29,594 research outputs found
A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating
An important part of system modeling is determining parameter values,
particularly for biomolecular systems, where direct measurements of individual
parameters are typically hard. While Extended Kalman Filters have been used for
this purpose, the choice of the process noise covariance is generally unclear.
In this chapter, we address this issue for biomolecular systems using a
combination of Monte Carlo simulations and experimental data, exploiting the
dependence of the process noise covariance on the states and parameters, as
given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering
technique by updating the process noise covariance at each time step based on
estimates. We compare the performance of this framework with different fixed
values of process noise covariance in biomolecular system models, including an
oscillator model, as well as in experimentally measured data for a negative
transcriptional feedback circuit. We find that the Extended Kalman Filter with
such process noise covariance update is closer to the optimality condition in
the sense that the innovation sequence becomes white and in achieving a balance
between the mean square estimation error and parameter convergence time. The
results of this chapter may help in the use of Extended Kalman Filters for
systems where process noise covariance depends on states and/or parameters.Comment: 23 pages, 9 figure
Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey
This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems
Stochastic reaction network models are widely utilized in biology and
chemistry to describe the probabilistic dynamics of biochemical systems in
general, and gene interaction networks in particular. Most often, statistical
analysis and inference of these systems is addressed by parametric approaches,
where the laws governing exogenous input processes, if present, are themselves
fixed in advance. Motivated by reporter gene systems, widely utilized in
biology to monitor gene activation at the individual cell level, we address the
analysis of reaction networks with state-affine reaction rates and arbitrary
input processes. We derive a generalization of the so-called moment equations
where the dynamics of the network statistics are expressed as a function of the
input process statistics. In stationary conditions, we provide a spectral
analysis of the system and elaborate on connections with linear filtering. We
then apply the theoretical results to develop a method for the reconstruction
of input process statistics, namely the gene activation autocovariance
function, from reporter gene population snapshot data, and demonstrate its
performance on a simulated case study
Modeling and control of complex dynamic systems: Applied mathematical aspects
The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
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
The combined Lagrangian advection method
We present and test a new hybrid numerical method for simulating layerwise-two-dimensional geophysical flows. The method radically extends the original Contour-Advective Semi-Lagrangian (CASL) algorithm by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudospectral method for large scales, (2) Lagrangian contours for intermediate to small scales, and (3) Lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely finescale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation
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