6,209 research outputs found
Hybrid PDE solver for data-driven problems and modern branching
The numerical solution of large-scale PDEs, such as those occurring in
data-driven applications, unavoidably require powerful parallel computers and
tailored parallel algorithms to make the best possible use of them. In fact,
considerations about the parallelization and scalability of realistic problems
are often critical enough to warrant acknowledgement in the modelling phase.
The purpose of this paper is to spread awareness of the Probabilistic Domain
Decomposition (PDD) method, a fresh approach to the parallelization of PDEs
with excellent scalability properties. The idea exploits the stochastic
representation of the PDE and its approximation via Monte Carlo in combination
with deterministic high-performance PDE solvers. We describe the ingredients of
PDD and its applicability in the scope of data science. In particular, we
highlight recent advances in stochastic representations for nonlinear PDEs
using branching diffusions, which have significantly broadened the scope of
PDD.
We envision this work as a dictionary giving large-scale PDE practitioners
references on the very latest algorithms and techniques of a non-standard, yet
highly parallelizable, methodology at the interface of deterministic and
probabilistic numerical methods. We close this work with an invitation to the
fully nonlinear case and open research questions.Comment: 23 pages, 7 figures; Final SMUR version; To appear in the European
Journal of Applied Mathematics (EJAM
Orientation of particle attachment and local isotropy in diffusion limited aggregation (DLA)
We simulate 50 off-lattice DLA clusters, one million particles each. The
probability distribution of the angle of attachment of arriving particles with
respect to the local radial direction is obtained numerically. For increasing
cluster size, , the distribution crosses over extremely accurately to a
cosine, whose amplitude decreases towards zero as a power-law in . From this
viewpoint, asymptotically large DLA clusters are locally . This
contradicts previous conclusions drawn from density-density correlation
measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We
present an intuitive phenomenological model random process for our numerical
findings.Comment: 10 pages, RevTex 3.0, 11-9
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness
We introduce the standard distribution width of fitness to characterize the
global and individual features of a ecosystem in the Bak-Sneppen evolution
model. Through tracking this quantity in evolution, a different hierarchy of
avalanche dynamics, avalanche is observed. The corresponding gap
equation and the self-organized threshold are obtained. The critical
exponents and , which describe the behavior of the
avalanche size distribution, the average avalanche size and the relaxation to
attractor, respectively, are calculated with numerical simulation. The exact
master equation and equation are derived. And the scaling relations
are established among the critical exponents of this new avalanche.Comment: 14 pages, 3 figure
Avalanche Dynamics in Evolution, Growth, and Depinning Models
The dynamics of complex systems in nature often occurs in terms of
punctuations, or avalanches, rather than following a smooth, gradual path. A
comprehensive theory of avalanche dynamics in models of growth, interface
depinning, and evolution is presented. Specifically, we include the Bak-Sneppen
evolution model, the Sneppen interface depinning model, the Zaitsev flux creep
model, invasion percolation, and several other depinning models into a unified
treatment encompassing a large class of far from equilibrium processes. The
formation of fractal structures, the appearance of noise, diffusion with
anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be
related to the same underlying avalanche dynamics. This dynamics can be
represented as a fractal in spatial plus one temporal dimension. We develop
a scaling theory that relates many of the critical exponents in this broad
category of extremal models, representing different universality classes, to
two basic exponents characterizing the fractal attractor. The exact equations
and the derived set of scaling relations are consistent with numerical
simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the
manuscript supplied on reques
General analysis of signals with two leptons and missing energy at the Large Hadron Collider
A signal of two leptons and missing energy is challenging to analyze at the
Large Hadron Collider (LHC) since it offers only few kinematical handles. This
signature generally arises from pair production of heavy charged particles
which each decay into a lepton and a weakly interacting stable particle. Here
this class of processes is analyzed with minimal model assumptions by
considering all possible combinations of spin 0, 1/2 or 1, and of weak
iso-singlets, -doublets or -triplets for the new particles. Adding to existing
work on mass and spin measurements, two new variables for spin determination
and an asymmetry for the determination of the couplings of the new particles
are introduced. It is shown that these observables allow one to independently
determine the spin and the couplings of the new particles, except for a few
cases that turn out to be indistinguishable at the LHC. These findings are
corroborated by results of an alternative analysis strategy based on an
automated likelihood test.Comment: 18 pages, 3 figures, LaTe
Unravelling an Extra Neutral Gauge Boson at the LHC using Third Generation Fermions
We study the potential to use measurements of extra neutral gauge bosons (Z')
properties in pp collisions at the Large Hadron Collider to unravel the
underlying physics. We focus on the usefulness of third generation final states
(tau, b, t) in distinguishing between models with non-universal Z'-fermion
couplings. We present an update of discovery limits of Z's including the
2010-2011 LHC run and include models with non-universal couplings. We show how
ratios of sigma(pp -> Z' -> ttbar), sigma(pp -> Z' -> bbbar), and sigma(pp ->
Z' -> tau^+tau^-) to sigma(pp -> Z' -> mu^+mu^-) can be used to distinguish
between models and measure parameters of the models. Of specific interest are
models with preferential couplings, such as models with generation dependent
couplings. We also find that forward-backward asymmetry measurements with third
generation fermions in the final state could provide important input to
understanding the nature of the Z'. Understanding detector resolution and
efficiencies will be crucial for extracting results
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