18,667 research outputs found
Transience and recurrence of random walks on percolation clusters in an ultrametric space
We study existence of percolation in the hierarchical group of order ,
which is an ultrametric space, and transience and recurrence of random walks on
the percolation clusters. The connection probability on the hierarchical group
for two points separated by distance is of the form , with , non-negative constants , and . Percolation was proved in Dawson and Gorostiza
(2013) for , with
. In this paper we improve the result for the critical case by
showing percolation for . We use a renormalization method of the type
in the previous paper in a new way which is more intrinsic to the model. The
proof involves ultrametric random graphs (described in the Introduction). The
results for simple (nearest neighbour) random walks on the percolation clusters
are: in the case the walk is transient, and in the critical case
, there exists a critical
such that the walk is recurrent for and transient for
. The proofs involve graph diameters, path lengths, and
electric circuit theory. Some comparisons are made with behaviours of random
walks on long-range percolation clusters in the one-dimensional Euclidean
lattice.Comment: 27 page
Hierarchical equilibria of branching populations
The objective of this paper is the study of the equilibrium behavior of a
population on the hierarchical group consisting of families of
individuals undergoing critical branching random walk and in addition these
families also develop according to a critical branching process. Strong
transience of the random walk guarantees existence of an equilibrium for this
two-level branching system. In the limit (called the hierarchical
mean field limit), the equilibrium aggregated populations in a nested sequence
of balls of hierarchical radius converge to a backward
Markov chain on . This limiting Markov chain can be explicitly
represented in terms of a cascade of subordinators which in turn makes possible
a description of the genealogy of the population.Comment: 62 page
Cognitive-Behavioural Therapy
Cognitive-behavioural therapy (CBT) is a generic term, encompassing both: (1) approaches underpinned by an assumption that presenting emotional and behavioural difficulties are cognitively mediated or moderated; and (2) atheoretical bricolages of cognitive and behavioural techniques. This latter category may include effective therapeutic packages (perhaps acting through mechanisms articulated in the first category) but, when theory is tacit, it becomes harder to make analytical generalisations or to extrapolate principles that could guide idiographic formulation and intervention. In contrast, the first category of approaches posits that presenting difficulties may be formulated from an assessment of individual cognitive content (thought processes and underlying beliefs) and implies that we can bring about change in presenting difficulties through change in associated cognitions. Within this chapter, we formulate the case of ‘Molly’, using the theoretical model of CBT articulated by A. T. Beck, to understand the client’s presentation, current difficulties, and potential areas for intervention
The influence of altitude on the anaerobic and aerobic capacities of men in work Final scientific report
Altitude influence on anaerobic and aerobic capacities of working me
Percolation in a hierarchical random graph
We study asymptotic percolation as in an infinite random graph
embedded in the hierarchical group of order , with connection
probabilities depending on an ultrametric distance between vertices. is structured as a cascade of finite random subgraphs of (approximate)
Erd\"os-Renyi type. We give a criterion for percolation, and show that
percolation takes place along giant components of giant components at the
previous level in the cascade of subgraphs for all consecutive hierarchical
distances. The proof involves a hierarchy of random graphs with vertices having
an internal structure and random connection probabilities.Comment: 19 pages and 1 figur
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