Molecular Networking

Section I Molecular networking analytics Chapter 1 Probabilities, distributions and statistics 1.1 MECHANICS 1.1.1 Newton, Lagrange, and Hamilton 1.1.2 Wave function and uncertainty 1.1.3 Quantum Energy and Density of States 1.2 THERMODYNAMICS 1.2.1 Processes, Work, and Heat 1.2.2 First, Second and Third Laws 1.2.3 Changing Conditions: Legendre Transformations 1.3 STATISTICS AND DISTRIBUTIONS 1.3.1 Maxwell-Boltzmann distribution 1.3.2 Phase space and probability distribution 1.3.3 Micro-Macro Connection Chapter 2 Communication Rules in Molecular Systems 2.1 COMMUNICATION AND INTERACTIONS 2.1.1 Interactions in a Quantum World 2.1.2 Coarse-graining: Tight-Binding 2.1.3 Further coarse-graining: a classical world 2.2 INTERACTIONS BETWEEN MOLECULES 2.2.1 Molecular Properties and Interactions 2.2.2 2-Body vs. Many-Body Potentials 2.2.3 Towards Macro- and Bio-molecules 2.3 BEYOND INTERACTIONS 2.3.1 Signaling 2.3.2 Phoresis and Active Matter 2.3.3 Chemotaxis Chapter 3 An Ensemble Approach: Finding descriptors and reducing dimensions 3.1 COLLECTIONS AND ENSEMBLES 3.1.1 Making Sense of the Microscopic Big Data 3.1.2 Defining Ensembles 3.1.3 The Concept of the Most Probable Distribution 3.2 INDIVIDUALS IN AN ISOTHERMAL WORLD: THE CANONICAL ENSEMBLE 3.2.1 Key Parameters and Multipliers 3.2.2 The Central Partition Function 3.2.3 Partition Function and Thermodynamics 3.3 INDIVIDUALS IN ISOLATION: THE MICROCANONICAL ENSEMBLE 3.3.1 Number and Density of States 3.3.2 Boltzmann’s Entropy 3.3.3 Thermodynamic Functions Chapter 4 Accounting for Individual Features and Changes 4.1 MOLECULES IN A CANONICAL WORLD 4.1.1 Features and Consequences 4.1.2 The Case of Diatomic Molecules 4.1.3 Molecular Symmetry and Polyatomic Molecules 4.2 CONNECTING WITH THE MACROSCOPIC WORLD 4.2.1 Are all Features Essential? 4.2.2 Model-Partition Function Interplay 4.2.3 Thermodynamic properties and Ideality 4.3 CHANGING IDENTITIES: CHEMICAL REACTIONS 4.3.1 Reaction properties and Parameters 4.3.2 Partition Functions and Equilibrium Constants 4.3.3 The Activated Complex Chapter 5 Machine Learning and Molecular Systems 5.1 DISTINGUISHING FROM THE MOLECULAR CROWD 5.1.1 Labels and Classes 5.1.2 Identifying and Handling Patterns 5.1.3 Learning under supervision 5.2 QUANTITATIVE MODELS FOR MOLECULAR GROUPS 5.2.1 Training regression models 5.2.2 Mapping numbers: Artificial Neural Networks 5.2.3 Optimization through back-propagation 5.3 BEYOND ARTIFICIAL NEURAL NETWORKS 5.3.1 Learning by watching: Convolutional Neural Networks 5.3.2 Time sequences and Recurrent Neural Networks 5.3.3 Understanding policies: the Advent of Reinforcement Learning Section II Static trends: equilibrium statistics Chapter 6 Polling a molecular population: Monte Carlo and Wang Landau simulations 6.1 THE BIRTH OF THE MONTE CARLO METHOD 6.1.1 Randomness and Integration 6.1.2 Sample Mean Approach 6.1.3 The Concept of Importance Sampling 6.2 THE METROPOLIS METHOD 6.2.1 Markov Chain and Stochastic Matrix 6.2.2 Randomness and Acceptance 6.2.3 Implementation and Testing 6.3 WANG-LANDAU SAMPLING 6.3.1 A Paradigm Shift: Evaluating the Density of States 6.3.2 The Biased Distribution 6.3.3 A Twist in the Monte Carlo plot Chapter 7 Molecular networking in insulation: adiabatic ensembles 7.1 ADIABATIC PROCESSES AND ENSEMBLES 7.1.1 Adiabatic vs. Isothermal 7.1.2 The Concept of Heat Function 7.1.3 Eight Statistical Ensembles 7.2 MECHANICS OF ADIABATIC ENSEMBLES 7.2.1 Microcanonical distribution and thermodynamic equations 7.2.2 The (μ, P,R) Ensemble 7.2.3 A Full Picture for the Four Adiabatic Ensembles 7.3 MONTE CARLO EXPLORATION OF ADIABATIC ENSEMBLES 7.3.1 Exploring the Microcanonical Ensemble 7.3.2 Musing in the (N, P,H) Ensemble 7.3.3 Direct Entropy Evaluations in the (μ, P,R) Ensemble Chapter 8 Networking under one (or more) cues: isothermal ensembles 8.1 THERMAL AND CHEMICAL CUES 8.1.1 The Grand-Canonical Ensemble 8.1.2 Monte Carlo Exploration 8.1.3 Grand Partition Function