Exact statistical moments of multi-mode stochastic hybrid systems with renewal transitions

Xu, Zhenci; Soltani, Mohammad; Singh, Abhyudai

doi:10.1109/cdc.2018.8619667

Cited by 2 publications

(3 citation statements)

References 45 publications

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“…T OF F ∼ h ON (τ )e − τ y=0 h ON (y)dy (18) with a constant rate h ON = 1/⟨T OF F ⟩ results in exponentially distributed T OF F [62], [64]. Once the gene switches ON, the timer is reset to zero and again linearly increases with time.…”

Section: Stochastic Dynamics Of Promoter Switchingmentioning

confidence: 99%

“…The switching back to the OFF state occurs with rate h OF F (τ ) resulting in the time the ON state to be an i.i.d. random variable with pdf The analysis of this system is exactly as done in [62], with the key difference being that while [62] models mRNA synthesis/degradation as on ordinary differential equation, we here model it stochastically with busty synthesis and exponentially-distributed mRNA lifespan CV L = 1. The steady-state moments of mRNA counts are given by…”

Section: Stochastic Dynamics Of Promoter Switchingmentioning

confidence: 99%

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Quantifying statistics of gene product copy-number fluctuations: A stochastic hybrid systems approach

Vahdat,

Singh

2024

Preprint

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Across diverse cell types, genes are often expressed at low levels resulting in significant stochastic fluctuations (noise) in intracellular copy number of mRNAs and proteins over time. Motivated by single-cell experiments, we capture this stochasticity by considering a given gene that toggles between a transcriptionally active and inactive state with the time spent in each state being an arbitrary random variable. mRNAs are synthesized from the active state as per a Poisson process and each molecule degrades after a random lifespan (i.e., random time from birth to death). Modeling this process using the Stochastic Hybrid System (SHS) formalism we derive exact analytical results for the statistical moments of molecular counts. Our results show that for fixed mean mRNA numbers, fluctuations in mRNA levels are amplified with decreasing noise in mRNA lifespan. Relaxing the Poisson process assumption, we next consider a scenario where transcription events occur such that the time between successive events is an arbitrarily distributed random variable. In this case, we show that decreasing noise in mRNA lifespan can both increase/decrease mRNA count fluctuations depending on the underlying transcriptional process. Finally, we extend these results to the protein level, where increasing noise in mRNA counts is sometimes associated with decreasing noise in protein copy numbers.

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Section: Stochastic Dynamics Of Promoter Switchingmentioning

confidence: 99%

Section: Stochastic Dynamics Of Promoter Switchingmentioning

confidence: 99%

Quantifying statistics of gene product copy-number fluctuations: A stochastic hybrid systems approach

Vahdat,

Singh

2024

Preprint

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“…where i, j ∈ {1, 2, 3}, and E stands for expectation value [26][27][28][29][30][31] .The signal y[n] has been defined in (4);…”

Section: Solving Fisher Information Matrixmentioning

confidence: 99%

Cramér-Rao Lower Bound for Forced Oscillations under Independent Multi-channel PMU measurements in Power Systems

Pierre

2022

2022 North American Power Symposium (NAPS)

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Forced oscillations threaten the reliability of wide-area power systems, and different approaches to estimate forced oscillation have been explored over the past several years. Though these efforts provide powerful tools to estimate a forced oscillation's amplitude, frequency, and phase, a benchmark for estimation accuracy has not been available. This paper provides initial results in such a benchmark called the Cramér-Rao Lower Bound which is a lower bound on the variance in those estimates. A direct approach to derive Cramér-Rao Lower Bound of forced oscillation in power systems is given. In the end, the MinniWECC model is applied to assess the impact of different factors on the bound.

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Exact statistical moments of multi-mode stochastic hybrid systems with renewal transitions

Cited by 2 publications

References 45 publications

Quantifying statistics of gene product copy-number fluctuations: A stochastic hybrid systems approach

Quantifying statistics of gene product copy-number fluctuations: A stochastic hybrid systems approach

Cramér-Rao Lower Bound for Forced Oscillations under Independent Multi-channel PMU measurements in Power Systems

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