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Tipping points: From patterns to predictions

There has been much talk about tipping points over the past few years, and about the warning signals that may precede them. You could be forgiven for thinking that the forecasting of epidemics and stock-market crashes is just around the corner. But no one has yet managed to use the theory on early warning signals to predict a natural catastrophe.

The rewards of bridging the gap between the real world and mathematical conceptualizations of catastrophic shifts would be vast. Climate scientists might be able to foresee major shifts in the ocean currents with a rise in global temperatures; ecologists could potentially stave off pest outbreaks; and policies might be implemented to avert the collapse of fisheries1. (A report out this week from the World Economic Forum outlines other risks facing the world2). But for such applications to emerge, researchers should resist the lure of general rules. We must instead use all the available data to develop tools to study the specific properties of real systems.

 

Tipping points: From patterns to predictions

Carl Boettiger & Alan Hastings

Nature 493, 157–158 (10 January 2013) http://dx.doi.org/10.1038/493157a

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The ultimate guide to memory - New Scientist

We are all collections of memories. They dictate how we think, act and make decisions, and even define our identity.

Yet memory, with its many virtues and flaws, has puzzled for centuries. How are memories made and stored in the brain? Why do we remember some events but not others? What do other animals remember? And how can we improve the flawed instrument handed to us by evolution?

In these articles we answer these questions and many more, starting with a revolutionary new understanding of memory’s purpose.


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Complex dynamics of elementary cellular automata emerging in chaotic rules

Complex dynamics of elementary cellular automata emerging in chaotic rules | Papers | Scoop.it

We show novel techniques of analysing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and disorder. A number of attempts have been made to classify CA functions on their spatio-temporal dynamics and to predict behavior of any given function. Examples include mechanical computation, lambda and Z-parameters, mean field theory, differential equations and number conserving features. We propose to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus in just a few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory.

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