3,931 research outputs found
Stein factors for negative binomial approximation in Wasserstein distance
The paper gives the bounds on the solutions to a Stein equation for the
negative binomial distribution that are needed for approximation in terms of
the Wasserstein metric. The proofs are probabilistic, and follow the approach
introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are
used to quantify the accuracy of negative binomial approximation to parasite
counts in hosts. Since the infectivity of a population can be expected to be
proportional to its total parasite burden, the Wasserstein metric is the
appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The geometry of the Barbour-Bertotti theories I. The reduction process
The dynamics of interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for . A comparison with similar methods in
molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit
Hydrographic data from R/V endeavor cruise #90
The final cruise of the NSF sponsored Warm Core Rings Program studied a Warm Core Ring (WCR) in the Fall of 1982 as it formed from a large northward meander of the Gulf Stream. This ring, known as 82-H or the eighth ring identified in 1982, formed over the New England Seamounts near 39.5 deg N, 65 deg W. Surveys using Expendable Bathythermographs, Conductivity-Temperature-Depth-Oxygen stations and Doppler Current Profiling provide a look at the genesis of a WCR. These measurements reveal that WCR 82-H separated from the Gulf Stream sometime between October 2-5. This ring was a typical WCR with a diameter of about 200 km and speeds in the high velocity core of the 175 cm/sec. Satellite imagery of 82-H following the cruise showed that it drifted WSW in the Slope Water region at almost 9 km/day, had at least one interaction with the Gulf Stream and was last observed on February 8, 1983 at 39 deg N, 72 deg W
Poisson approximations for the Ising model
A -dimensional Ising model on a lattice torus is considered. As the size
of the lattice tends to infinity, a Poisson approximation is given for the
distribution of the number of copies in the lattice of any given local
configuration, provided the magnetic field tends to and the
pair potential remains fixed. Using the Stein-Chen method, a bound is given
for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur
A law of large numbers approximation for Markov population processes with countably many types
When modelling metapopulation dynamics, the influence of a single patch on
the metapopulation depends on the number of individuals in the patch. Since the
population size has no natural upper limit, this leads to systems in which
there are countably infinitely many possible types of individual. Analogous
considerations apply in the transmission of parasitic diseases. In this paper,
we prove a law of large numbers for rather general systems of this kind,
together with a rather sharp bound on the rate of convergence in an
appropriately chosen weighted norm.Comment: revised version in response to referee comments, 34 page
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
I show how there is an ambiguity in how one treats auxiliary variables in
gauge theories including general relativity cast as 3 + 1 geometrodynamics.
Auxiliary variables may be treated pre-variationally as multiplier coordinates
or as the velocities corresponding to cyclic coordinates. The latter treatment
works through the physical meaninglessness of auxiliary variables' values
applying also to the end points (or end spatial hypersurfaces) of the
variation, so that these are free rather than fixed. [This is also known as
variation with natural boundary conditions.] Further principles of dynamics
workings such as Routhian reduction and the Dirac procedure are shown to have
parallel counterparts for this new formalism. One advantage of the new scheme
is that the corresponding actions are more manifestly relational. While the
electric potential is usually regarded as a multiplier coordinate and Arnowitt,
Deser and Misner have regarded the lapse and shift likewise, this paper's
scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose
corresponding velocities are, respectively, the abovementioned previously used
variables. This paper's way of thinking about gauge theory furthermore admits
interesting generalizations, which shall be provided in a second paper.Comment: 11 page
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Strategies intended to resolve the problem of time in quantum gravity by
means of emergent or hidden timefunctions are considered in the arena of
relational particle toy models. In situations with `heavy' and `light' degrees
of freedom, two notions of emergent semiclassical WKB time emerge; these are
furthermore equivalent to two notions of emergent classical
`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,
in a geometric phase formalism, extended to include linear constraints, and
with particular care to make explicit those approximations and assumptions
used. I propose a new iterative scheme for this in the cosmologically-motivated
case with one heavy degree of freedom. I find that the usual semiclassical
quantum cosmology emergence of time comes hand in hand with the emergence of
other qualitatively significant terms, including back-reactions on the heavy
subsystem and second time derivatives. I illustrate my analysis by taking it
further for relational particle models with linearly-coupled harmonic
oscillator potentials. As these examples are exactly soluble by means outside
the semiclassical approach, they are additionally useful for testing the
justifiability of some of the approximations and assumptions habitually made in
the semiclassical approach to quantum cosmology. Finally, I contrast the
emergent semiclassical timefunction with its hidden dilational Euler time
counterpart.Comment: References Update
Foundations of Relational Particle Dynamics
Relational particle dynamics include the dynamics of pure shape and cases in
which absolute scale or absolute rotation are additionally meaningful. These
are interesting as regards the absolute versus relative motion debate as well
as discussion of conceptual issues connected with the problem of time in
quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces
of shapes are n-spheres and complex projective spaces, from which knowledge I
construct natural mechanics on these spaces. I also show that these coincide
with Barbour's indirectly-constructed relational dynamics by performing a full
reduction on the latter. Then the identification of the configuration spaces as
n-spheres and complex projective spaces, for which spaces much mathematics is
available, significantly advances the understanding of Barbour's relational
theory in spatial dimensions 1 and 2. I also provide the parallel study of a
new theory for which positon and scale are purely relative but orientation is
absolute. The configuration space for this is an n-sphere regardless of the
spatial dimension, which renders this theory a more tractable arena for
investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update
Quenched QCD at finite density
Simulations of quenched at relatively small but {\it nonzero} chemical
potential on lattices indicate that the nucleon
screening mass decreases linearly as increases predicting a critical
chemical potential of one third the nucleon mass, , by extrapolation.
The meson spectrum does not change as increases over the same range, from
zero to . Past studies of quenched lattice QCD have suggested that
there is phase transition at . We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for ranging from to
. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte
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