4,131 research outputs found
A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices
Quantum counterparts of certain simple classical systems can exhibit chaotic
behaviour through the statistics of their energy levels and the irregular
spectra of chaotic systems are modelled by eigenvalues of infinite random
matrices. We use known bounds on the distribution function for eigenvalue
spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real
symmetric matrices and show that gamma distributions, which have an important
uniqueness property, can yield an approximation to the GOE distribution. That
has the advantage that then both chaotic and non chaotic cases fit in the
information geometric framework of the manifold of gamma distributions, which
has been the subject of recent work on neighbourhoods of randomness for general
stochastic systems. Additionally, gamma distributions give approximations, to
eigenvalue spacings for the Gaussian unitary ensemble (GUE) of infinite random
hermitian matrices and for the Gaussian symplectic ensemble (GSE) of infinite
random hermitian matrices with real quaternionic elements, except near the
origin. Gamma distributions do not precisely model the various analytic systems
discussed here, but some features may be useful in studies of qualitative
generic properties in applications to data from real systems which manifestly
seem to exhibit behaviour reminiscent of near-random processes.Comment: 9 pages, 5 figures, 2 tables, 27 references. Updates version 1 with
data and references from feedback receive
Some recent work in Frechet geometry
Some recent work in Frechet geometry is briefly reviewed. In particular an
earlier result on the structure of second tangent bundles in the finite
dimensional case was extended to infinite dimensional Banach manifolds and
Frechet manifolds that could be represented as projective limits of Banach
manifolds. This led to further results concerning the characterization of
second tangent bundles and differential equations in the more general Frechet
structure needed for applications. A summary is given of recent results on
hypercyclicity of operators on Frechet spaces.Comment: 14 pages 48 reference
An inhomogeneous stochastic rate process for evolution from states in an information geometric neighbourhood of uniform fitness
This study elaborates some examples of a simple evolutionary stochastic rate
process where the population rate of change depends on the distribution of
properties--so different cohorts change at different rates. We investigate the
effect on the evolution arising from parametrized perturbations of uniformity
for the initial inhomogeneity. The information geometric neighbourhood system
yields also solutions for a wide range of other initial inhomogeneity
distributions, including approximations to truncated Gaussians of arbitrarily
small variance and distributions with pronounced extreme values. It is found
that, under quite considerable alterations in the shape and variance of the
initial distribution of inhomogeneity in unfitness, the decline of the mean
does change markedly with the variation in starting conditions, but the net
population evolution seems surprisingly stable.Comment: 9 pages, 11 figures, 9 reference
On the entropy flows to disorder
Gamma distributions, which contain the exponential as a special case, have a
distinguished place in the representation of near-Poisson randomness for
statistical processes; typically, they represent distributions of spacings
between events or voids among objects. Here we look at the properties of the
Shannon entropy function and calculate its corresponding flow curves. We
consider univariate and bivariate gamma, as well as Weibull distributions which
also include exponential distributions.Comment: Enlarged version of original. 11 pages, 6 figures, 15 reference
Prothonotary warbler nestling growth and condition inresponse to variation in aquatic and terrestrial preyavailability
Aquatic prey subsidies entering terrestrial habitats are well documented, but little is known about the degree to which these resources provide fitness benefits to riparian consumers. Riparian species take advantage of seasonal pulses of both terrestrial and aquatic prey, although aquatic resources are often over-looked in studies of how diet influences the reproductive ecology of these organisms. Ideally, the timing of resource pulses should occur at the time of highest reproductive demand. This study investigates the availability of aquatic(mayfly) and terrestrial (caterpillar) prey resources as well as the nestling diet of the prothonotary warbler (Protonotaria citrea) at two sites along the lower James River in Virginia during the 2014 breeding season. We found large differences in availability of prey items between the two sites, with one having significantly higher mayfly availability. Nestling diet was generally reflective of prey availability, and nestlings had faster mean growth rates at the site with higher aquatic prey availability. Terrestrial prey were fed more readily at the site with lower aquatic prey availability, and at this site, nestlings fed mayflies had higher mean growth rates than nestlings fed only terrestrial prey. Our results suggest that aquatic subsidies are an important resource for nestling birds and are crucial to understanding the breeding ecology of riparian species
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