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Course Introduction
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The Challenge of Causality
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What is a Mechanistic Model?
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Logic, Reasoning, and Simplicity
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Probability and Statistics
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Perturbation Analysis and Machine Learning
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Computation in Causality
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Modeling from Observation
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Causality as Computation
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Inference and Complexity
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The Future of Causality
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Basic Definitions
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Subgraphs and Graph Representations
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Isomorphic Graphs
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Connectivity and Trees
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Properties of Graphs
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Network Models
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Biological Networks
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Unit 2 Exercises
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A Probabilistic Law
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Classical Information
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Shannon Entropy and Meaning
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Joint, Conditional, Mutual Information, and a Case Study
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Entropy Rate and Multidimensional Objects
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Redundancy, Noise, and Biological Information
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Turing Machines
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The Halting Problem and Turing Universality
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Busy Beaver Functions and the Decidability Frontier
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Enumeration and Systems Behavior
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Computability and Predictability
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Demo 1: Cellular Automata
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Demo 2: Constructing Networks
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Demo 3: Networks from Real Data
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Intuitive Randomness
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Sources of Randomness
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Pseudo-Randomness
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Algorithmic Complexity and Compressibility
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The Invariance Theorem
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Convergence of Definitions
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Chaitin's Omega Number
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Epistemological Aspects of Infinite Wisdom
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The Chaitin-Leibniz Medal
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Algorithmic Probability and the Universal Distribution
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The Infinite Programming Monkey
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The Algorithmic Coding Theorem
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Logical Depth: A Measure of Sophistication
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Unit 4 Quiz
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What is a Dynamical System?
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Dynamical Systems Terminology
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Dynamical Systems Analysis
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2D Dynamical Systems
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The Lorenz System
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Discrete Dynamical Systems
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Kauffman Model
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Unit 5 Quiz
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Limitations of Shannon Entropy and Computable Measures
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Computing the Uncomputable: The Coding Theorem Method
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Shannon Entropy and Algorithmic Complexity Joining Forces: The Block Decomposition Method (BDM)
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Summary: The Block Decomposition Method (BDM)
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Graph and Tensor Algorithmic Complexity
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Summary: Graph Complexity
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Algorithmic Information Dynamics
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Moving Objects Towards & Away From Randomness
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Reconstructing Dynamical Systems
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System's Reprogrammability
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Summary: A Reprogrammable World
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Does Nature Compute?
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Natural Phenomena as Computation
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How Complexity Characterizes Life
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Algorithmic Dynamics of Graph Spectra and Network Reconstruction
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Applications to Molecular Biology and Genetic Networks
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Cell Dynamics and Attractor Landscapes
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Integer and Behavioural Sequences, and Algorithmic Cognition
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Summary: Algorithmic Cognition
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Evolutionary Biology and Genetic Algorithms
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Summary: Steering and Reprogramming Life
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Applications of Logical Depth to Image Classification
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Algorithmic Machine Learning
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The Future of Algorithmic Information Dynamics
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Final Exam
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2.8 Unit 2 Exercises » Unit 2 Problem Set: Exercises and Answers
To download the problem set for Unit 2, click here.
To download the problem set with answers for Unit 2, click here.
To download the Mathematica notebook, click here.