Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic Behaviour of Strongly Reinforced Polya Urns : Convergence and
  Stability   We consider, as proposed and studied in Hofstad et.\ al.\ \cite{HHKR}, a
class of graph-based "interacting urn"-type Polya urn model inspired by
neuronal processing in the brain where a signal enters the brain at some
(randomly) chosen neuron and is transmitted to a (random) single neighbouring
neuron with a probability depending on the relative `efficiency' of the
synapses connecting the neurons, and in doing so the efficiency of the utilized
synapse is improved/reinforced. We study the structures (or architectures) and
relative efficiency of the neuronal networks that can arise from repeating this
process a very large number of times in a "strong reinforcement regime". Under
the most general conditions, we prove in the affirmative a part of the main
open conjecture in \cite{HHKR} i.e. the zero probability of convergence of the
corresponding "urn process" to any 'unstable' equilibrium. Under very generic
conditions, i.e., for an open and dense subset of parameters with full measure,
we also prove the full open conjecture by showing the finiteness of the
equilibrium set and hence the unit probability of convergence of the "urn
process" to some 'stable' equilibrium.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio