Elements of random walk and diffusion processes [[electronic resource] /] / Oliver C. Ibe

• Record Nr.: UNINA9910139012803321
• Autore: Ibe Oliver C (Oliver Chukwudi), <1947->
• Pubbl/distr/stampa: Hoboken, N.J., : John Wiley & Sons, Inc., 2013
• ISBN: 1-118-61793-2; 1-118-61805-X; 1-118-62985-X
• Descrizione fisica: 1 online resource (278 p.)
• Collana: Wiley series in operations research and management science
• Classificazione: MAT003000
• Disciplina: 519.2/82
• Soggetti: Random walks (Mathematics); Diffusion processes
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Elements of Random Walk and Diffusion Processes; Copyright; Contents; Preface; Acknowledgments; 1 Review of Probability Theory; 1.1 Introduction; 1.2 Random Variables; 1.2.1 Distribution Functions; 1.2.2 Discrete Random Variables; 1.2.3 Continuous Random Variables; 1.2.4 Expectations; 1.2.5 Moments of Random Variables and the Variance; 1.3 Transform Methods; 1.3.1 The Characteristic Function; 1.3.2 Moment-Generating Property of the Characteristic Function; 1.3.3 The s-Transform; 1.3.4 Moment-Generating Property of the s-Transform; 1.3.5 The z-Transform; 1.3.6 Moment-Generating Property of the z-Transform1.4 Covariance and Correlation Coefficient; 1.5 Sums of Independent Random Variables; 1.6 Some Probability Distributions; 1.6.1 The Bernoulli Distribution; 1.6.2 The Binomial Distribution; 1.6.3 The Geometric Distribution; 1.6.4 The Poisson Distribution; 1.6.5 The Exponential Distribution; 1.6.6 Normal Distribution; 1.7 Limit Theorems; 1.7.1 Markov Inequality; 1.7.2 Chebyshev Inequality; 1.7.3 Laws of Large Numbers; 1.7.4 The Central Limit Theorem; Problems; 2 Overview of Stochastic Processes; 2.1 Introduction; 2.2 Classification of Stochastic Processes2.3 Mean and Autocorrelation Function; 2.4 Stationary Processes; 2.4.1 Strict-Sense Stationary Processes; 2.4.2 Wide-Sense Stationary Processes; 2.5 Power Spectral ; Density; 2.6 Counting Processes; 2.7 Independent Increment Processes; 2.8 Stationary Increment Process; 2.9 Poisson Processes; 2.9.1 Compound Poisson Process; 2.10 Markov Processes; 2.10.1 Discrete-Time Markov Chains; 2.10.2 State Transition Probability Matrix; 2.10.3 The k-Step State Transition Probability; 2.10.4 State Transition Diagrams; 2.10.5 Classification of States; 2.10.6 Limiting-State Probabilities2.10.7 Doubly Stochastic Matrix; 2.10.8 Continuous-Time Markov Chains; 2.10.9 Birth and Death Processes; 2.11 Gaussian Processes; 2.12 Martingales; 2.12.1 Stopping Times; Problems; 3 One-Dimensional Random Walk; 3.1 Introduction; 3.2 Occupancy Probability; 3.3 Random Walk as a Markov Chain; 3.4 Symmetric Random Walk as a Martingale; 3.5 Random Walk with Barriers; 3.6 Mean-Square Displacement; 3.7 Gambler's Ruin; 3.7.1 Ruin Probability; 3.7.2 Alternative Derivation of Ruin Probability; 3.7.3 Duration of a Game; 3.8 Random Walk with Stay; 3.9 First Return to the Origin3.10 First Passage Times for Symmetric Random Walk; 3.10.1 First Passage Time via the Generating Function; 3.10.2 First Passage Time via the Reflection Principle; 3.10.3 Hitting Time and the Reflection Principle; 3.11 The Ballot Problem and the Reflection Principle; 3.11.1 The Conditional Probability Method; 3.12 Returns to the Origin and the Arc-Sine Law; 3.13 Maximum of a Random Walk; 3.14 Two Symmetric Random Walkers; 3.15 Random Walk on a Graph; 3.15.1 Proximity Measures; 3.15.2 Directed Graphs; 3.15.3 Random Walk on an Undirected Graph; 3.15.4 Random Walk on a Weighted Graph
• Sommario/riassunto: "Featuring an introduction to stochastic calculus, this book uniquely blends diffusion equations and random walk theory and provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. It covers standard methods and applications of Brownian motion and discusses Levy motion; addresses fractional calculus; introduces percolation theory and its relationship to diffusion processes; and more"--

