Introduction and Motivation for Complex Networks IV124 Josef Spurný & Eva Výtvarová Faculty of Informatics, Masaryk University February 17, 2023 Course Organization Course Organization Formally: 0 + 2 Practically: lecture, hands-on activities (laptop is welcome), demonstrations, discussion Pass-the-Course Criteria: 60 % attendance submission of seminar work scope: at least 3 NP either Reader’s Journal or Project Report J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 2 / 29 Complex Systems Overview Complex Systems Areas J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 3 / 29 Complex Systems Overview Emergence of Complex Systems Theory "You don’t see something until you have the right metaphor to let you perceive it." James Gleick, Chaos: Making a New Science From 1960’ onwards, scientists were randomly discovering that an observation made in one domain can be successfully applied in another domain These observations were collected and generalized, which gave foundations to the Chaos Theory Further development in this area lead to the emergence of the Complex Systems Theory J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 4 / 29 Complex Systems Overview Blind Men and an Elephant J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 5 / 29 Complex Systems Overview Definition of CS CS consists of many components (agents) Agents interact together in a non-trivial manner (typically adjust their behavior based on what others do) The system as a whole shows certain behavior or quality that cannot be attributed to (or perceived at the level of) an individual agent J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 6 / 29 Energy Flow Some Underlying Physics There are principles which are common to all natural systems These are based on physical laws In particular, second thermodynamic law: Hot objects transfer heat to cold objects (not vice versa) Ordered systems become less ordered (more random) – entropy increases Systems "seek" energetic optima J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 7 / 29 Energy Flow Second Law of Thermodynamics J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 8 / 29 Energy Flow You Get on a Train... J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 9 / 29 Energy Flow Energetic Field A motion is created as a consequence of two neighbouring fields with different energy concentration. J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 10 / 29 Energy Flow Systems "Prefer" Efficient Energy Flow When there are more paths or channels through energy may flow, natural systems will prefer those with higher capacity ... both organic and anorganic! J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 11 / 29 Following Paths You Want to Get to the Tree... J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 12 / 29 Following Paths You Want to Get to the Tree... Lowest resistance = most efficient way how to invest energy Once created, existing paths tend to be followed, hence becoming more attractive J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 13 / 29 Following Paths Systems Prefer Existing Paths Ant Colony Simulation – NetLogo Demo J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 14 / 29 Following Paths Systems Prefer Existing Paths J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 15 / 29 Following Paths Systems Prefer Existing Paths Personality Structure Learning New Information Psychotherapy J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 16 / 29 Self-Organization Self-Organization Natural systems prefer efficient energy flow but there is no central coordination It is self-organized Self-organization is achieved by positive and negative feedback loops Feedback is balancing the system which searches for energetic optimum J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 17 / 29 Self-Organization Order Order is more efficient for energy transfer than chaos Order or coherence is spontaneously emerging in both organic and anorganic systems which seek energetic optima J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 18 / 29 Self-Organization Emergent Property Dicyostellium Positive feedback: cell expansion Negative feedback: limited resources Chemical communication Starvation → tension → novel behavior J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 19 / 29 Self-Organization Conscious Knowledge as Emergent Property Positive feedback: willpower to learn something new Negative feedback: forgetting (weak paths, links perish) Communication through neurotransmitters Stimulation → critical threshold → conscious awareness J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 20 / 29 Fractals Self-organization Produces Self-similarity J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 21 / 29 Fractals Fractal Structure Feedback loops typically apply over multiple scales ("levels of zoom") Same "forces" or "processes" apply at macro-level as well as micro-level Coastline Paradox – the more precise measurement, the longer the coast length (virtually infinite) Google Maps: Fractals in Tibet J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 22 / 29 Fractals Fractals Around Us Energy is exchanged through a surface – the bigger the surface, the more energy may be transferred However, we live in a limited space Fractal structure is nature’s architecture how to get virtually infinite surface in a finite space J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 23 / 29 Tipping Points Different Perspective on Change Our intuitive thinking leads to linear perspective of change – inputs are commensurate to outputs However, changes in real-world systems are rarely linear Rather than that, a system "re-organizes" once the accumulated tension reaches a "tipping point" J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 24 / 29 Tipping Points Stability & Instability Complex systems may be very robust to change in certain settings but also very sensitive to change in a different setting A tiny input may cause massive change – "Butterfly Effect" A huge input may cause nothing at all Why? → Attractors J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 25 / 29 Tipping Points Phase Space & Attractors Observing dynamics of a system, some states are more probable than other: Equifinality – a tendency of a system to reach similar final states from different initial conditions. J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 26 / 29 Tipping Points Phase Space & Attractors In an attractor domain, the system is stable, robust to change and locally (not globally) predictable At a saddle between two attractors, the system is unstable and sensitive to input conditions – small inputs may result in two qualitatively different states The saddle may be also called "repellor" Interactive Introduction to Attractor Landscapes J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 27 / 29 Resumé Complexity Concepts in Networks Attractors (hubs) Self-organization (network formation) Pattern-formation (network motifs) Emergent properties (global phenomena) Fractal structure (self-similarity) Tipping points (giant component emergence) J. Spurný, E. Výtvarová ·Introduction ·February 17, 2023 28 / 29