Random @math -intersection graphs have recently received much interest in a wide range of application areas. Broadly speaking, a random @math -intersection graph is constructed by first assigning each vertex a set of items in some random manner, and then putting an undirected edge between all pairs of vertices that share at least @math items (the graph is called a random intersection graph when @math ). A special case of particular interest is a uniform random @math -intersection graph, where each vertex independently selects the same number of items uniformly at random from a common item pool. Another important case is a binomial random @math -intersection graph, where each item from a pool is independently assigned to each vertex with the same probability. Both models have found numerous applications thus far including cryptanalysis, and the modeling of recommender systems, secure sensor networks, online social networks, trust networks and small-world networks (uniform random @math -intersection graphs), as well as clustering analysis, classification, and the design of integrated circuits (binomial random @math -intersection graphs). In this paper, for binomial uniform random @math -intersection graphs, we present results related to @math -connectivity and minimum vertex degree. Specifically, we derive the asymptotically exact probabilities and zero-one laws for the following three properties: (i) @math -vertex-connectivity, (ii) @math -edge-connectivity and (iii) the property of minimum vertex degree being at least @math .
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1 Preliminaries.- 1.1 Introduction.- 1.2 Measures and Functions.- 1.3 Weak Topologies.- 1.4 Convergence of Measures.- 1.5 Complements.- 1.6 Notes.- I Markov Chains and Ergodicity.- 2 Markov Chains and Ergodic Theorems.- 2.1 Introduction.- 2.2 Basic Notation and Definitions.- 2.3 Ergodic Theorems.- 2.4 The Ergodicity Property.- 2.5 Pathwise Results.- 2.6 Notes.- 3 Countable Markov Chains.- 3.1 Introduction.- 3.2 Classification of States and Class Properties.- 3.3 Limit Theorems.- 3.4 Notes.- 4 Harris Markov Chains.- 4.1 Introduction.- 4.2 Basic Definitions and Properties.- 4.3 Characterization of Harris recurrence.- 4.4 Sufficient Conditions for P.H.R.- 4.5 Harris and Doeblin Decompositions.- 4.6 Notes.- 5 Markov Chains in Metric Spaces.- 5.1 Introduction.- 5.2 The Limit in Ergodic Theorems.- 5.3 Yosida's Ergodic Decomposition.- 5.4 Pathwise Results.- 5.5 Proofs.- 5.6 Notes.- 6 Classification of Markov Chains via Occupation Measures.- 6.1 Introduction.- 6.2 A Classification.- 6.3 On the Birkhoff Individual Ergodic Theorem.- 6.4 Notes.- II Further Ergodicity Properties.- 7 Feller Markov Chains.- 7.1 Introduction.- 7.2 Weak-and Strong-Feller Markov Chains.- 7.3 Quasi Feller Chains.- 7.4 Notes.- 8 The Poisson Equation.- 8.1 Introduction.- 8.2 The Poisson Equation.- 8.3 Canonical Pairs.- 8.4 The Cesaro-Averages Approach.- 8.5 The Abelian Approach.- 8.6 Notes.- 9 Strong and Uniform Ergodicity.- 9.1 Introduction.- 9.2 Strong and Uniform Ergodicity.- 9.3 Weak and Weak Uniform Ergodicity.- 9.4 Notes.- III Existence and Approximation of Invariant Probability Measures.- 10 Existence of Invariant Probability Measures.- 10.1 Introduction and Statement of the Problems.