Concepts, Frames and Cascades in Semantics, Cognition and Ontology

• Record Nr.: UNINA9910482867903321
• Autore: Löbner Sebastian
• Pubbl/distr/stampa: Springer Nature, 2021; Cham : , : Springer International Publishing AG, , 2021; ©2021
• ISBN: 9783030502003; 3030502007
• Descrizione fisica: 1 online resource (475 pages)
• Collana: Language, Cognition, and Mind ; ; v.7
• Classificazione: LAN009000PHI015000PSY040000
• Altri autori (Persone): GamerschlagThomas; KalenscherTobias; SchrenkMarkus; ZeevatHenk
• Soggetti: linguistics; Philosophy of mind; Experimental psychology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- Introduction -- 1 Cognitive Structures in Natural Language Semantics -- 2 Cognitive Structures in Philosophy -- 3 Cognitive Structures in Psychology -- 4 Summaries -- 4.1 Part I Pushing the Boundaries of Formal Semantics -- 4.2 Part II Concept Theory -- 4.3 Part III Conceptualizing Eventualities -- 4.4 Part IV Prototypes and Probabilities -- 4.5 Part V Cognition and Psychology -- References -- Pushing the Boundaries of Formal Semantics -- A Compositional Pluralist Semantics for Extensional and Attitude Verbs -- 1 Introduction -- 2 Accounts of Truth-Conditional and Attitude Content -- 2.1 The Relation Between Truth-Conditional and Attitude Content -- 2.2 Attempts at (Re-)Connecting Truth-Conditional and Attitude Content -- 2.3 Desiderata for an Account of Truth-Conditional and Attitude Content -- 3 Integrated Semantics -- 3.1 Centered Informational Situations -- 3.2 The Integrated Content of Sentences -- 3.3 The Interpretation of Proper Names -- 4 The Compositional ; Interpretation of VPs -- 5 Extensional and Attitude Verbs in IS -- 5.1 The Interpretation of Extensional Verbs -- 5.2 The Interpretation of Attitude Verbs -- 5.3 Attitudinal Embeddings of Extensional Verbs -- 6 Conclusion and Future Work -- References -- Counting Possible Configurations -- 1 Introduction -- 2 The Problem with Configurations -- 3 An Individual Concept Analysis -- 4 Generalizing the Individual Concept Analysis -- 4.1 Is Everything an Individual Concept? -- 4.2 Coercion to Constituting Parts -- 4.3 Joining and Counting Individual Concepts -- 4.4 Collective and Cumulative Interpretations -- 5 The Property Analysis -- 6 Conclusion -- References -- Structure and Ontology in Nonlocal Readings of Adjectives -- 1 Introduction -- 2 Nonlocal Readings of Adjectives -- 2.1 On `Occasional' -- 2.2 Returning to `Average' -- 2.3 Wrong.; 2.4 `Whole' and `Entire' -- 2.5 Epistemic Adjectives -- 2.6 Same and Different -- 2.7 Modal Superlatives: `Possible' and Its Kin -- 2.8 Miscellaneous Obscurities and Novelties -- 3 Three Classes of Nonlocal Readings -- 4 Some Background -- 4.1 Incorporation -- 4.2 Structure Versus Ontology: The First Step -- 4.3 The Kind Analysis of `Occasional' -- 5 The Modular Strategy -- 5.1 Determiner-Like Adjectives -- 5.2 Determiners That Work -- 5.3 Determiners That Don't Work -- 5.4 A Word About `Occasional' -- 5.5 The Weak Quantifier Class -- 5.6 Summary -- 6 Taking Stock -- 6.1 Could Things Be so Simple? -- 6.2 Kinds and Concepts -- 7 Final Remarks -- References -- Concept Theory -- How Can Semantics Avoid the Troubles with the Analytic/Synthetic Distinction? -- 1 Semantics and the Architecture of Cognition -- 2 The Analytic/Synthetic Distinction and Semantic Theories -- 2.1 Causatives -- 2.2 Indeterminacy (or "Coercion") -- 3 Alternative: Atomism and Inferences -- 3.1 Back to Causatives -- 3.2 Back to "Coercion" -- 3.3 Conclusion: