669 research outputs found
A quasitopos containing CONV and MET as full subcategories
We show that convergence spaces with continuous maps and metric spaces with
contractions, can be viewed as entities of the same kind. Both can be characterized by a limit function λ which with each filter ℱ associates a map λℱ from the underlying set to the extended positive real line. Continuous maps and contractions can both be characterized as limit function preserving maps
Weak representations of quantified hyperspace structures
AbstractIt is the aim of this note, to show that several results from Beer (1993), Beer et al. (1992) and Beer and Lucchetti (1993) about the description of some hypertopologies as weak or initial topologies can be generalized to the quantitative setting of approach hyperspace structures as introduced by Lowen and Sioen (1996, 1998)
Distances on probability measures and random variables
AbstractIn this paper we lift fundamental topological structures on probability measures and random variables, in particular the weak topology, convergence in law and finite-dimensional convergence to an isometric level. This allows for an isometric quantitative study of important concepts such as relative compactness, tightness, stochastic equicontinuity, Prohorov's theorem and σ-smoothness. In doing so we obtain numerical results which allow for the development of an intrinsic approximation theory and from which moreover all classical topological results follow as easy corollaries
Non-equilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the
quantitative analysis of physical and biological systems, such as the
generation of action potentials by nerve cells, the release and reuptake of
vesicles at a synapse, and the counting of particles by detector devices. Here
we present an extension of renewal theory to describe ensembles of point
processes with time varying input. This is made possible by a representation in
terms of occupation numbers of two states: Active and refractory. The dynamics
of these occupation numbers follows a distributed delay differential equation.
In particular, our theory enables us to uncover the effect of refractoriness on
the time-dependent rate of an ensemble of encoding point processes in response
to modulation of the input. We present exact solutions that demonstrate generic
features, such as stochastic transients and oscillations in the step response
as well as resonances, phase jumps and frequency doubling in the transfer of
periodic signals. We show that a large class of renewal processes can indeed be
regarded as special cases of the model we analyze. Hence our approach
represents a widely applicable framework to define and analyze non-stationary
renewal processes.Comment: 8 pages, 4 figure
Quantum Diffusion and Localization in Disordered Electronic Systems
The diffusion of electronic wave packets in one-dimensional systems with
on-site, binary disorder is numerically investigated within the framework of a
single-band tight-binding model. Fractal properties are incorporated by
assuming that the distribution of distances between consecutive
impurities obeys a power law, . For suitable
ranges of , one finds system-wide anomalous diffusion. Asymmetric
diffusion effects are introduced through the application of an external
electric field, leading to results similar to those observed in the case of
photogenerated electron-hole plasmas in tilted InP/InGaAs/InP quantum wells.Comment: RevTex4, 6 pages, 6 .eps figures: published versio
Curve counting via stable pairs in the derived category
For a nonsingular projective 3-fold , we define integer invariants
virtually enumerating pairs where is an embedded curve and
is a divisor. A virtual class is constructed on the associated
moduli space by viewing a pair as an object in the derived category of . The
resulting invariants are conjecturally equivalent, after universal
transformations, to both the Gromov-Witten and DT theories of . For
Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing
formula in the derived category.
Several calculations of the new invariants are carried out. In the Fano case,
the local contributions of nonsingular embedded curves are found. In the local
toric Calabi-Yau case, a completely new form of the topological vertex is
described.
The virtual enumeration of pairs is closely related to the geometry
underlying the BPS state counts of Gopakumar and Vafa. We prove that our
integrality predictions for Gromov-Witten invariants agree with the BPS
integrality. Conversely, the BPS geometry imposes strong conditions on the
enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page
Liquid-liquid equilibrium for monodisperse spherical particles
A system of identical particles interacting through an isotropic potential
that allows for two preferred interparticle distances is numerically studied.
When the parameters of the interaction potential are adequately chosen, the
system exhibits coexistence between two different liquid phases (in addition to
the usual liquid-gas coexistence). It is shown that this coexistence can occur
at equilibrium, namely, in the region where the liquid is thermodynamically
stable.Comment: 6 pages, 8 figures. Published versio
Integrated random processes exhibiting long tails, finite moments and 1/f spectra
A dynamical model based on a continuous addition of colored shot noises is
presented. The resulting process is colored and non-Gaussian. A general
expression for the characteristic function of the process is obtained, which,
after a scaling assumption, takes on a form that is the basis of the results
derived in the rest of the paper. One of these is an expansion for the
cumulants, which are all finite, subject to mild conditions on the functions
defining the process. This is in contrast with the Levy distribution -which can
be obtained from our model in certain limits- which has no finite moments. The
evaluation of the power spectrum and the form of the probability density
function in the tails of the distribution shows that the model exhibits a 1/f
spectrum and long tails in a natural way. A careful analysis of the
characteristic function shows that it may be separated into a part representing
a Levy processes together with another part representing the deviation of our
model from the Levy process. This allows our process to be viewed as a
generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.
Onset of negative interspike interval correlations in adapting neurons
Negative serial correlations in single spike trains are an effective method
to reduce the variability of spike counts. One of the factors contributing to
the development of negative correlations between successive interspike
intervals is the presence of adaptation currents. In this work, based on a
hidden Markov model and a proper statistical description of conditional
responses, we obtain analytically these correlations in an adequate dynamical
neuron model resembling adaptation. We derive the serial correlation
coefficients for arbitrary lags, under a small adaptation scenario. In this
case, the behavior of correlations is universal and depends on the first-order
statistical description of an exponentially driven time-inhomogeneous
stochastic process.Comment: 12 pages (10 pages in the journal version), 6 figures, published in
Phys. Rev. E; http://link.aps.org/doi/10.1103/PhysRevE.84.04190
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