- 10.2 Notation and Definitions Preface 1 INTRODUCTION 1.1 Examples of Time Series 1.2 Objectives of Time Series Analysis 1.3 Some Simple Time Series Models 1.3.3 A General Approach to Time Series Modelling 1.4 Stationary Models and the Autocorrelation Function 1.4.1 The Sample Autocorrelation Function 1.4.2 A Model for the Lake Huron Data 1.5 Estimation and Elimination of Trend and Seasonal Components 1.5.1 Estimation and Elimination of Trend in the Absence of Seasonality 1.5.2 Estimation and Elimination of Both Trend and Seasonality 1.6 Testing the Estimated Noise Sequence 1.7 Problems 2 STATIONARY PROCESSES 2.1 Basic Properties 2.2 Linear Processes 2.3 Introduction to ARMA Processes 2.4 Properties of the Sample Mean and Autocorrelation Function 2.4.2 Estimation of @math and @math 2.5 Forecasting Stationary Time Series 2.5.3 Prediction of a Stationary Process in Terms of Infinitely Many Past Values 2.6 The Wold Decomposition 1.7 Problems 3 ARMA MODELS 3.1 ARMA( @math ) Processes 3.2 The ACF and PACF of an ARMA @math Process 3.2.1 Calculation of the ACVF 3.2.2 The Autocorrelation Function 3.2.3 The Partial Autocorrelation Function 3.3 Forecasting ARMA Processes 1.7 Problems 4 SPECTRAL ANALYSIS 4.1 Spectral Densities 4.2 The Periodogram 4.3 Time-Invariant Linear Filters 4.4 The Spectral Density of an ARMA Process 1.7 Problems 5 MODELLING AND PREDICTION WITH ARMA PROCESSES 5.1 Preliminary Estimation 5.1.1 Yule-Walker Estimation 5.1.3 The Innovations Algorithm 5.1.4 The Hannan-Rissanen Algorithm 5.2 Maximum Likelihood Estimation 5.3 Diagnostic Checking 5.3.1 The Graph of $ =1, ,n 5.3.2 The Sample ACF of the Residuals I. Introduction.- 1.1. General Remarks.- 1.2. The Robbins-Monro Process.- 1.3. A "Continuous" Process Version of Section 2.- 1.4. Regulation of a Dynamical System a simple example.- 1.5. Function Minimization: The Kiefer-Wolfowitz Procedure.- 1.6. Constrained Problems.- 1.7. An Economics Example.- II. Convergence w.p.1 for Unconstrained Systems.- 2.1. Preliminaries and Motivation.- 2.2. The Robbins-Monro and Kiefer-Wolfowitz Algorithms: Conditions and Discussion.- 2.3. Convergence Proofs for RM and KW-like Procedures.- 2.3.1. A Basic RM-like Procedure.- 2.3.2. One Dimensional RM and Accelerated RM Procedures.- 2.3.3. A Continuous Parameter RM Procedure.- 2.3.4. The Basic Kiefer-Wolfowitz Procedure.- 2.3.5. Random Directions KW Methods.- 2.4. A General Robbins-Monro Process: "Exogenous Noise".- 2.4.1. The Case of Bounded h(*,*).- 2.4.2. Unbounded h(*,*): Exogenous Noise.- 2.5. A General RM Process State Dependent Noise.- 2.5.1. Extensions and Localizations of Theorem 2.5.2.- 2.6. Some Applications.- 2.7. Mensov-Rademacher Estimates.- III. Weak Convergence of Probability Measures.- IV. Weak Convergence for Unconstrained Systems.- 4.1. Conditions and General Discussion.- 4.2. The Robbins-Monro and Kiefer-Wolfowitz Procedures.- 4.2.1. The Basic Robbins-Monro Procedure.- 4.2.2. The One-Dimensional Robbins-Monro Procedure.- 4.2.3. The Kiefer-Wolfowitz Procedure.- 4.2.4. A Case Where the Limit Satisfies a Generalized ODE.- 4.2.5. A Continuous Parameter KW Procedure.- 4.3. A General Robbins-Monro Process: Exogenous Noise.- 4.4. A General RM Process: State Dependent Noise.- 4.5. The Identification Problem.- 4.6. A Counter-Example to Tightness.