Atomic Concepts and Inferences -- References -- Linguistic Relativity and Flexibility of Mental Representations: Color Terms in a Frame Based Analysis -- 1 Introduction -- 2 Color Terms and Whorfianism: Some Coordinates -- 2.1 Universalism, ``deep'' and ``shallow'' Whorfianism -- Intertwined Issues -- 2.2 ``Shallow'' Effects of Color labelling -- 3 Frames and Representation of Colors -- 4 Color Words and Flexible Use of Representations' Features -- 5 A Brief Excursus into Another Conceptual Domain: Counting and Motor Representations -- 6 Back on Colors: Stroop Task And Language-Perception Interface -- 7 Conclusions and Open Questions -- References -- Implicatures and Naturalness -- 1 Theoretical Background -- 2 Input Data -- 3 Building an Implicature Space -- 4 Naturalness -- 5 Concluding Remarks -- References.; Perception, Types and Frames -- 1 Introduction -- 2 Types and Cognition -- 3 Record Types and Frames -- 4 Conclusion -- References -- Conceptualizing Eventualities -- An XMG Account of Multiplicity of Meaning in Derivation -- 1 Introduction -- 2 Data and Analysis -- 3 XMG Implementation -- 4 Conclusion -- References -- Operationalizing the Role of Context in Language Variation: The Role of Perspective Alignment in the Spanish Imperfective Domain -- 1 Introduction -- 2 On the Spanish Present-Progressive and Simple-Present Markers -- 3 The Meaning of the Progressive and the Imperfective: A Communicative Perspective -- 4 The Markers of the Spanish Progressive Are not in Free Variation: Implications -- 5 Analysis: The Psychological Roots of Shared Perceptual Access -- 6 Summary and Conclusions -- References -- A Frame-Based Analysis of Verbal Particles in Hungarian -- 1 The Verbal Particle in Hungarian -- 2 Scalar Analysis and Frame-Semantic Representation -- 3 Semantic Analysis of Verbal Particles -- 4 Semantic Composition and the Syntax-; Semantics Interface -- 5 Summary -- References -- On the Fictive Reading of German Steigen 'Climb, Rise': A Frame Account -- 1 Introduction -- 2 Previous Accounts of Fictive Motion -- 3 The Four Major Readings of Steigen 'Climb, Rise, Step' -- 4 Frame Analysis of Dynamic Steigen: Manner and Directional Reading -- 4.1 Frames for Objects -- 4.2 Steigenmm -- 4.3 Steigendir -- 5 Steigenfict: Admissible Modifiers and Subject Referents -- 6 Frame Analysis of Steigenfict -- 7 Steigenins -- 8 Conclusion -- References -- Cascades. Goldman's Level-Generation, Multilevel Categorization of Action, and Multilevel Verb Semantics -- 1 Introduction -- 1.1 The Intuitive Notion of "Level-Generation" -- 1.2 The Structure of the Chapter -- 2 Level-Generation: Doing Multiple Things in One.; 2.1 Preliminary: Act-Tokens, Act-Types, and Act-TTs -- 2.2 Goldman's Theory of Act-Levels -- 2.3 Critics of Goldman's Theory -- 2.4 Goldman's Theory of Human Action Applied to Cognitive Representation -- 2.5 Level-Generation and Augmentation Generation -- 2.6 C- Constitution -- 3 Cascades and Verb Classes -- 3.1 Basic Versus Non-basic Act-Types -- 3.2 Verbs of Basic and Non-basic Action -- 3.3 Criterion Predicates -- 3.4 Means of Explicit Level-Generation -- 3.5 Implicit Level-Generation -- 4 Cascades and Frames -- 4.1 Barsalou Frames -- 4.2 Cascades in Frame Theory -- 5 The Writing Cascade -- 5.1 Austin's Speech Act Cascade -- 5.2 The Cascade Structure of Writing by Hand -- 5.3 Types of Products and Levels of Manner Modification -- 5.4 Agencies at Cascade Levels -- 5.5 Objects at Cascade Levels -- 5.6 A Multitrack Notion of C-Constitution -- 6 Reference and Composition -- 6.1 Meaning and Reference of the Verb Write -- 6.2 Cascades and Composition -- 7 Conclusion: Cascades in Cognition, Semantics, and Life -- References -- Prototypes