441 research outputs found
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
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.
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
Ultrametricity and Memory in a Solvable Model of Self-Organized Criticality
Slowly driven dissipative systems may evolve to a critical state where long
periods of apparent equilibrium are punctuated by intermittent avalanches of
activity. We present a self-organized critical model of punctuated equilibrium
behavior in the context of biological evolution, and solve it in the limit that
the number of independent traits for each species diverges. We derive an exact
equation of motion for the avalanche dynamics from the microscopic rules. In
the continuum limit, avalanches propagate via a diffusion equation with a
nonlocal, history-dependent potential representing memory. This nonlocal
potential gives rise to a non-Gaussian (fat) tail for the subdiffusive
spreading of activity. The probability for the activity to spread beyond a
distance in time decays as for . The potential
represents a hierarchy of time scales that is dynamically generated by the
ultrametric structure of avalanches, which can be quantified in terms of
``backward'' avalanches. In addition, a number of other correlation functions
characterizing the punctuated equilibrium dynamics are determined exactly.Comment: 44 pages, Revtex, (12 ps-figures included
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
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
Point-occurrence self-similarity in crackling-noise systems and in other complex systems
It has been recently found that a number of systems displaying crackling
noise also show a remarkable behavior regarding the temporal occurrence of
successive events versus their size: a scaling law for the probability
distributions of waiting times as a function of a minimum size is fulfilled,
signaling the existence on those systems of self-similarity in time-size. This
property is also present in some non-crackling systems. Here, the uncommon
character of the scaling law is illustrated with simple marked renewal
processes, built by definition with no correlations. Whereas processes with a
finite mean waiting time do not fulfill a scaling law in general and tend
towards a Poisson process in the limit of very high sizes, processes without a
finite mean tend to another class of distributions, characterized by double
power-law waiting-time densities. This is somehow reminiscent of the
generalized central limit theorem. A model with short-range correlations is not
able to escape from the attraction of those limit distributions. A discussion
on open problems in the modeling of these properties is provided.Comment: Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon),
topic: crackling nois
(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
We develop a kind of pregeometry consisting of a web of overlapping fuzzy
lumps which interact with each other. The individual lumps are understood as
certain closely entangled subgraphs (cliques) in a dynamically evolving network
which, in a certain approximation, can be visualized as a time-dependent random
graph. This strand of ideas is merged with another one, deriving from ideas,
developed some time ago by Menger et al, that is, the concept of probabilistic-
or random metric spaces, representing a natural extension of the metrical
continuum into a more microscopic regime. It is our general goal to find a
better adapted geometric environment for the description of microphysics. In
this sense one may it also view as a dynamical randomisation of the causal-set
framework developed by e.g. Sorkin et al. In doing this we incorporate, as a
perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor
changes added relating to previous wor
Absolute Humidity and the Seasonal Onset of Influenza in the Continental United States
Here, the authors demonstrate that variations of absolute humidity explain both the onset of wintertime influenza transmission and the overarching seasonality of this pathogen in temperate regions
- âŠ