- 4.7. Boundedness of Xn and Tightness of Xn(*) .- V 0 Introduction.- I Themes and Problems.- 1.0 Introduction.- 1.1 The theory of finance capital.- 1.2 Interlocking directorates and economic power.- 1.3 Financial groups.- 1.4 Corporate elite and capitalist class.- 1.5 Summary.- II Between Market and Hierarchy.- 2.0 Introduction.- 2.1 The organization of firms and markets: a neo-classical explanation.- 2.2 Some definitions of firms.- 2.3 Power and control.- 2.4 Ownership and control.- 2.5 Competition, cooperation and control.- 2.5.1 Concentration and centralization.- 2.5.2 The level-of-analysis problem.- 2.6 Summary.- III Imperialism in the Seventies: two models.- 3.0 Introduction.- 3.1 Theories of imperialism.- 3.1.1 Their origins.- 3.1.2 After World War II.- 3.2 Two models.- 3.3 Research design.- 3.4 Summary.- IV The International Corporate Elite.- 4.0 Introduction.- 4.1 The organization of the supervising and executive function in different countries.- 4.2 Selection of the international corporate elite.- 4.3 Network characteristics of the international corporate elite.- 4.3.0 Introduction.- 4.3.1 The finance capitalists.- 4.3.2 The big linkers.- 4.4 Types of interlocking directorates.- 4.4.0 Introduction.- 4.4.1 Multiple interlocks.- 4.5 Summary.- V National Versus International Integration.- 5.0 Introduction to some graph-theoretical concepts.- 5.1 General patterns in the international network.- 5.1.1 Compactness of the international network.- 5.1.2 International integration of national networks.- 5.2 The international network of Western firms.- 5.2.0 Introduction.- 5.2.1 Local centrality.- 5.2.2 Global centrality.- 5.2.3 Overall centrality.- 5.3 Industrial concentration versus economic centralization.- 5.4 Summary.- VI Domination an 1 Model Problem and Its Discretization.- 1.1 Conservation Laws.- 1.2 Finite Volume Methods.- 2 Multiscale Setting.- 2.1 Hierarchy of Meshes.- 2.2 Motivation.- 2.3 Box Wavelet.- 2.3.1 Box Wavelet on a Cartesian Grid Hierarchy.- 2.3.2 Box Wavelet on an Arbitrary Nested Grid Hierarchy.- 2.4 Change of Stable Completion.- 2.5 Box Wavelet with Higher Vanishing Moments.- 2.5.1 Definition and Construction.- 2.5.2 A Univariate Example.- 2.5.3 A Remark on Compression Rates.- 2.6 Multiscale Transformation.- 3 Locally Refined Spaces.- 3.1 Adaptive Grid and Significant Details.- 3.2 Grading.- 3.3 Local Multiscale Transformation.- 3.4 Grading Parameter.- 3.5 Locally Uniform Grids.- 3.6 Algorithms: Encoding, Thresholding, Grading, Decoding.- 3.7 Conservation Property.- 3.8 Application to Curvilinear Grids.- 4 Adaptive Finite Volume Scheme.- 4.1 Construction.- 4.1.1 Strategies for Local Flux Evaluation.- 4.1.2 Strategies for Prediction of Details.- 4.2 A gorithms: Initial data, Prediction, Fluxes and Evolution.- 5 Error Analysis.- 5.1 Perturbation Error.- 5.2 Stability of Approximation.- 5.3 Reliability of Prediction.- 6 Data Structures and Memory Management.- 6.1 Algorithmic Requirements and Design Criteria.- 6.2 Hashing.- 6.3 Data Structures.- 7 Numerical Experiments.- 7.1 Parameter Studies.- 7.1.1 Test Configurations.- 7.1.2 Discretization.- 7.1.3 Computational Complexity and Stability.- 7.1.4 Hash Parameters.- 7.2 Real World Application.- 7.2.1 Configurations.- 7.2.2 Discretization.