and Probabilities -- Modification and Default Inheritance -- 1 Prototype Compositionality and Modification -- 2 An Extended Modification Model -- 3 Experimental Data -- 3.1 Constraint Influences in the Data of Connolly et al. (ch14Connollyetal2007) -- 3.2 Experiments -- 4 Conclusion -- References -- A Frame-Theoretic Model of Bayesian Category Learning -- 1 Introduction -- 2 Weighted Bayesian Models of Categorisation -- 3 Frames -- 3.1 Challenges and Future Developments -- 4 Conclusion -- References -- Extremes are Typical. A Game Theoretical Derivation -- 1 Typicality: Prototypes Versus Stereotypes -- 2 Typicality and Structured Meaning Spaces -- 3 Extremes and Iterated Best Response -- 4 Conclusion and Outlook -- References -- Grading Similarity -- 1 Introduction -- 2 Similarity Demonstratives.; 3 Three Types of Similarity Expressions -- 4 Gradability of ähnlich/similar -- 4.1 What Does It Mean to Be More Similar? -- 4.2 Gradability and Granularity -- 5 Conclusion -- Appendix: Granularity in Multi-dimensional Attribute Spaces -- Domains and Representations -- Indiscernibility -- Granularity and Gradability -- References -- Cognition and Psychology -- Escitalopram Restores Reversal Learning Impairments in Rats with Lesions of Orbital Frontal Cortex -- 1 Introduction -- 1.1 How Is Behavioural Flexibility Measured and Cognitive Flexibility Inferred? -- 2 Methods -- 2.1 Animals -- 2.2 Apparatus -- 2.3 Surgery -- 2.4 Experiment 1: The Effects of Escitalopram on Reversal Learning -- 2.5 Experiment 2: Fos Activity After 1 mg/kg Escitalopram -- 3 Results -- 3.1 Experiment 1 -- 3.2 Experiment 2 -- 4 Discussion -- 4.1 Reversal Learning -- 4.2 The Effects of OFC Lesions on Reversal Learning -- 4.3 The Effects of Escitalopram on Reversal Learning -- 4.4 Fos Activity -- References -- Rat Ultrasonic Vocalizations as Social Reinforcers-Implications for a Multilevel Model of the Cognitive Representation of Action ; and Rats' Social World -- 1 Introduction -- 2 Methods -- 2.1 Subjects -- 2.2 Experimental Setup -- 2.3 Acoustic Stimuli -- 2.4 Task Design -- 2.5 Data Analysis -- 3 Results -- 4 Discussion -- 5 A Cognitive Perspective: Acting at Multiple Levels -- 5.1 Goldman's Multilevel Theory of Human Action -- 5.2 Cascades and Learning -- 5.3 Applying Cascade Theory to Rat Behavior in the Experiments Reported -- 5.4 Psychological Commitments of the Cascade Approach -- 5.5 What Can the Cascade Approach Buy Us? -- 6 Conclusions -- References -- Influence of Manner Adverbs on Action Verb Processing -- 1 Introduction -- 2 Experiment 1 -- 2.1 Methods -- 2.2 Results -- 3 Experiment 2 -- 3.1 Methods -- 3.2 Results -- 3.3 Discussion -- References.; When Mechanical Computations Explain Better.
• Sommario/riassunto: This open access book presents novel theoretical, empirical and experimental work exploring the nature of mental representations that support natural language production and understanding, and other manifestations of cognition. One fundamental question raised in the text is whether requisite knowledge structures can be adequately modeled by means of a uniform representational format, and if so, what exactly is its nature. Frames are a key topic covered which have had a strong impact on the exploration of knowledge representations in artificial intelligence, psychology and linguistics; cascades are a novel development in frame theory. Other key subject areas explored are: concepts and categorization, the experimental investigation of mental representation, as well as cognitive analysis in semantics. This book is of interest to students, researchers, and professionals working on cognition in the fields of linguistics, philosophy, and psychology.