8,573 research outputs found
Hybrid deterministic/stochastic algorithm for large sets of rate equations
We propose a hybrid algorithm for the time integration of large sets of rate
equations coupled by a relatively small number of degrees of freedom. A subset
containing fast degrees of freedom evolves deterministically, while the rest of
the variables evolves stochastically. The emphasis is put on the coupling
between the two subsets, in order to achieve both accuracy and efficiency. The
algorithm is tested on the problem of nucleation, growth and coarsening of
clusters of defects in iron, treated by the formalism of cluster dynamics. We
show that it is possible to obtain results indistinguishable from fully
deterministic and fully stochastic calculations, while speeding up
significantly the computations with respect to these two cases.Comment: 9 pages, 7 figure
A Primer on Causality in Data Science
Many questions in Data Science are fundamentally causal in that our objective
is to learn the effect of some exposure, randomized or not, on an outcome
interest. Even studies that are seemingly non-causal, such as those with the
goal of prediction or prevalence estimation, have causal elements, including
differential censoring or measurement. As a result, we, as Data Scientists,
need to consider the underlying causal mechanisms that gave rise to the data,
rather than simply the pattern or association observed in those data. In this
work, we review the 'Causal Roadmap' of Petersen and van der Laan (2014) to
provide an introduction to some key concepts in causal inference. Similar to
other causal frameworks, the steps of the Roadmap include clearly stating the
scientific question, defining of the causal model, translating the scientific
question into a causal parameter, assessing the assumptions needed to express
the causal parameter as a statistical estimand, implementation of statistical
estimators including parametric and semi-parametric methods, and interpretation
of our findings. We believe that using such a framework in Data Science will
help to ensure that our statistical analyses are guided by the scientific
question driving our research, while avoiding over-interpreting our results. We
focus on the effect of an exposure occurring at a single time point and
highlight the use of targeted maximum likelihood estimation (TMLE) with Super
Learner.Comment: 26 pages (with references); 4 figure
Asymptotics of work distributions in a stochastically driven system
We determine the asymptotic forms of work distributions at arbitrary times
, in a class of driven stochastic systems using a theory developed by Engel
and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is
based on the contraction principle of large deviation theory. In this paper, we
extend the theory, previously applied in the context of deterministically
driven systems, to a model in which the driving is stochastic. The models we
study are described by overdamped Langevin equations and the work distributions
in the path integral form, are characterised by having quadratic actions. We
first illustrate EN theory, for a deterministically driven system - the
breathing parabola model, and show that within its framework, the Crooks
flucutation theorem manifests itself as a reflection symmetry property of a
certain characteristic polynomial function. We then extend our analysis to a
stochastically driven system, studied in ( arXiv:1212.0704v2
[cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a
moment-generating-function method, for both equilibrium and non - equilibrium
steady state initial distributions. In both cases we obtain new analytic
solutions for the asymptotic forms of (dissipated) work distributions at
arbitrary . For dissipated work in the steady state, we compare the large
asymptotic behaviour of our solution to that already obtained in (
arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is
placed on the computation of the pre-exponential factor and the results show
excellent agreement with the numerical simulations. Our solutions are exact in
the low noise limit.Comment: 26 pages, 8 figures. Changes from version 1: Several typos and
equations corrected, references added, pictures modified. Version to appear
in EPJ
Unscented Orientation Estimation Based on the Bingham Distribution
Orientation estimation for 3D objects is a common problem that is usually
tackled with traditional nonlinear filtering techniques such as the extended
Kalman filter (EKF) or the unscented Kalman filter (UKF). Most of these
techniques assume Gaussian distributions to account for system noise and
uncertain measurements. This distributional assumption does not consider the
periodic nature of pose and orientation uncertainty. We propose a filter that
considers the periodicity of the orientation estimation problem in its
distributional assumption. This is achieved by making use of the Bingham
distribution, which is defined on the hypersphere and thus inherently more
suitable to periodic problems. Furthermore, handling of non-trivial system
functions is done using deterministic sampling in an efficient way. A
deterministic sampling scheme reminiscent of the UKF is proposed for the
nonlinear manifold of orientations. It is the first deterministic sampling
scheme that truly reflects the nonlinear manifold of the orientation
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