Poisson channel with binary Markov input and average sojourn time constraint

Sinzger, Mark; Gehri, Maximilian; Koeppl, Heinz

doi:10.1109/isit44484.2020.9174360

Cited by 4 publications

(3 citation statements)

References 39 publications

(51 reference statements)

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“…We identify eq. ( 43) as a reparametrization of the integral representation previously reported [49] for ω = ω 1 and Π t (1)…”

Section: Case Studies a Random Telegraph Permits An Analytic Solutionmentioning

confidence: 96%

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ACID: A Low Dimensional Characterization of Markov-Modulated and Self-Exciting Counting Processes

Sinzger-D'Angelo¹,

Koeppl²

2022

Preprint

Self Cite

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The conditional intensity (CI) of a counting process Yt is based on the minimal knowledge F Y t , i.e., on the observation of Yt alone. Prominently, the mutual information rate of a signal and its Poisson channel output is a difference functional between the CI and the intensity that has full knowledge about the input. While the CI of Markov-modulated Poisson processes evolves according to Snyder's filter, self-exciting processes, e.g., Hawkes processes, specify the CI via the history of Yt. The emergence of the CI as a self-contained stochastic process prompts us to bring its statistical ensemble into focus. We investigate the asymptotic conditional intensity distribution (ACID) and emphasize its rich information content. We assume the case in which the CI is determined from a sufficient statistic that progresses as a Markov process. We present a simulation-free method to compute the ACID when the dimension of the sufficient statistic is low. The method is made possible by introducing a backward recurrence time parametrization, which has the advantage to align all probability inflow in a boundary condition for the master equation. Case studies illustrate the usage of ACID for three primary examples: 1) the Poisson channels with binary Markovian input (as an example of a Markov-modulated Poisson process), 2) the standard Hawkes process with exponential kernel (as an example of a self-exciting counting process) and 3) the Gamma filter (as an example of an approximate filter to a Markov-modulated Poisson process).

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“…We identify eq. ( 43) as a reparametrization of the integral representation previously reported [49] for ω = ω 1 and Π t (1)…”

Section: Case Studies a Random Telegraph Permits An Analytic Solutionmentioning

confidence: 96%

“…Consequently, an increased dark current can qualitatively alter monotonicity and optimality properties in the (k 1 , k 2 )-phase plane. For example, the On favoring region increases with dark current [49].…”

Section: B Random Telegraph With Dark Currentmentioning

confidence: 99%

ACID: A Low Dimensional Characterization of Markov-Modulated and Self-Exciting Counting Processes

Sinzger-D'Angelo¹,

Koeppl²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Recently, some progress has been made towards addressing this challenge. In [10], for instance, the authors derive exact expressions for the trajectory-level mutual information and channel capacity for a simple Markov chain model of transcription. For more complex systems, however, analytical solutions are generally not available and one has to resort to approximation techniques.…”

mentioning

confidence: 99%

Dynamic Information Transfer in Stochastic Biochemical Networks

Moor¹,

Zechner²

2022

Preprint

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We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuoustime Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this work, we generalize this approach to biochemical networks involving an arbitrary number of molecular components. We present an efficient Monte Carlo method as well as an analytical approximation to calculate the path mutual information and show how it can be decomposed into a pair of transfer entropies that capture the causal flow of information between two network components. We apply our methodology to study information transfer in a simple three-node feedforward network, as well as a more complex positive feedback system that switches stochastically between two metastable modes.Introduction. Information theory provides a powerful mathematical framework to study information transfer in complex dynamical systems. Originating from man-made communication systems [1], information theory has made its way into the biological sciences where it has helped to understand diverse biological processes, ranging from tissue patterning [2] to signal transduction [3].

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Entropy production constrains information throughput in gene regulation

Gehri,

Stelzl,

Koeppl

2024

Preprint

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Biological signal processing typically requires energy, leading us to hypothesize that a cell's information processing capacity is constrained by its energy dissipation. Signals and their processing mechanisms are often modeled using Markovian chemical reaction networks (CRNs). To enable rigorous analysis, we review and reformulate stochastic thermodynamics for open CRNs, utilizing Kurtz's process-based formulation. In particular, we revisit the identification of the energy dissipation rate with the entropy production rate (EPR) at the non-equilibrium steady state (NESS). We also highlight potential inconsistencies in traditional formulations for generic Markov processes when applied to open CRNs, which may lead to erroneous conclusions about equilibrium, reversibility, and the EPR. Additionally, we review the concepts of mutual information (MI) and directed information (DI) between continuous-time trajectories of CRNs, which capture the transmission of spatiotemporal patterns. We generalize existing expressions for the MI, originally accounting for transmission between two species, to now include transmission between arbitrary subnetworks. A rigorous derivation of the DI between subnetworks is presented. Based on channel coding theorems for continuous-time channels with feedback, we argue that directed information is the appropriate metric for quantifying information throughput in cellular signal processing. To support our initial hypothesis within the context of gene regulation, we present two case studies involving small promoter models: a two-state nonequilibrium promoter and a three-state promoter featuring two activation levels. We provide analytical expressions of the directed information rate (DIR) and maximize them subject to an upper bound on the EPR. The maximum is shown to increase with the EPR.

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Poisson channel with binary Markov input and average sojourn time constraint

Cited by 4 publications

References 39 publications

ACID: A Low Dimensional Characterization of Markov-Modulated and Self-Exciting Counting Processes

ACID: A Low Dimensional Characterization of Markov-Modulated and Self-Exciting Counting Processes

Dynamic Information Transfer in Stochastic Biochemical Networks

Entropy production constrains information throughput in gene regulation

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