- 7.2.3 Discussion of Results.- A Plots of Numerical Experiments.- B The Context of Biorthogonal Wavelets.- B.1 General Setting.- B.1.1 Multiscale Basis.- B.1.2 Stable Completion.- B.1.3 Multiscale Transformation.- B.2 1. Introduction and Overview.- 1.1 Why Integrate Neurons and Symbols?.- 1.2 Strategies of Neural-Symbolic Integration.- 1.3 Neural-Symbolic Learning Systems.- 1.4 A Simple Example.- 1.5 How to Read this Book.- 1.6 Summary.- 2. Background.- 2.1 General Preliminaries.- 2.2 Inductive Learning.- 2.3 Neural Networks.- 2.3.1 Architectures.- 2.3.2 Learning Strategy.- 2.3.3 Recurrent Networks.- 2.4 Logic Programming.- 2.4.1 What is Logic Programming?.- 2.4.2 Fixpoints and Definite Programs.- 2.5 Nonmonotonic Reasoning.- 2.5.1 Stable Models and Acceptable Programs.- 2.6 Belief Revision.- 2.6.1 Truth Maintenance Systems.- 2.6.2 Compromise Revision.- I. Knowledge Refinement in Neural Networks.- 3. Theory Refinement in Neural Networks.- 3.1 Inserting Background Knowledge.- 3.2 Massively Parallel Deduction.- 3.3 Performing Inductive Learning.- 3.4 Adding Classical Negation.- 3.5 Adding Met alevel Priorities.- 3.6 Summary and Further Reading.- 4. Experiments on Theory Refinement.- 4.1 DNA Sequence Analysis.- 4.2 Power Systems Fault Diagnosis.- 4.3.Discussion.- 4.4.Appendix.- II. Knowledge Extraction from Neural Networks.- 5. Knowledge Extraction from Trained Networks.- 5.1 The Extraction Problem.- 5.2 The Case of Regular Networks.- 5.2.1 Positive Networks.- 5.2.2 Regular Networks.- 5.3 The General Case Extraction.- 5.3.1 Regular Subnetworks.- 5.3.2 Knowledge Extraction from Subnetworks.- 5.3.3 Assembling the Final Rule Set.- 5.4 Knowledge Representation Issues.- 5.5 Summary and Further Reading.- 6. Experiments on Knowledge Extraction.- 6.1 Implementation.- 6.2 The Monk's Problems.- 6.3 DNA Sequence Analysis.- 6.4 Power Systems Fault Diagnosis.- 6.5 Discussion.- III. Knowledge Revision in Neural Netw 1. Introduction and Historical Background 1.1 Why make human figure models? 1.2 Historical roots 1.3 What is currently possible? 1.4 Manipulation, animation, and simulation 1.5 What did we leave out? 2. Mody Modeling 2.1 Geometric body modeling 2.2 Representing articulated figures 2.3 A flexible torso model 2.4 Shoulder complex 2.5 Clothing models 2.6 The anthropometry database 2.7 The anthropometry spreadsheet 2.8 Strength and torque display 3. Spatial Interaction 3.1 Direct manipulation 3.2 Manipulation with constraints 3.3 Inverse kinematic positioning 4. Behavioral Control of Articulated Figures 4.1 An interactive system for postural control 4.2 Interactive manipulation with behaviors 4.3 The animation interface 4.4 Human figure motions 4.5 Virtual human control 5. Simulation with Societies of Behaviors 5.1 Forward simulation with behaviors 5.2 Locomotion 5.3 Strength guided motion 5.4 Collision-free path and motion planning 5.5 Posture planning 6. Task-level Specifications 6.1 Performance simulation with simple commands 6.2 Natural language expressions of kinematics and space 6.3 Task-level simulation 6.4 A framework for instruction understanding 7. Epilogue 7.1 A road map toward the future 7.2 Conclusion 1.1. Introduction.- 1.2. Outer Integrals and Measurable Majorants.- 1.3. Weak Convergence.- 1.4. Product Spaces.- 1.5. Spaces of Bounded Functions.