CROSSING IN COMPLEXITY: INTERDISCIPLINARY APPLICATION OF PHYSICS IN BIOLOGICAL AND SOCIAL SYSTEMS

CROSSING IN COMPLEXITY: INTERDISCIPLINARY APPLICATION OF PHYSICS IN BIOLOGICAL AND SOCIAL SYSTEMS

CONTENTS

FOREWORD

Chapter 1 LIVING WITH RADICAL UNCERTAINTY: THE EXEMPLARY CASE OF FOLDING PROTEIN

Abstract

1. “ZIP Filing the World”

2. The Folding Problem

3. Radical Emergence: Pyrococcus Furiosus

4. Uncertainty’s Fecundity: A Systemic Conclusion

Acknowledgments

References

Chapter 2 THE LIMITS OF ATOMISM: THE BOHM WAY OF A NEW ONTOLOGY

Abstract

Brief History of Atomism

Necessity of the New Ontology

Philosophical Viewpoint from Substance to Function

Process and the Cyclic Ontology

Mathematical Formalism of Cyclic Ontology

The Heisenberg Equation

The Bohm Equation

Conclusion

References

Chapter 3 DOING MATHEMATICS ABOUT AND WITH THE BRAIN*

Introduction

Doing Mathematics about the Brain

Hodgkin and Huxley

Warren McCulloch

Brains, Machines and Mathematics

The Automata-Theoretic Approach to Brain Theory

The Many Levels of Brain Analysis

Below the Neuron

Population Coding and the Ergodic Hypothesis

Cooperative Computation in Neural Fields

Regularization

Schema Theory

Synthetic PET

Space, The Final Frontier

Information Theory and Statistical Mechanics

Nonlinear Dynamic Systems

Bringing in Plasticity: Hebbian, Error-Based and Reinforcement

Bridging the Levels: From Behavior to Neurochemistry

Self-Organization

Brain Evolution

From Brain to Mind: Psychology and Linguistics

The Brain Doing Mathematics

Against Platonism

References

Chapter 4 PHYSICS OF LIFE FROM FIRST PRINCIPLES

Abstract

1. Introduction

2. Dynamics with Liouville Feedback

A. Destabilizing Effect of Liouville feedback

B. Emergence of Randomness

C. Emergence of Entanglement

D. Summary

3. From Disorder to Order

A. Information Potential

B. Negative Diffusion

C. Drift

D. Summary

4. Model of Livings

A. General Model

B. Simplified Model

C. Invariant Formulation

D. Variation Principle

Remark

E. Summary

5. Interpretation of the Model

A. Mathematical Viewpoint

B. Physical Viewpoint

α.Superposition

β. Entanglement

γ. Decoherence

δ. Uncertainty Principle

C. Biological Viewpoint

D. Psychological Viewpoint

E. Neuro-Science Viewpoint

β. Mystery of Mirror Neuron

γ. Mirror Neural Nets

δ. Link to Quantum Entanglement

F. Social and Economic Viewpoint

G. Language Communications Viewpoint

H. Summary

6. Complexity for Survival of Livings

A. Measure of Survivability

B. Mental Complexity via Reflection of Information

C. Image Dynamics: What Do You Think I Think You Think…

D. Chain of Abstractions

α. Attractors in Motor Dynamics

β. Attractors in Mental Dynamics

E. Hierarchy of Higher Mental Abstractions

F. Abstraction and Survivability

G. Activation of New Levels of Abstractions

H. Summary

7. Intelligence in Livings

A. Definition and General Remarks

B. Intelligent Control in Livings

C. Modeling Common Sense

α. General Remarks

β. The Model

γ. Decision Making Process

δ. Decision via Choice of Attractors

ε. Decision via Phase Transition

D. Emergent Intelligence

E. Summary

8. Data-Driven Model Discovery

Remark

9. Discussion and Conclusion

A. General Remarks

B. Model Extension

C. Summary

Acknowledgment

References

Chapter 5THEORETICAL PHYSICS OF DNA:NEW IDEAS AND TENDENCIES IN THE MODELINGOF THE DNA NONLINEAR DYNAMICS

Abstract

1. Introduction

2. New Stimuli for Nonlinear Modeling of DNA

2.1. Charge-Transfer in DNA

2.2. Manipulations with Single DNA Molecule

3. Two Tendencies in Theoretical Studies of NonlinearDNA Dynamics

3.1. Tendency to Complicate DNA Models by Including Additional Details ofthe DNA Structure and Interactions

3.1.a. Inclusion of the Details on Differences in Mass of Bases in Watson-Crick Pairs

