Endogenous vs exogenous causality
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Endogenous vs. Exogenous Causality. Dr. Green. Extreme Events. Mass Biological Extinctions occurred 65 million years ago when 75% of the species went extinct Exogenous—meteor or volcano Endogenous—cascade of collapse from interdependencies. Extreme Events. Immune Deficiencies

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Endogenous vs. Exogenous Causality

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Endogenous vs exogenous causality

Endogenous vs. ExogenousCausality

Dr. Green


Extreme events

Extreme Events

  • Mass Biological Extinctions occurred 65 million years ago when 75% of the species went extinct

    • Exogenous—meteor or volcano

    • Endogenous—cascade of collapse from interdependencies


Extreme events1

Extreme Events

  • Immune Deficiencies

    • Exogenous—virus

    • Endogenous—regulatory failure

  • Discoveries

    • Exogenous—unpredicted and discontinuous

    • Endogenous—result of previous build up of knowledge


Thing ontology

Thing Ontology

  • Things are lumpy

  • To be cut off from other things it has to have an identity constituted by some internal traits


Normal distributrion

Normal Distributrion


Normal distribution

Normal Distribution

  • Values cluster around a central or “typical” value

  • This assumes that many small, independent effects are additively contributing to each observation.


Normal distribution1

Normal Distribution

  • A sequence is independent and identically distributed if

    • each has the same probability distribution as the others

    • all are mutually independent.


Exogenous

Exogenous

  • Serious of random shocks

  • Each random shock

    • Abrupt peak

    • Power law relaxation as a fast rate


Random walk

Random Walk

  • an individual walking on a straight line who at each point of time either takes one step to the right with probability p or one step to the left with probability 1 − p.

  • The individual is subject to a series of random, external shocks


Random walk1

Random Walk


Random walk2

Random Walk

  • http://www.rpi.edu/dept/materials/MEG/Java_Modules_files/RandomWalk/RandomWalkApplet.html


Process ontology

Process Ontology

  • Processes can vary from minutely small to tremendously large

  • There need be no typical size


Endogenous causality and an interconnected world

Endogenous Causality and an Interconnected World

  • Many aspects of reality do not follow a normal distribution, i.e., there is no central hump

  • There is no typical

    • Earthquake size

    • Forest fire size

    • Avalanche size in a sand pile


Power law

Power Law


Power law1

Power Law


Power law2

Power Law

  • Fingers of instability of all possible lengths

  • Even the greatest event have no exceptional cause

    • The same causes can cause small or larger avalanches

  • Size of the avalanche has to do not with the original cause but with the unstable organization of the critical state


Power law3

Power Law

  • Structure due to fact that constituents are not independent, as in the normal distribution, but interconnected

  • No built-in bias toward a typical value


Copper

Copper

  • Melt copper so that it becomes a liquid

    • A steady state of randomly moving particles

    • No history because one moment is like another


Copper1

Copper

  • Place the melted copper in a bath of ice water

    • It is now far-from equilibrium

    • History develops in the movement toward solidity

      • Directionality – moving toward solidity

      • Irreversibility –the solid does not spontaneously melt

  • Complexity develops

    • Snow flake like appearance

    • Uniqueness of each structure, no one typical form

  • Internal structure develops

    • Scale-invariance or self-similarity


History

History

  • Interaction among components dominates the system

    • Self-reinforcing processes

    • Pattern building


Ising model

Ising Model

  • http://physics.syr.edu/courses/ijmp_c/Ising.html


Networks

Networks

  • Average number of others that an individual influences (n)

    • n<1 , then avalanche dies off quickly

    • n=1 , then critical point and avalanche cascades through the system

    • n> 1, then super-critical state and the possibility of growing exponentially is highly probable


Supercritical

Supercritical


Singularity

Singularity


Exogenous1

Exogenous

  • http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf

    • P. 6


Endogenous

Endogenous

  • Slow Acceleration with power law growth due to growing interdependencies on larger and larger scales

  • Power law relaxation due to cascades

  • http://arxiv.org/PS_cache/physics/pdf/0412/0412026v1.pdf

    • P. 6


Endogenous1

Endogenous

  • Outliers (extreme events) occur more often than predicted by chance

    • Extreme earthquakes

    • Extreme extinctions

    • Stock market crashes


Log periodic power law

Log-Periodic Power Law

  • Discrete scale invariance

    • looks the same if multiplied by a fixed number. (Benoit Mandelbrot, Fractals)

  • Positive feedback creates an accelerating cycle

  • Super-exponential growth occurs

  • At critical time, a singularity is reached.


Discrete scale invariance

Discrete-Scale Invariance


Log periodic power law1

Log-Periodic Power Law


Log periodic power law2

Log-Periodic Power Law


Log periodic power law3

Log-Periodic Power Law


Log periodic power law4

Log-Periodic Power Law


Linear limitations

Linear Limitations

  • Linear models appear to work when viewed (and experienced) for a brief period of time, particularly in the early stages of an exponential trend when not much is happening.

  • At the bend in the curve, exponential growth explodes, and the linear models break down.


Linear limitations1

Linear Limitations


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