241 research outputs found
Let my people go (home) to Spain: a genealogical model of Jewish identities since 1492
The Spanish government recently announced an official fast-track path to
citizenship for any individual who is Jewish and whose ancestors were expelled
from Spain during the inquisition-related dislocation of Spanish Jews in 1492.
It would seem that this policy targets a small subset of the global Jewish
population, i.e., restricted to individuals who retain cultural practices
associated with ancestral origins in Spain. However, the central contribution
of this manuscript is to demonstrate how and why the policy is far more likely
to apply to a very large fraction (i.e., the vast majority) of Jews. This claim
is supported using a series of genealogical models that include transmissable
"identities" and preferential intra-group mating. Model analysis reveals that
even when intra-group mating is strong and even if only a small subset of a
present-day population retains cultural practices typically associated with
that of an ancestral group, it is highly likely that nearly all members of that
population have direct geneaological links to that ancestral group, given
sufficient number of generations have elapsed. The basis for this conclusion is
that not having a link to an ancestral group must be a property of all of an
individual's ancestors, the probability of which declines (nearly)
superexponentially with each successive generation. These findings highlight
unexpected incongruities induced by genealogical dynamics between present-day
and ancestral identities.Comment: 6 page, 4 figure
Packing-Limited Growth
We consider growing spheres seeded by random injection in time and space.
Growth stops when two spheres meet leading eventually to a jammed state. We
study the statistics of growth limited by packing theoretically in d dimensions
and via simulation in d=2, 3, and 4. We show how a broad class of such models
exhibit distributions of sphere radii with a universal exponent. We construct a
scaling theory that relates the fractal structure of these models to the decay
of their pore space, a theory that we confirm via numerical simulations. The
scaling theory also predicts an upper bound for the universal exponent and is
in exact agreement with numerical results for d=4.Comment: 6 pages, 5 figures, 4 tables, revtex4 to appear in Phys. Rev. E, May
200
An Objective Definition of Damage Spreading - Application to Directed Percolation
We present a general definition of damage spreading in a pair of models.
Using this general framework, one can define damage spreading in an objective
manner, that does not depend on the particular dynamic procedure that is being
used. The formalism is applied to the Domany-Kinzel cellular automaton in one
dimension; the active phase of this model is shown to consist of three
sub-phases, characterized by different damage-spreading properties.Comment: 10 pages, RevTex, 2 ps figure
The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion
Tip-driven growth processes underlie the development of many plants. To date,
tip-driven growth processes have been modelled as an elongating path or series
of segments without taking into account lateral expansion during elongation.
Instead, models of growth often introduce an explicit thickness by expanding
the area around the completed elongated path. Modelling expansion in this way
can lead to contradictions in the physical plausibility of the resulting
surface and to uncertainty about how the object reached certain regions of
space. Here, we introduce "fiber walks" as a self-avoiding random walk model
for tip-driven growth processes that includes lateral expansion. In 2D, the
fiber walk takes place on a square lattice and the space occupied by the fiber
is modelled as a lateral contraction of the lattice. This contraction
influences the possible follow-up steps of the fiber walk. The boundary of the
area consumed by the contraction is derived as the dual of the lattice faces
adjacent to the fiber. We show that fiber walks generate fibers that have
well-defined curvatures, enable the identification of the process underlying
the occupancy of physical space. Hence, fiber walks provide a base from which
to model both the extension and expansion of physical biological objects with
finite thickness.Comment: Plos One (in press
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