- 1.6. Spaces of Locally Bounded Functions.- 1.7. The Ball Sigma-Field and Measurability of Suprema.- 1.8. Hilbert Spaces.- 1.9. Convergence: Almost Surely and in Probability.- 1.10. Convergence: Weak, Almost Uniform, and in Probability.- 1.11. Refinements.- 1.12. Uniformity and Metrization.- 2.1. Introduction.- 2.2. Maximal Inequalities and Covering Numbers.- 2.3. Symmetrization and Measurability.- 2.4. Glivenko-Cantelli Theorems.- 2.5. Donsker Theorems.- 2.6. Uniform Entropy Numbers.- 2.7. Bracketing Numbers.- 2.8. Uniformity in the Underlying Distribution.- 2.9. Multiplier Central Limit Theorems.- 2.10. Permanence of the Donsker Property.- 2.11. The Central Limit Theorem for Processes.- 2.12. Partial-Sum Processes.- 2.13. Other Donsker Classes.- 2.14. Tail Bounds.- 3.1. Introduction.- 3.2. M-Estimators.- 3.3. Z-Estimators.- 3.4. Rates of Convergence.- 3.5. Random Sample Size, Poissonization and Kac Processes.- 3.6. The Bootstrap.- 3.7. The Two-Sample Problem.- 3.8. Independence Empirical Processes.- 3.9. The Delta-Method.- 3.10. Contiguity.- 3.11. Convolution and Minimax Theorems.- A. Appendix.- A.1. Inequalities.- A.2. Gaussian Processes.- A.2.1. Inequalities and Gaussian Comparison.- A.2.2. Exponential Bounds.- A.2.3. Majorizing Measures.- A.2.4. Further Results.- A.3. Rademacher Processes.- A.4. Isoperimetric Inequalities for Product Measures.- A.5. Some Limit Theorems.- A.6. More Inequalities.- A.6.1. Binomial Random Variables.- A.6.2. Multinomial Random Vectors.- A.6.3. Rademacher Sums.- Notes.- References.- Author Index.- List of Sy Preface. 1 Introduction. 1.1 Autonomous Agents. 1.2 Characteristics of Agents. 1.3 Multi-Agent Systems. 1.4 Hello World! 2 The BDI Agent Model. 2.1 Agent-Oriented Programming. 2.2 Practical Reasoning. 2.3 A Computational Model of BDI Practical Reasoning. 2.4 The Procedural Reasoning System. 2.5 Agent Communication. 3 The Jason Agent Programming Language. 3.1 Beliefs. 3.2 Goals. 3.3 Plans. 3.4 Example: A Complete Agent Program. 3.5 Exercises. 4 Jason Interpreter. 4.1 The Reasoning Cycle. 4.2 Plan Failure. 4.3 Interpreter Configuration and Execution Modes. 4.4 Pre-Defined Plan Annotations. 4.5 Exercises. 5 Environments. 5.1 Support for Defining Simulated Environments. 5.2 Example: Running a System of Multiple Situated Agents. 5.3 Exercises. 6 Communication and Interaction. 6.1 Available Performatives. 6.2 Informal Semantics of Receiving Messages. 6.3 Example: Contract Net Protocol. 6.4 Exercises. 7 User-Defined Components. 7.1 Defining New Internal Actions. 7.2 Customising the Agent Class. 7.3 Customising the Overall Architecture. 7.4 Customising the Belief Base. 7.5 Pre-Processing Directives. 7.6 Exercises. 8 Advanced Goal-Based Programming. 8.1 BDI Programming. 8.2 Declarative (Achievement) Goal Patterns. 8.3 Commitment Strategy Patterns. 8.4 Other Useful Patterns. 8.5 Pre-Processing Directives for Plan Patterns. 9 Case Studies. 9.1 Case Study I: Gold Miners. 9.2 Case Study II: Electronic Bookstore. 10 Formal Semantics. 10.1 Semantic Rules. 10.2 Semantics of Message Exchange in a Multi-Agent System. 10.3 Semantic Rules for Receiving Messages. 10.4 Semantics of the BDI Modalities for AgentSpeak. 11 Conclusions. 11.1 Jason and Agent-Oriented Programming. 11.2 Ongoing Work and Related Res