20,389 research outputs found
A particle system in interaction with a rapidly varying environment: Mean field limits and applications
We study an interacting particle system whose dynamics depends on an
interacting random environment. As the number of particles grows large, the
transition rate of the particles slows down (perhaps because they share a
common resource of fixed capacity). The transition rate of a particle is
determined by its state, by the empirical distribution of all the particles and
by a rapidly varying environment. The transitions of the environment are
determined by the empirical distribution of the particles. We prove the
propagation of chaos on the path space of the particles and establish that the
limiting trajectory of the empirical measure of the states of the particles
satisfies a deterministic differential equation. This deterministic
differential equation involves the time averages of the environment process.
We apply our results to analyze the performance of communication networks
where users access some resources using random distributed multi-access
algorithms. For these networks, we show that the environment process
corresponds to a process describing the number of clients in a certain loss
network, which allows us provide simple and explicit expressions of the network
performance.Comment: 31 pages, 2 figure
One-Class Support Measure Machines for Group Anomaly Detection
We propose one-class support measure machines (OCSMMs) for group anomaly
detection which aims at recognizing anomalous aggregate behaviors of data
points. The OCSMMs generalize well-known one-class support vector machines
(OCSVMs) to a space of probability measures. By formulating the problem as
quantile estimation on distributions, we can establish an interesting
connection to the OCSVMs and variable kernel density estimators (VKDEs) over
the input space on which the distributions are defined, bridging the gap
between large-margin methods and kernel density estimators. In particular, we
show that various types of VKDEs can be considered as solutions to a class of
regularization problems studied in this paper. Experiments on Sloan Digital Sky
Survey dataset and High Energy Particle Physics dataset demonstrate the
benefits of the proposed framework in real-world applications.Comment: Conference on Uncertainty in Artificial Intelligence (UAI2013
Parallelization of Kinetic Theory Simulations
Numerical studies of shock waves in large scale systems via kinetic
simulations with millions of particles are too computationally demanding to be
processed in serial. In this work we focus on optimizing the parallel
performance of a kinetic Monte Carlo code for astrophysical simulations such as
core-collapse supernovae. Our goal is to attain a flexible program that scales
well with the architecture of modern supercomputers. This approach requires a
hybrid model of programming that combines a message passing interface (MPI)
with a multithreading model (OpenMP) in C++. We report on our approach to
implement the hybrid design into the kinetic code and show first results which
demonstrate a significant gain in performance when many processors are applied.Comment: 10 pages, 3 figures, conference proceeding
Stochastic boundary conditions for molecular dynamics simulations
In this paper we develop a stochastic boundary conditions (SBC) for
event-driven molecular dynamics simulations of a finite volume embedded within
an infinite environment. In this method, we first collect the statistics of
injection/ejection events in periodic boundary conditions (PBC). Once
sufficient statistics are collected, we remove the PBC and turn on the SBC. In
the SBC simulations, we allow particles leaving the system to be truly ejected
from the simulation, and randomly inject particles at the boundaries by
resampling from the injection/ejection statistics collected from the current or
previous simulations. With the SBC, we can measure thermodynamic quantities
within the grand canonical ensemble, based on the particle number and energy
fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a
hard disk gas and measured the pair distribution function, the compressibility
and the specific heat, comparing them against literature values.Comment: 24 pages, 16 figure
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