5,061 research outputs found
Percolation of hard disks
Random arrangements of points in the plane, interacting only through a simple
hard core exclusion, are considered. An intensity parameter controls the
average density of arrangements, in analogy with the Poisson point process. It
is proved that at high intensity, an infinite connected cluster of excluded
volume appears with positive probability.Comment: 16 pages, 6 figure
The moment index of minima (II)
The moment index of a nonnegative random variable X has the property that the moment index of the minimum of two independent r.v.s X and Y is greater than or equal to the sum of the moment indices of X and Y. We characterize conditions under which equality holds for a given r.v. X and every independent nonnegative r.v. Y, and discuss extensions to related r.v.s and their distributions
Dynamics of Rumor Spreading in Complex Networks
We derive the mean-field equations characterizing the dynamics of a rumor
process that takes place on top of complex heterogeneous networks. These
equations are solved numerically by means of a stochastic approach. First, we
present analytical and Monte Carlo calculations for homogeneous networks and
compare the results with those obtained by the numerical method. Then, we study
the spreading process in detail for random scale-free networks. The time
profiles for several quantities are numerically computed, which allow us to
distinguish among different variants of rumor spreading algorithms. Our
conclusions are directed to possible applications in replicated database
maintenance, peer to peer communication networks and social spreading
phenomena.Comment: Final version to appear in PR
Fault-Tolerant Dissipative Preparation of Atomic Quantum Registers with Fermions
We propose a fault tolerant loading scheme to produce an array of fermions in
an optical lattice of the high fidelity required for applications in quantum
information processing and the modelling of strongly correlated systems. A cold
reservoir of Fermions plays a dual role as a source of atoms to be loaded into
the lattice via a Raman process and as a heat bath for sympathetic cooling of
lattice atoms. Atoms are initially transferred into an excited motional state
in each lattice site, and then decay to the motional ground state, creating
particle-hole pairs in the reservoir. Atoms transferred into the ground
motional level are no longer coupled back to the reservoir, and doubly occupied
sites in the motional ground state are prevented by Pauli blocking. This scheme
has strong conceptual connections with optical pumping, and can be extended to
load high-fidelity patterns of atoms.Comment: 12 pages, 7 figures, RevTex
Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications
Directionally convex () ordering is a tool for comparison of dependence
structure of random vectors that also takes into account the variability of the
marginal distributions. When extended to random fields it concerns comparison
of all finite dimensional distributions. Viewing locally finite measures as
non-negative fields of measure-values indexed by the bounded Borel subsets of
the space, in this paper we formulate and study the ordering of random
measures on locally compact spaces. We show that the order is preserved
under some of the natural operations considered on random measures and point
processes, such as deterministic displacement of points, independent
superposition and thinning as well as independent, identically distributed
marking. Further operations such as position dependent marking and displacement
of points though do not preserve the order on all point processes, are
shown to preserve the order on Cox point processes. We also examine the impact
of order on the second moment properties, in particular on clustering and
on Palm distributions. Comparisons of Ripley's functions, pair correlation
functions as well as examples seem to indicate that point processes higher in
order cluster more. As the main result, we show that non-negative
integral shot-noise fields with respect to ordered random measures
inherit this ordering from the measures. Numerous applications of this result
are shown, in particular to comparison of various Cox processes and some
performance measures of wireless networks, in both of which shot-noise fields
appear as key ingredients. We also mention a few pertinent open questions.Comment: Accepted in Advances in Applied Probability. Propn. 3.2 strengthened
and as a consequence Cor 6.1,6.2,6.
Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part II: Application to the Many-Body Problem
We analyze the ground state phase diagram of attractive lattice bosons, which
are stabilized by a three-body onsite hardcore constraint. A salient feature of
this model is an Ising type transition from a conventional atomic superfluid to
a dimer superfluid with vanishing atomic condensate. The study builds on an
exact mapping of the constrained model to a theory of coupled bosons with
polynomial interactions, proposed in a related paper [11]. In this framework,
we focus by analytical means on aspects of the phase diagram which are
intimately connected to interactions, and are thus not accessible in a mean
field plus spin wave approach. First, we determine shifts in the mean field
phase border, which are most pronounced in the low density regime. Second, the
investigation of the strong coupling limit reveals the existence of a new
collective mode, which emerges as a consequence of enhanced symmetries in this
regime. Third, we show that the Ising type phase transition, driven first order
via the competition of long wavelength modes at generic fillings, terminates
into a true Ising quantum critical point in the vicinity of half filling.Comment: 22 pages, 5 figure
Investigations into the Sarcomeric Protein and Ca2+-Regulation Abnormalities Underlying Hypertrophic Cardiomyopathy in Cats (Felix catus).
Hypertrophic cardiomyopathy (HCM) is the most common single gene inherited cardiomyopathy. In cats (Felix catus) HCM is even more prevalent and affects 16% of the outbred population and up to 26% in pedigree breeds such as Maine Coon and Ragdoll. Homozygous MYBPC3 mutations have been identified in these breeds but the mutations in other cats are unknown. At the clinical and physiological level feline HCM is closely analogous to human HCM but little is known about the primary causative mechanism. Most identified HCM causing mutations are in the genes coding for proteins of the sarcomere. We therefore investigated contractile and regulatory proteins in left ventricular tissue from 25 cats, 18 diagnosed with HCM, including a Ragdoll cat with a homozygous MYBPC3 R820W, and 7 non-HCM cats in comparison with human HCM (from septal myectomy) and donor heart tissue. Myofibrillar protein expression was normal except that we observed 20â44% MyBP-C haploinsufficiency in 5 of the HCM cats. Troponin extracted from 8 HCM and 5 non-HCM cat hearts was incorporated into thin filaments and studied by in vitro motility assay. All HCM cat hearts had a higher (2.06 ± 0.13 fold) Ca2+-sensitivity than non-HCM cats and, in all the HCM cats, Ca2+-sensitivity was not modulated by troponin I phosphorylation. We were able to restore modulation of Ca2+-sensitivity by replacing troponin T with wild-type protein or by adding 100 ÎŒM Epigallocatechin 3-gallate (EGCG). These fundamental regulatory characteristics closely mimic those seen in human HCM indicating a common molecular mechanism that is independent of the causative mutation. Thus, the HCM cat is a potentially useful large animal model
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