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

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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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

Driven by the visions of Internet of Things and 5G communications, recent years have seen a paradigm shift in mobile computing, from the centralized mobile cloud computing toward mobile edge computing (MEC). The main feature of MEC is to push mobile computing, network control and storage to the network edges (e.g., base stations and access points) so as to enable computation-intensive and latency-critical applications at the resource-limited mobile devices. MEC promises dramatic reduction in latency and mobile energy consumption, tackling the key challenges for materializing 5G vision. The promised gains of MEC have motivated extensive efforts in both academia and industry on developing the technology. A main thrust of MEC research is to seamlessly merge the two disciplines of wireless communications and mobile computing, resulting in a wide-range of new designs ranging from techniques for computation offloading to network architectures. This paper provides a comprehensive survey of the state-of-the-art MEC research with a focus on joint radio-and-computational resource management. We also discuss a set of issues, challenges, and future research directions for MEC research, including MEC system deployment, cache-enabled MEC, mobility management for MEC, green MEC, as well as privacy-aware MEC. Advancements in these directions will facilitate the transformation of MEC from theory to practice. Finally, we introduce recent standardization efforts on MEC as well as some typical MEC application scenarios.

A Survey on Mobile Edge Computing: The Communication Perspective

To reduce the energy consumption caused by cloud computing in cloud data centers, virtual machine (VM) dynamic migration technology has been widely used. With the VM dynamic migration technology, VMs can be migrated and consolidated dynamically, as such the number of active physical machines (PMs) is reduced, leading to the considerable energy saving. In this paper, we propose a QoS-Guaranteed energyefficient VM dynamic migration strategy, by taking the user quality of service (QoS) requirements and system load into account. With a more accurate energy consumption model, we first study the effect of system load and user QoS differentiation on the total energy consumption, and then define the migration threshold as a function of the variance of user QoS requirements and system load. We observe that an adaptive migration threshold is beneficial to minimize the total energy consumption, which should be set to be decreased with the growth of system load to lower the variance of user QoS requirements within each PM. Simulation results show the effectiveness of our proposed strategy in energy saving by comparing with the existing algorithms.

A QoS-Guaranteed Energy-Efficient VM Dynamic Migration Strategy in Cloud Data Centers

In wireless resource allocation, improving system throughput and simultaneously enhancing user fairness are two fundamental but contradictory objectives. As for fairness, both short-term and long-term fairness are of significant importance. However, less effort has been dedicated to explore the optimal tradeoff between system throughput and the two mentioned fairness in terms of widely used Jain's index. In this context, we aim to maximize system throughput subject to constraints on both short-term and long-term fairness in single cell downlink OFDMA systems. The difficulty of this issue lies in that the considered subchannel and slot allocation problem is a nonlinear integer programming problem, and furthermore seems to be non-causal. To overcome these challenges, we first relax the integer variables. Second, we prove that short-term fairness ensures long-term fairness so that the long-term fairness constraint is redundant and can be removed. Third, the problem is decomposed into a sequence of short-term convex optimization problems that can be easily solved. Numerical results show that the proposed method achieves a good suboptimal solution with small deviations from the optimal relaxed system throughput and the Jain's index constraint.

Throughput maximization with short- and long-term Jain's index guarantees in OFDMA systems

From an end-to-end performance perspective, a multi-agent-based cognitive resource management (MA-CRM) framework is proposed in this article. More importantly, we introduce a novel concept of resource flow (RF) as integrated CRM in a multi-dimensional environment scenario. We concentrate on the autonomous CRM framework in cognitive radio (CR) networks. Specifically, we first summarize the necessity of the novel concept for implementing intelligent and autonomous resource management considering both the requirements of various types of resource and the unified framework of the CRM scheme. Then, we introduce the concept of RF, including the technical aspects, purpose, classification, and description. Finally, we give a use case of RF for autonomous CRM, where the optimal RF is achieved to guarantee the resource-imbalanced requests of different service traffic flows.

https://link.springer.com/content/pdf/10.1007%2Fs11434-012-5209-9.pdf

Resource flow: Autonomous cognitive resource management framework for future networks

The next generation wireless network will be composed by various heterogenous wireless access networks, such as cellular network, worldwide interoperability for microwave access (WiMAX), wireless local area network (WLAN), etc. Different access networks cooperatively provide high-bandwidth connectivity with bandwidth guarantees. This paper proposes a utility-based access point selection scheme, which selects an accessible point for each user, such that the bandwidth requirement of each user is satisfied, and also the defined utility function is maximized. Due to the NP-complete nature of the problem, the existing proposals apply the greedy method to find a solution. We find that belief propagation is an efficient tool to solve this problem, and thus, we derive the same optimization objective in a new way, and then draw a factor graph representation which describes our combinatorial optimization problem. Afterwards, we develop the belief propagation algorithm, and show that our algorithm converges. Finally, we conduct numerical experiments to evaluate the convergency and accuracy of the belief propagation in load balancing problem.

Access point selection in heterogeneous wireless networks using belief propagation

In this paper, we investigate the individual channel estimation for three-node one-way relay network (OWRN), where both source and destination are equipped with multiple antennas. Without resorting to the composite channel estimation, as did in the traditional work, we directly estimate the individual channels from an iterative linear minimum mean-square-error (LMMSE) estimator. The closed-form least square (LS) channel estimator is also derived through matrix unitary diagonalization to provide a good initialization for the iterative LMMSE estimator. To make the work more complete, we present two performance lower bounds: Bayesian Cramer lower bound (BCRB) and linear estimation lower bound (LELB), for the proposed algorithm. Numerical results are provided to corroborate our proposed studies.

Min Sheng

Papers

A QoS-Guaranteed Energy-Efficient VM Dynamic Migration Strategy in Cloud Data Centers

Throughput maximization with short- and long-term Jain's index guarantees in OFDMA systems

Resource flow: Autonomous cognitive resource management framework for future networks

Access point selection in heterogeneous wireless networks using belief propagation

Iterative LMMSE individual channel estimation with superimposed training over one-way relay networks