1,750 research outputs found
Two new algorithms to compute steady-state bounds for Markov models with slow forward and fast backward transitions
Two new algorithms are proposed for the computation of bounds for the steady-state reward rate of irreducible finite Markov models with slow forward and fast backward transitions. The algorithms use detailed knowledge of the model in a subset of generated states G and partial information about the model in the non-generated portion U of the state space. U is assumed partitioned into subsets U_k,1\leq k\leq N with a “nearest neighbor” structure. The algorithms
involve the solution of, respectively, |M| + 2 and 4 linear systems of size |G|, where M is the set of values of k corresponding to the subsets U_k through which the model can jump from G to U. Previously proposed algorithms for the same type of models required the solution of |S| linear systems of size |G| + N , where S is the subset of G through which the model can enter G from U, to achieve the same bounds as our algorithms, or gave less tighter bounds if state cloning techniques were used to reduce the number of solved linear systems. An availability model with system state dependent repair rates is used to illustrate the application and performance of the algorithms.Postprint (published version
Stochastic models and numerical algorithms for a class of regulatory gene networks
Regulatory gene networks contain generic modules like those involving
feedback loops, which are essential for the regulation of many biological
functions. We consider a class of self-regulated genes which are the building
blocks of many regulatory gene networks, and study the steady state
distributions of the associated Gillespie algorithm by providing efficient
numerical algorithms. We also study a regulatory gene network of interest in
synthetic biology and in gene therapy, using mean-field models with time
delays. Convergence of the related time-nonhomogeneous Markov chain is
established for a class of linear catalytic networks with feedback loop
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
A method for the computation of reliability bounds for non-repairable fault-tolerant systems
A realistic modeling of fault-tolerant systems requires to take into account phenomena such as the dependence of component failure rates and coverage parameters on the operational configuration of the system, which cannot be properly captured using combinatorial techniques. Such dependencies can be modeled with detail using continuous-time Markov chains (CTMC’s). However, the use of CTMC models is limited by the well-known state space explosion problem. In this paper we develop a method for the computation of bounds for the reliability of non-repairable fault-tolerant systems which requires the generation of only a subset of states. The tightness of the bounds increases as more detailed states are generated. The method uses the failure distance concept and is illustrated using an example of a quite complex fault-tolerant system whose failure behavior has the above mentioned types of dependencies.Postprint (published version
Tight steady-state availability bounds using the failure distance concept
Continuous-time Markov chains are commonly used for dependability modeling of repairable
fault-tolerant computer systems. Realistic models of non-trivial fault-tolerant systems often have very large state spaces. An attractive approach for dealing with the largeness problem is the use of pruningmethods with error bounds. Several such methods for computing steady-state
availability bounds have been proposed recently. This paper presents a new method which exploits the failure distance concept to bound more efficiently the behavior in the non-generated state space. It is proved that the bounding method gives tighter bounds than previous methods.
Numerical analysis shows that the new bounds can be significantly tighter.Postprint (published version
Failure distance based bounds for steady-state availability without the kwnowledge of minimal cuts
We propose an algorithm to compute bounds for the steady-state unavailability using continuous-time Markov chains, which is based on the failure distance concept. The algorithm generates incrementally a subset of the state space until the tightness of the bounds is the specified one. In contrast with a previous algorithm also based on the failure distance concept, the proposed algorithm uses lower bounds for failure distances which are computed on the fault tree of the system, and does not require the knowledge of the minimal cuts. This is advantageous when the number of minimal cuts is large or their computation is time-consuming.Postprint (published version
Event-chain Monte Carlo: foundations, applications, and prospects
This review treats the mathematical and algorithmic foundations of
non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC),
a continuous-time lifted Markov chain that employs the factorized Metropolis
algorithm. It analyzes a number of model applications, and then reviews the
formulation as well as the performance of ECMC in key models in statistical
physics. Finally, the review reports on an ongoing initiative to apply the
method to the sampling problem in molecular simulation, that is, to real-world
models of peptides, proteins, and polymers in aqueous solution.Comment: 35 pages, no figure
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