1,140 research outputs found
Evangelistic Sermons
https://digitalcommons.acu.edu/crs_books/1406/thumbnail.jp
Extinction in Lotka-Volterra model
Competitive birth-death processes often exhibit an oscillatory behavior. We
investigate a particular case where the oscillation cycles are marginally
stable on the mean-field level. An iconic example of such a system is the
Lotka-Volterra model of predator-prey competition. Fluctuation effects due to
discreteness of the populations destroy the mean-field stability and eventually
drive the system toward extinction of one or both species. We show that the
corresponding extinction time scales as a certain power-law of the population
sizes. This behavior should be contrasted with the extinction of models stable
in the mean-field approximation. In the latter case the extinction time scales
exponentially with size.Comment: 11 pages, 17 figure
Mean-Field Interacting Boson Random Point Fields in Weak Harmonic Traps
A model of the mean-field interacting boson gas trapped by a weak harmonic
potential is considered by the \textit{boson random point fields} methods. We
prove that in the Weak Harmonic Trap (WHT) limit there are two phases
distinguished by the boson condensation and by a different behaviour of the
local particle density. For chemical potentials less than a certain critical
value, the resulting Random Point Field (RPF) coincides with the usual boson
RPF, which corresponds to a non-interacting (ideal) boson gas. For the chemical
potentials greater than the critical value, the boson RPF describes a divergent
(local) density, which is due to \textit{localization} of the macroscopic
number of condensed particles. Notice that it is this kind of transition that
observed in experiments producing the Bose-Einstein Condensation in traps
R-local Delaunay inhibition model
Let us consider the local specification system of Gibbs point process with
inhib ition pairwise interaction acting on some Delaunay subgraph specifically
not con taining the edges of Delaunay triangles with circumscribed circle of
radius grea ter than some fixed positive real value . Even if we think that
there exists at least a stationary Gibbs state associated to such system, we do
not know yet how to prove it mainly due to some uncontrolled "negative"
contribution in the expression of the local energy needed to insert any number
of points in some large enough empty region of the space. This is solved by
introducing some subgraph, called the -local Delaunay graph, which is a
slight but tailored modification of the previous one. This kind of model does
not inherit the local stability property but satisfies s ome new extension
called -local stability. This weakened property combined with the local
property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page
Atomic lattice excitons: from condensates to crystals
We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed
by fermionic atoms in two bands of an optical lattice. Such a system provides a
clean setup to study fundamental properties of excitons, ranging from
condensation to exciton crystals (which appear for a large effective mass ratio
between particles and holes). Using both mean-field treatments and 1D numerical
computation, we discuss the properities of ALEs under varying conditions, and
discuss in particular their preparation and measurement.Comment: 19 pages, 15 figures, changed formatting for journal submission,
corrected minor errors in reference list and tex
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
Recommended from our members
Improving the condition number of estimated covariance matrices
High dimensional error covariance matrices and their inverses are used to weight the
contribution of observation and background information in data assimilation procedures. As
observation error covariance matrices are often obtained by sampling methods, estimates are
often degenerate or ill-conditioned, making it impossible to invert an observation error
covariance matrix without the use of techniques to reduce its condition number. In this paper
we present new theory for two existing methods that can be used to ‘recondition’ any covariance
matrix: ridge regression, and the minimum eigenvalue method. We compare these methods
with multiplicative variance inflation, which cannot alter the condition number of a matrix, but
is often used to account for neglected correlation information. We investigate the impact of
reconditioning on variances and correlations of a general covariance matrix in both a theoretical
and practical setting. Improved theoretical understanding provides guidance to users regarding
method selection, and choice of target condition number. The new theory shows that, for the
same target condition number, both methods increase variances compared to the original
matrix, with larger increases for ridge regression than the minimum eigenvalue method. We
prove that the ridge regression method strictly decreases the absolute value of off-diagonal
correlations. Theoretical comparison of the impact of reconditioning and multiplicative
variance inflation on the data assimilation objective function shows that variance inflation alters
information across all scales uniformly, whereas reconditioning has a larger effect on scales
corresponding to smaller eigenvalues. We then consider two examples: a general correlation
function, and an observation error covariance matrix arising from interchannel correlations. The
minimum eigenvalue method results in smaller overall changes to the correlation matrix than
ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal
that reconditioning corrects spurious noise in the analysis but underestimates the true signal
compared to multiplicative variance inflation
Eynard-Mehta theorem, Schur process, and their pfaffian analogs
We give simple linear algebraic proofs of Eynard-Mehta theorem,
Okounkov-Reshetikhin formula for the correlation kernel of the Schur process,
and Pfaffian analogs of these results. We also discuss certain general
properties of the spaces of all determinantal and Pfaffian processes on a given
finite set.Comment: AMSTeX, 21 pages, a new section adde
Quantum gases in trimerized kagom\'e lattices
We study low temperature properties of atomic gases in trimerized optical
kagom\'{e} lattices. The laser arrangements that can be used to create these
lattices are briefly described. We also present explicit results for the
coupling constants of the generalized Hubbard models that can be realized in
such lattices. In the case of a single component Bose gas the existence of a
Mott insulator phase with fractional numbers of particles per trimer is
verified in a mean field approach. The main emphasis of the paper is on an
atomic spinless interacting Fermi gas in the trimerized kagom\'{e} lattice with
two fermions per site. This system is shown to be described by a quantum spin
1/2 model on the triangular lattice with couplings that depend on the bond
directions. We investigate this model by means of exact diagonalization. Our
key finding is that the system exhibits non-standard properties of a quantum
spin-liquid crystal: it combines planar antiferromagnetic order in the ground
state with an exceptionally large number of low energy excitations. The
possibilities of experimental verification of our theoretical results are
critically discussed.Comment: 19 pages/14 figures, version to appear in Phys. Rev. A., numerous
minor corrections with respect to former lanl submissio
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that
generalizes existing schemata recently proposed in the literature. In our
model, agents change behaviors/opinions on the basis of information collected
from their neighbors in a time interval of bounded size whereas agents are
assumed to have unbounded memory in previously studied scenarios. In our
mathematical framework, one is given a network , an integer value
for each node , and a time window size . The goal is to
determine a small set of nodes (target set) that influences the whole graph.
The spread of influence proceeds in rounds as follows: initially all nodes in
the target set are influenced; subsequently, in each round, any uninfluenced
node becomes influenced if the number of its neighbors that have been
influenced in the previous rounds is greater than or equal to .
We prove that the problem of finding a minimum cardinality target set that
influences the whole network is hard to approximate within a
polylogarithmic factor. On the positive side, we design exact polynomial time
algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared
in: Proceedings of 20th International Colloquium on Structural Information
and Communication Complexity (Sirocco 2013), Lectures Notes in Computer
Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201
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