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Approximate Filtering Distributions for Characterizing Input-Output Behavior of Biochemical Networks

Characterizing complex biochemical networks in terms of their input-output behavior is at the core of rational circuit design. The theory of stochastic filtering offers an elegant methodology to describe such behavior by means of conditional probability distributions. The latter are relevant to various applications such as biomolecular estimation and control, robustness analysis and information transmission, to name a few. However, finding the conditional distributions as a function of time r...

Automated Generation of Conditional Moment Equations for Stochastic Reaction Networks

The dynamics of biochemical reaction networks require a stochastic description when copy number fluctuations become significant. Such description is provided by moment equations that capture the statistical properties of the involved molecular components such as their average abundance and variability. Certain applications require a special form of moment equations, where the statistics of some components are described conditionally on complete trajectories of other components. Typical exampl...

Bayesian learning of echo state networks with tunable filters and delay & sum readouts

In this paper we investigate the problem of learning Echo State Networks (ESN) with adaptable filter neurons and delay&sum readouts. A brute-force solution to this learning problem is often impractical due to nonlinearity and high dimensionality of the resulting optimization problem. In this work we propose an approximate solution to the ESN learning by appealing to the variational Bayesian EM-type of estimation algorithm. We show that such approach allows to significantly reduce the dime...

Phase-based algorithm for 2D displacement estimation of laser speckle patterns

Robust, computationally efficient and accurate estimation of 2D speckle pattern displacement is the key signal processing task in most digital speckle photography principles. State-of-the-art techniques are based on the evaluation of correlation functions with high computational complexity when sub-pixel accuracy is needed. Within this paper we describe a new algorithm based on the evaluation of 2D phase data of laser speckle patterns, capable of estimating 2D speckle pattern displacement wit...

Recursive Bayesian Estimation of Stochastic Rate Constants from Heterogeneous Cell Populations

Robust estimation of kinetic parameters of intracellular processes requires large amounts of quantitative data. Due to the high uncertainty of such processes and the fact that recent single-cell measurement techniques have limited resolution and dimensionality, estimation should pool recordings of multiple cells of an isogenic cell population. However, experimental results have shown that several factors such as cell volume or cell-cycle stage can drastically affect signaling as well as prote...

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