177 research outputs found
Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments
The dynamics of stochastic reaction networks within cells are inevitably
modulated by factors considered extrinsic to the network such as for instance
the fluctuations in ribsome copy numbers for a gene regulatory network. While
several recent studies demonstrate the importance of accounting for such
extrinsic components, the resulting models are typically hard to analyze. In
this work we develop a general mathematical framework that allows to uncouple
the network from its dynamic environment by incorporating only the
environment's effect onto the network into a new model. More technically, we
show how such fluctuating extrinsic components (e.g., chemical species) can be
marginalized in order to obtain this decoupled model. We derive its
corresponding process- and master equations and show how stochastic simulations
can be performed. Using several case studies, we demonstrate the significance
of the approach. For instance, we exemplarily formulate and solve a marginal
master equation describing the protein translation and degradation in a
fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio
Moment-Based Variational Inference for Markov Jump Processes
We propose moment-based variational inference as a flexible framework for
approximate smoothing of latent Markov jump processes. The main ingredient of
our approach is to partition the set of all transitions of the latent process
into classes. This allows to express the Kullback-Leibler divergence between
the approximate and the exact posterior process in terms of a set of moment
functions that arise naturally from the chosen partition. To illustrate
possible choices of the partition, we consider special classes of jump
processes that frequently occur in applications. We then extend the results to
parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning
(ICML 2019
Marginal process framework: A model reduction tool for Markov jump processes
Markov jump process models have many applications across science. Often,
these models are defined on a state-space of product form and only one of the
components of the process is of direct interest. In this paper, we extend the
marginal process framework, which provides a marginal description of the
component of interest, to the case of fully coupled processes. We use entropic
matching to obtain a finite-dimensional approximation of the filtering
equation, which governs the transition rates of the marginal process. The
resulting equations can be seen as a combination of two projection operations
applied to the full master equation, so that we obtain a principled model
reduction framework. We demonstrate the resulting reduced description on the
totally asymmetric exclusion process. An important class of Markov jump
processes are stochastic reaction networks, which have applications in chemical
and biomolecular kinetics, ecological models and models of social networks. We
obtain a particularly simple instantiation of the marginal process framework
for mass-action systems by using product-Poisson distributions for the
approximate solution of the filtering equation. We investigate the resulting
approximate marginal process analytically and numerically.Comment: 16 pages, 5 figures; accepted for publication in Physical Review
A variational approach to path estimation and parameter inference of hidden diffusion processes
We consider a hidden Markov model, where the signal process, given by a
diffusion, is only indirectly observed through some noisy measurements. The
article develops a variational method for approximating the hidden states of
the signal process given the full set of observations. This, in particular,
leads to systematic approximations of the smoothing densities of the signal
process. The paper then demonstrates how an efficient inference scheme, based
on this variational approach to the approximation of the hidden states, can be
designed to estimate the unknown parameters of stochastic differential
equations. Two examples at the end illustrate the efficacy and the accuracy of
the presented method.Comment: 37 pages, 2 figures, revise
Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms
Biochemical reactions can happen on different time scales and also the
abundance of species in these reactions can be very different from each other.
Classical approaches, such as deterministic or stochastic approach, fail to
account for or to exploit this multi-scale nature, respectively. In this paper,
we propose a jump-diffusion approximation for multi-scale Markov jump processes
that couples the two modeling approaches. An error bound of the proposed
approximation is derived and used to partition the reactions into fast and slow
sets, where the fast set is simulated by a stochastic differential equation and
the slow set is modeled by a discrete chain. The error bound leads to a very
efficient dynamic partitioning algorithm which has been implemented for several
multi-scale reaction systems. The gain in computational efficiency is
illustrated by a realistically sized model of a signal transduction cascade
coupled to a gene expression dynamics.Comment: 32 pages, 7 figure
Under-approximating Cut Sets for Reachability in Large Scale Automata Networks
In the scope of discrete finite-state models of interacting components, we
present a novel algorithm for identifying sets of local states of components
whose activity is necessary for the reachability of a given local state. If all
the local states from such a set are disabled in the model, the concerned
reachability is impossible. Those sets are referred to as cut sets and are
computed from a particular abstract causality structure, so-called Graph of
Local Causality, inspired from previous work and generalised here to finite
automata networks. The extracted sets of local states form an
under-approximation of the complete minimal cut sets of the dynamics: there may
exist smaller or additional cut sets for the given reachability. Applied to
qualitative models of biological systems, such cut sets provide potential
therapeutic targets that are proven to prevent molecules of interest to become
active, up to the correctness of the model. Our new method makes tractable the
formal analysis of very large scale networks, as illustrated by the computation
of cut sets within a Boolean model of biological pathways interactions
gathering more than 9000 components
Inverse Reinforcement Learning in Swarm Systems
Inverse reinforcement learning (IRL) has become a useful tool for learning
behavioral models from demonstration data. However, IRL remains mostly
unexplored for multi-agent systems. In this paper, we show how the principle of
IRL can be extended to homogeneous large-scale problems, inspired by the
collective swarming behavior of natural systems. In particular, we make the
following contributions to the field: 1) We introduce the swarMDP framework, a
sub-class of decentralized partially observable Markov decision processes
endowed with a swarm characterization. 2) Exploiting the inherent homogeneity
of this framework, we reduce the resulting multi-agent IRL problem to a
single-agent one by proving that the agent-specific value functions in this
model coincide. 3) To solve the corresponding control problem, we propose a
novel heterogeneous learning scheme that is particularly tailored to the swarm
setting. Results on two example systems demonstrate that our framework is able
to produce meaningful local reward models from which we can replicate the
observed global system dynamics.Comment: 9 pages, 8 figures; ### Version 2 ### version accepted at AAMAS 201
A Comprehensive Analysis of Swarming-based Live Streaming to Leverage Client Heterogeneity
Due to missing IP multicast support on an Internet scale, over-the-top media
streams are delivered with the help of overlays as used by content delivery
networks and their peer-to-peer (P2P) extensions. In this context,
mesh/pull-based swarming plays an important role either as pure streaming
approach or in combination with tree/push mechanisms. However, the impact of
realistic client populations with heterogeneous resources is not yet fully
understood. In this technical report, we contribute to closing this gap by
mathematically analysing the most basic scheduling mechanisms latest deadline
first (LDF) and earliest deadline first (EDF) in a continuous time Markov chain
framework and combining them into a simple, yet powerful, mixed strategy to
leverage inherent differences in client resources. The main contributions are
twofold: (1) a mathematical framework for swarming on random graphs is proposed
with a focus on LDF and EDF strategies in heterogeneous scenarios; (2) a mixed
strategy, named SchedMix, is proposed that leverages peer heterogeneity. The
proposed strategy, SchedMix is shown to outperform the other two strategies
using different abstractions: a mean-field theoretic analysis of buffer
probabilities, simulations of a stochastic model on random graphs, and a
full-stack implementation of a P2P streaming system.Comment: Technical report and supplementary material to
http://ieeexplore.ieee.org/document/7497234
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