Determination 8.2 THERMAL AND MECHANICAL CUES 8.2.1 The Isothermal-Isobaric Ensemble 8.2.2 Properties Calculations 8.2.3 Partition Function Computation 8.3 VARIATIONS AND APPLICATIONS 8.3.1 Multi-Component Systems and Semi-Grand Approach 8.3.2 A First Step towards Coexistence: Gibbs Ensemble Monte Carlo method 8.3.3 Recycling and Reweighting Chapter 9 Collective properties from partition functions 9.1 GENERATING DATA ON PARTITION FUNCTIONS 9.1.1 Starting from A 9.1.2 From dilute to condensed phases 9.1.3 Direct determination of partition functions 9.2 THE CASE OF PHASE TRANSITIONS 9.2.1 Matching Probabilities 9.2.2 Features of coexistence 9.2.3 Extension to Multi-Component Systems 9.3 GAS STORAGE AND SEPARATION APPLICATIONS 9.3.1 Partition Functions for Adsorbed Fluids 9.3.2 Thermodynamic Properties of Adsorption 9.3.3 Environmental and Energy Applications Chapter 10 Machine Learning Molecular Trends 10.1 LEARNING INTERMOLECULAR INTERACTIONS 10.1.1 Starting from empirical datasets 10.1.2 Training on tight-binding data 10.1.3 Neural network potentials 10.2 LEARNING PARTITION FUNCTIONS 10.2.1 Single-component systems 10.2.2 Multicomponent mixtures 10.2.3 Adsorbed Phases 10.3 LEARNING TRANSITIONS 10.3.1 Spanning Pathways 10.3.2 From Partition Functions to Reaction Coordinates 10.3.3 On-The-Fly Learning of Collective Variables Section III Dynamic trends: motion statistics Chapter 11 Molecular evolution and fluctuations: time-resolved statistics 11.1 COMPUTING MOLECULAR TRAJECTORIES 11.1.1 Ensemble and Time Averages Equivalency 11.1.2 Molecular Equations of Motion 11.1.3 Integration Schemes 11.2 MOLECULAR TRAJECTORIES 11.2.1 Gauss’ principle of least constraint 11.2.2 Keeping the temperature in check 11.2.3 Nos´e-Hoover Thermostat 11.3 MULTIPLE-TIME STEPS AND HYBRID SCHEMES 11.3.1 Time-splitting 11.3.2 Controlling pressure 11.3.3 Hybrid schemes Chapter 12 Noise and information: correlation functions 12.1 MOTION AND TRANSPORT 12.1.1 Brownian Motion 12.1.2 Langevin Equation & Fluctuation-Dissipation 12.1.3 Einstein Diffusion Equation 12.2 TRANSPORT FROM CORRELATION 12.2.1 D from a Correlation Function 12.2.2 The Mori-Zwanzig approach 12.2.3 Evaluation of Transport Coefficients 12.3 RESPONSE THEORY 12.3.1 Linear response theory 12.3.2 Time-Dependent Linear Response 12.3.3 Nonlinear Response, Dynamical Stability, and Chaos Chapter 13 External fields and agents: new communication paradigms 13.1 NONEQUILIBRIUM MOLECULAR TRAJECTORIES 13.1.1 Boundary-Driven and Synthetic Setups 13.1.2 Accounting for Heat Dissipation 13.1.3 Extracting Transport Coefficients 13.2 COMPUTING NONEQUILIBRIUM TRAJECTORIES 13.2.1 Physical Boundaries vs Periodic Boundaries 13.2.2 Nonequilibrium Definitions for Temperature 13.2.3 Transport in the Steady-State 13.3 TRANSIENT-TIME CORRELATION FUNCTION 13.3.1 Formalism 13.3.2 Bridging between Equilibrium and Nonequilibrium 13.3.3 Transport close(r) to Equilibrium Chapter 14 Fluctuation Theorems, Molecular Machines and Emergent Behavior in Active Matter 14.1 FLUCTUATION THEOREMS 14.1.1 Formalism 14.1.2 Negative Entropy Production Trajectories 14.1.3 Free Energy Differences 14.2 TOWARDS A NEW PHYSICS OF LIVING SYSTEMS 14.2.1 Work Relations and RNA Folding 14.2.2 Mutating, stretching, binding, and unbinding 14.2.3 Free energy calculations via steered MD 14.3 EMERGENCE IN ACTIVE MATTER 14.3.1 Dry Active Matter 14.3.2 Active Brownian Matter & MIPS 14.3.3 Entropy Production: from Active Matter to Molecular Machines Chapter 15 Learning evolution and transport 15.1 LEARNING TRANSPORT 15.1.1 Rationale for Diffusion Learning 15.1.2 RNNs and LSTMs in Action 15.1.3 Classifying Diffusion Behaviors 15.2 LEARNING DYNAMICS 15.2.1 Learning Equations of Motion for Mesoscopic and Structured Systems 15.2.2 Learning Differential Equations 15.2.3 Data-Driven Identification of Governing Equations 15.3 LEARNING NAVIGATION 15.3.1 Adapting to the Environment 15.3.2 Identifying Navigation Strategies 15.3.3 Learning Collective Motion