How uncertainty-related ideas can provide theoretical explanation for empirical dependencies / / Martine Ceberio and Vladik Kreinovich (editors)

• Record Nr.: UNINA9910484321203321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-65324-2
• Descrizione fisica: 1 online resource (152 pages) : illustrations
• Collana: Studies in Systems, Decision and Control ; ; v.306
• Disciplina: 003.54
• Soggetti: Justification (Theory of knowledge); Uncertainty (Information theory); Incertesa (Teoria de la informació); Justificació (Teoria del coneixement); Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- Status Quo Bias Actually Helps Decision Makers to Take Nonlinearity into Account: An Explanation -- 1 Formulation of the Problem -- 2 Analysis of the Problem and the Resulting Explanation -- References -- A Natural Explanation for the Minimum Entropy Production Principle -- 1 Formulation of the Problem -- 2 How Complex Problems Are Solved: Reminder and Related Analysis -- 3 How This Analysis Helps Explain the Minimum Entropy Production Principle -- References -- Why Class-D Audio Amplifiers Work Well: A Theoretical Explanation -- 1 Formulation of the Problem -- 2 Why Pulses -- 3 Why the Pulse's Duration Should Linearly Depend on the Amplitude of the Input Signal -- Reference -- How Can We Explain Different Number Systems? -- 1 Formulation of the Problem -- 2 Which Bases Appear if We Consider Divisibility by All Small Numbers from 1 to Some k -- 3 What if We Can Skip One Number -- 4 What if We Can Skip Two Numbers -- 5 What if We Can Skip Three or More Numbers -- References -- Why Immediate Repetition Is Good for Short-Time Learning Results but Bad for Long-Time Learning: ; Explanation Based on Decision Theory -- 1 Formulation of the Problem: How to Explain Recent Observations Comparing Long-Term Results of Immediate and Delayed Repetition -- 2 Main Idea Behind Our Explanation: Using Decision Theory -- 3 So When Do We Learn: Analysis of the Problem and the Resulting Explanation -- References -- Absence of Remotely Triggered Large Earthquakes: A Geometric Explanation -- 1 Formulation of the Problem -- 2 Geometric Explanation -- References -- Why Gamma Distribution of Seismic Inter-Event Times: A Theoretical Explanation -- 1 Formulation of the Problem -- 2 Our Explanation -- References -- Quantum Computing as a Particular Case of Computing with Tensors -- 1 Why Tensors -- 2 Tensors in Physics: A Brief Reminder.; 3 From Tensors in Physics to Computing with Tensors -- 4 Modern Algorithm for Multiplying Large Matrices -- 5 Quantum Computing as Computing with Tensors -- 6 New Idea: Tensors to Describe Constraints -- 7 Computing with Tensors Can Also Help Physics -- 8 Remaining Open Problem -- References -- A ``Fuzzy'' Like Button Can Decrease Echo Chamber Effect -- 1 Formulation of the Problem -- 2 Proposed Solution -- References -- Intuitive Idea of Implication Versus Formal Definition: How to Define the Corresponding Degree -- 1 Formulation of the Problem -- 2 How to Define the Degree of Implication: A Seemingly Reasonable Idea and Its Limitations -- 3 Towards a New Definition of Degree of Implication -- References -- Dimension Compactification-A Possible Explanation for Superclusters and for Empirical Evidence Usually Interpreted as Dark Matter -- 1 Main Idea -- 2 Geometric Consequences of the Main Idea -- 3 Towards Physical Consequences of the Main Idea -- 4 Physical Consequences of the Main Idea -- 5 Observable Predictions of Our New Idea -- 6 Natural Open Questions -- References -- Fundamental Properties of Pair-Wise Interactions Naturally Lead to Quarks and Quark Confinement: A Theorem Motivated by Neural Universal Approximation Results -- 1 Formulation of the Problem -- 2 Definitions and the Main Result -- 3 Proof -- 4 Physical Interpretation of the Result -- References -- Linear Neural Networks Revisited: From PageRank to Family Happiness -- 1 Linear Neural Networks: A Brief Reminder -- 2 Linear Neural Networks: A Precise Description -- 3 Linear Neural Networks: From the General Case to the Simplest Case -- 4 First Application: PageRank Algorithm as an Example of a Linear Neural Network -- 5 Second Application: Family Dynamics -- References -- Why 3 Basic Colors? Why 4 Basic Tastes? -- 1 Introduction -- 2 Why 3 Basic Colors? -- 3 Why 4 Basic Tastes?.; References -- What Segments Are the Best in Representing Contours? -- 1 Introduction to the Problem -- 2 Motivations of the Proposed Mathematical Definitions -- 3 Definitions and the Main Result -- 4 Proofs -- References -- Strength of Lime Stabilized Pavement Materials: Possible Theoretical Explanation of Empirical Dependencies -- 1 Formulation of the Problem -- 2 Our Explanation -- References -- Towards a Theoretical Explanation of How Pavement Condition Index Deteriorates over Time -- 1 Formulation of the Problem -- 2 General Invariances -- 3 First Attempt: Let Us Directly Apply Invariance Ideas to Our Problem -- 4 Let Us Now Apply Invariance Ideas Indirectly -- References -- A Recent Result About Random Metric Spaces Explains Why All of Us Have Similar Learning Potential -- 1 Formulation of the Problem -- 2 Our Explanation -- References -- Finitely Generated Sets of Fuzzy Values: If ``And'' Is Exact, Then ``Or'' Is Almost Always Approximate, and Vice Versa-A Theorem -- 1 Formulation of the Problem -- 2 Definitions and the Main Result -- 3 How General Is This Result? -- 4 What if We Allow Unlimited Number of ``And''-Operations ; and Negations: Case Study -- References -- Fuzzy Logic Explains the Usual Choice of Logical Operations in 2-Valued Logic -- 1 Formulation of the Problem -- 2 Our Explanation -- 3 Auxiliary Result: Why the Usual Quantifiers? -- References.