Parallel Relaying in Free-Space Optical Systems

Diversity-Multiplexing Tradeoff for Log-Normal Fading Channels