Uncertainty, Constraints, and Decision Making

Preface.- directory Preface.- 1. Applications to Biology and Medicine.- Hunting Habits of Predatory Birds: Theoretical Explanation of an Empirical Formula.- Why Rectified Power (RePU) Activation Functions Are Efficient in Deep Learning: A Theoretical Explanation.- Aquatic Ecotoxicology: Theoretical Explanation of Empirical Formulas.- How Hot Is Too Hot.- How Order and Disorder Affect People's Behavior: An Explanation.- Shape of an Egg: Towards a Natural Simple Universal Formula.- A General Commonsense Explanation of Several Medical Results.- Why Immunodepressive Drugs Often Make People Happier.- Systems Approach Explains Why Low Heart Rate Variability Is Correlated with Depression (and Suicidal Thoughts).- 2. Applications to Economics and Politics.- How to Make Inflation Optimal and Fair.- Why Seneca Effect?.- Why Rarity Score Is a Good Evaluation of a Non-Fungible Token.- Resource Allocation for Multi-Tasking Optimization: Explanation of an Empirical Formula.- Everyone Is Above Average: Is It Possible? Is It Good?.- How Probable is a Revolution? A Natural ReLU-Like Formula that Fits the Historical Data.- Why Should Exactly 1/4 Be Returned to the Original Owner: An Economic Explanation of an Ancient Recommendation.- Why Would Anyone Invest in a High-Risk Low-Profit Enterprise?.- Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion.- How to Solve the Apportionment Paradox.- In the Absence of Information, the Only Reasonable Negotiation Scheme Is Offering a Certain Percentage of the Original Request: A Proof.- 3. Applications to Education.- How to Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis of Measurement Uncertainty Can Help.- Physical Meaning Often Leads to Natural Derivations in Elementary Mathematics: On the Examples of Solving Quadratic and Cubic Equations.- Towards Better Ways to Compute the Overall Grade for a Class.- Why Some Theoretically Possible Representations of Natural Numbers Were Historically Used andSome Were Not: An Algorithm-Based Explanation.- 4. Applications to Engineering.- Dielectric Barrier Discharge (DBD) Thrusters -- Aerospace Engines of the Future: Invariance-Based Analysis.- Need for Optimal Distributed Measurement of Cumulative Quantities Explains the Ubiquity of Absolute and Relative Error Components.- Over-Measurement Paradox: Suspension of Thermonuclear Research Center and Need to Update Standards.- How to Get the Most Accurate Measurement-Based Estimates.- How to Estimate The Present Serviceability Rating of a Road Segment: Explanation of an Empirical Formula.- 5. Applications to Linguistics.- Word Representation: Theoretical Explanation of an Empirical Fact.- Why Menzerath's Law?.- 6. Applications to Machine Learning.- One More Physics-Based Explanation for Rectified Linear Neurons.- Why Deep Neural Networks: Yet Another Explanation.- 7. Applications to Mathematics.- Really Good Theorems Are Those That End Their Life as Definitions: Why.- 8. Applications to Physics.- How to Describe Hypothetic Truly Rare Events (with Probability 0).- Spiral Arms Around a Star: Geometric Explanation.- Why Physical Power Laws Usually Have Rational Exponents.- Freedom of Will, Non-Uniqueness of Cauchy Problem, Fractal Processes, Renormalization, Phase Transitions, and Stealth Aircraft.- How Can the Opposite to a True Theory Be Also True? A Similar Talmudic Discussion Helps Make This Famous Bohr's Statement Logically Consistent.- How to Detect (and Analyze) Independent Subsystems of a Black-Box (or Grey-Box) System.- 9. Applications to Psychology and Decision Making.- Why Decision Paralysis.- Why Time Seems to Pass Slowly for Unpleasant Experiences and Quickly for Pleasant Experiences: An Explanation Based on Decision Theory.- How to Deal with Conflict of Interest Situations When Selecting the Best Submission.- Why Aspirational Goals: Geometric Explanation.- Why Hate: Analysis Based on Decision Theory.- Why Self-Esteem Helps to Solve Problems: An Algorithmic Explanation.- Why Five Stages of Solar Activity, Why Five Stages of Grief, Why Seven Plus Minus Two: A General Geometric Explanation.- 10. Applications to Software Engineering.- Anomaly Detection in Crowdsourcing: Why Midpoints in Interval-Valued Approach.- Unexpected Economic Consequence of Cloud Computing: A Boost to Algorithmic Creativity.- Unreachable Statements Are Inevitable In Software Testing: Theoretical Explanation.- 11. General Computational Techniques.- Why Constraint Interval Arithmetic Techniques Work Well: A Theorem Explains Empirical Success".- "How to Describe Relative Approximation Error? A New Justification for Gustafson's Logarithmic Expression".- Search Under Uncertainty Should be Randomized: A Lesson From the 2021 Nobel Prize in Medicine".- Why Convex Combination Is an Effective Crossover Operation in Continuous Optimization: A Theoretical Explanation".- "Why Optimization Is Faster than Solving Systems of Equations: A Qualitative Explanation".- Estimating Skewness and Higher Central Moments of an Interval-Valued.- Fuzzy Set".- How to Detect the Fundamental Frequency: Approach Motivated by Soft.- Computing and Computational Complexity".- What If There Are Too Many Outliers?".- What Is a Natural Probability Distribution on the Class of All Continuous Functions: Maximum Entropy Approach Leads to Wiener Measure".- An Argument in Favor of Piecewise-Constant Membership Functions".- "Data Processing under Fuzzy Uncertainty: Towards More Accurate Algorithms".- "Epistemic vs. Aleatory: Case of Interval Uncertainty".- "Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples".- "Monotonic Bit-Invariant Permutation-Invariant Metrics on the Set of All Infinite Binary Sequences".- Computing the Range of a Function-of-Few-Linear-Combinations Under Linear Constraints: A Feasible Algorithm".- "How to Select a Representative Sample for a Family of Functions?.