15,904 research outputs found
Effective Fitness Landscapes for Evolutionary Systems
In evolution theory the concept of a fitness landscape has played an
important role, evolution itself being portrayed as a hill-climbing process on
a rugged landscape. In this article it is shown that in general, in the
presence of other genetic operators such as mutation and recombination,
hill-climbing is the exception rather than the rule. This descrepency can be
traced to the different ways that the concept of fitness appears --- as a
measure of the number of fit offspring, or as a measure of the probability to
reach reproductive age. Effective fitness models the former not the latter and
gives an intuitive way to understand population dynamics as flows on an
effective fitness landscape when genetic operators other than selection play an
important role. The efficacy of the concept is shown using several simple
analytic examples and also some more complicated cases illustrated by
simulations.Comment: 11 pages, 8 postscript figure
Environmentally Friendly Renormalization
We analyze the renormalization of systems whose effective degrees of freedom
are described in terms of fluctuations which are ``environment'' dependent.
Relevant environmental parameters considered are: temperature, system size,
boundary conditions, and external fields. The points in the space of \lq\lq
coupling constants'' at which such systems exhibit scale invariance coincide
only with the fixed points of a global renormalization group which is
necessarily environment dependent. Using such a renormalization group we give
formal expressions to two loops for effective critical exponents for a generic
crossover induced by a relevant mass scale . These effective exponents are
seen to obey scaling laws across the entire crossover, including hyperscaling,
but in terms of an effective dimensionality, d\ef=4-\gl, which represents the
effects of the leading irrelevant operator. We analyze the crossover of an
model on a dimensional layered geometry with periodic, antiperiodic
and Dirichlet boundary conditions. Explicit results to two loops for effective
exponents are obtained using a [2,1] Pad\'e resummed coupling, for: the
``Gaussian model'' (), spherical model (), Ising Model (),
polymers (), XY-model () and Heisenberg () models in four
dimensions. We also give two loop Pad\'e resummed results for a three
dimensional Ising ferromagnet in a transverse magnetic field and corresponding
one loop results for the two dimensional model. One loop results are also
presented for a three dimensional layered Ising model with Dirichlet and
antiperiodic boundary conditions. Asymptotically the effective exponents are in
excellent agreement with known results.Comment: 76 pages of Plain Tex, Postscript figures available upon request from
[email protected], preprint numbers THU-93/14, DIAS-STP-93-1
Geometry the Renormalization Group and Gravity
We discuss the relationship between geometry, the renormalization group (RG)
and gravity. We begin by reviewing our recent work on crossover problems in
field theory. By crossover we mean the interpolation between different
representations of the conformal group by the action of relevant operators. At
the level of the RG this crossover is manifest in the flow between different
fixed points induced by these operators. The description of such flows requires
a RG which is capable of interpolating between qualitatively different degrees
of freedom. Using the conceptual notion of course graining we construct some
simple examples of such a group introducing the concept of a ``floating'' fixed
point around which one constructs a perturbation theory. Our consideration of
crossovers indicates that one should consider classes of field theories,
described by a set of parameters, rather than focus on a particular one. The
space of parameters has a natural metric structure. We examine the geometry of
this space in some simple models and draw some analogies between this space,
superspace and minisuperspace.Comment: 16 pages of LaTex, DIAS-STP-92-3
Schemata as Building Blocks: Does Size Matter?
We analyze the schema theorem and the building block hypothesis using a
recently derived, exact schemata evolution equation. We derive a new schema
theorem based on the concept of effective fitness showing that schemata of
higher than average effective fitness receive an exponentially increasing
number of trials over time. The building block hypothesis is a natural
consequence in that the equation shows how fit schemata are constructed from
fit sub-schemata. However, we show that generically there is no preference for
short, low-order schemata. In the case where schema reconstruction is favoured
over schema destruction large schemata tend to be favoured. As a corollary of
the evolution equation we prove Geiringer's theorem. We give supporting
numerical evidence for our claims in both non-epsitatic and epistatic
landscapes.Comment: 17 pages, 10 postscript figure
Direct innervation of capillary endothelial cells in the lamina propria of the ferret stomach
Direct innervation of capillary endothelial cells in lamina propria of ferret stomac
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