3.1.b. Inclusion of the Details on Differences in Frequencies of Base RotationalOscillations in Phase and Out of Phase

3.1.c. Inclusion of the Details on Interactions between Bases in Watson-Crick Pairs

3.2. Tendency to Simplify DNA Models Up to the Model of Englander

3.2a. Englander’s Model Applied to Study Effects of Dissipations

3.2.b. Englander’s Model Applied to Study Effects of External Field

3.2.c. Englander’s Model Applied to Study the Balance between the Action ofDissipation and External Fields

3.2.d. Englander’s Model Applied to Study DNA Kink Propagation through theBoundary between Two Homogeneous Regions

4. Conclusive Remarks

Dedication

References

Chapter6MATHEMATICALANDDATAMININGCONTRIBUTIONSTODYNAMICSANDOPTIMIZATIONOFGENE-ENVIRONMENTNETWORKS

Abstract

1.Introduction

1.1.AnalyzingandOptimizinginBiotechnology

1.2.StabilityinGeneticsandApproachtoMatrices

1.3.ExtractingGeneticNetworksfromGene-ExpressionData

2.ModelingGene-ExpressionData

2.1.ModelingGeneNetworkswithOrdinaryDifferentialEquations

2.2.OurModelandItsPossibleExtensions

2.2.1.AQuasi-Linear,MultiplicativeModel

2.3.GeneRegulation—AnExample

2.3.1.NonlinearModelwithQuadraticorHigherDegreePolynomials

2.4.TheExtendedModel

3.Time-DiscretizationandtheStabilityAnalysis

3.1.Runge-KuttaMethod

3.2.AlgebraofMatrixProducts

3.3.StabilityAnalysisofaSetofMatrices

3.3.1.OntheAlgorithm

3.4.ModelingGeneRegulatoryNetworkswithPiecewiseLinearDifferentialEquations

3.5.OnAdditiveModels,SplineRegressionandStochasticDifferentialEquations

3.5.1.Introduction

3.5.2.ClassicalAdditiveModels

3.5.3.EstimationEquationsforAdditiveModels

3.5.4.PenalizedRegressionProblemsandInverseProblems

3.5.5.RegressionProblemsandFlows

3.5.6.StochasticDifferentialEquations

3.6.RelatedTopicsandFutureProjects

4.Conclusion

References

Chapter 7FOLDING PROTEINS: HOW TO SET UP AN EFFICIENTMETRICS FOR DEALING WITH COMPLEX SYSTEMS

Abstract

Introduction

Results and Discussion: A Tale of Formalization

Conclusion

Aknowledgements

References

Chapter8THE(UNFORTUNATE)COMPLEXITYOFTHEECONOMY

Abstract

References

Chapter 9 EVOLUTION OF NORMS IN A MULTI-LEVEL SELECTION MODEL OF CONFLICT AND COOPERATION

Abstract

Introduction

The Mathematics of Give and Take

From the Pleistocene to the Internet

A World in Black and White

The Leading Eight

A Model of Conflict and Cooperation

Results

Prompt Forgiving and Implacable Punishment

The Emergence of Good and Evil

Discussion

Methods

Acknowledgments

References

Chapter10DYNAMICSOFCOUPLEDPLAYERSANDTHEEVOLUTIONOFSYNCHRONOUSCOOPERATION—DYNAMICALSYSTEMSGAMESASGENERALFRAMEFORSYSTEMSINTER-RELATIONSHIP

Abstract

1.EvolutionofCooperativeBehaviors

2.DescriptionofGamesasDynamicalSystems

3.TheLumberjack’sDilemmaGame

4.ReviewofAkiyama&Kaneko2002

5.DynamicsofCoupledPlayers

5.1.TheEffectoftheEnvironmentalCoupling

5.2.TheEffectofthePlayer’sCoupling

5.3.StrategySpaceforProductiveDynamics

6.Summary

Acknowledgement

References

Chapter 11 FRACTAL TIME, OBSERVER PERSPECTIVES AND LEVELS OF DESCRIPTION IN NATURE

Abstract

Introduction

Notions of Time

Levels of Description: The Endo and Exo-Perspective

Simultaneity, Succession, Duration and the Now: Physical Theories are Secondary Constructs of Our Primary Experiences of Time

A. Simultaneity

B. Succession

C. Duration and the Now

Fractal Time

Temporal Natural Constraints

Observer Perspectives: The Fractal Temporal Interface

Participation: Temporal Embedding

TNCs Revisited: Embodiment

Conclusion

References

INDEX

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