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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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5.1 What is a Dynamical System? » 5.1 What is a Dynamical System? Download Video Subtitles & Transcripts
Download the subtitles for all the Unit 5 videos here: https://www.complexityexplorer.org/system//courses/media/files/000/001/609/original/text_5.dynamical_system.docx?1535306076