7,351 research outputs found
Central limit approximations 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
there is usually no obvious natural upper limit on the number of individuals in
a patch, this leads to systems in which there are countably infinitely many
possible types of entity. Analogous considerations apply in the transmission of
parasitic diseases. In this paper, we prove central limit theorems for quite
general systems of this kind, together with bounds on the rate of convergence
in an appropriately chosen weighted norm.Comment: 24 page
Interacting vector fields in Relativity without Relativity
Barbour, Foster and \'{O} Murchadha have recently developed a new framework,
called here {\it{the 3-space approach}}, for the formulation of classical
bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime
are presupposed. Both arise as emergent features of the world from
geodesic-type dynamics on a space of 3-dimensional metric--matter
configurations. In fact gravity, the universal light cone and Abelian gauge
theory minimally coupled to gravity all arise naturally through a single common
mechanism. It yields relativity -- and more -- without presupposing relativity.
This paper completes the recovery of the presently known bosonic sector within
the 3-space approach. We show, for a rather general ansatz, that 3-vector
fields can interact among themselves only as Yang--Mills fields minimally
coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity
(14 pages, no figures
Towards the Unification of Gravity and other Interactions: What has been Missed?
Faced with the persisting problem of the unification of gravity with other
fundamental interactions we investigate the possibility of a new paradigm,
according to which the basic space of physics is a multidimensional space
associated with matter configurations. We consider general
relativity in . In spacetime, which is a 4-dimensional subspace of
, we have not only the 4-dimensional gravity, but also other
interactions, just as in Kaluza-Klein theories. We then consider a finite
dimensional description of extended objects in terms of the center of mass,
area, and volume degrees of freedom, which altogether form a 16-dimensional
manifold whose tangent space at any point is Clifford algebra Cl(1,3). The
latter algebra is very promising for the unification, and it provides
description of fermions.Comment: 11 pages; Talk presented at "First Mediterranean Conference on
Classical and Quantum Gravity", Kolymbari, Crete, Greece, 14-18 September
200
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
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
Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
We apply the Glasgow method for lattice QCD at finite chemical potential to a
schematic random matrix model (RMM). In this method the zeros of the partition
function are obtained by averaging the coefficients of its expansion in powers
of the chemical potential. In this paper we investigate the phase structure by
means of Glasgow averaging and demonstrate that the method converges to the
correct analytically known result. We conclude that the statistics needed for
complete convergence grows exponentially with the size of the system, in our
case, the dimension of the Dirac matrix. The use of an unquenched ensemble at
does not give an improvement over a quenched ensemble.
We elucidate the phenomenon of a faster convergence of certain zeros of the
partition function. The imprecision affecting the coefficients of the
polynomial in the chemical potential can be interpeted as the appearance of a
spurious phase. This phase dominates in the regions where the exact partition
function is exponentially small, introducing additional phase boundaries, and
hiding part of the true ones. The zeros along the surviving parts of the true
boundaries remain unaffected.Comment: 17 pages, 14 figures, typos correcte
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 quite general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted â 1 nor
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