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Dynamic instability is defined as the stochastic switching between states of polymerization and rapid depolymerization (Mitchison and Kirschner, 1984a).
A fault in a GRN is defined as the stochastic behavior of a node or the logic gate in the GRN.
We modeled these GRNs under increasing number of faults in the network, where a fault is defined as the stochastic behavior of a node (for SIN) or the logic gate (for SIF) in the GRN.
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The Ornstein-Uhlenbeck process defined as the solution (19) to the stochastic differential equation (18) is also a Markov process with stationary transition probabilities.
where S ( t ) = ∑ k = 1 t r ( k ) is the time-accumulated service process, and {r k),k=1,2,…} is defined as the discrete-time, stationary, and ergodic stochastic service process.
Therefore, we interpreted the measurements as random variates that were generated by a stochastic process, which is defined as the deterministic solution of the differential equation model perturbed by additive stochastic noise terms.
Here stochastic persistence is defined as the mean of the sample paths of the solution in time.
Briefly, stochastic gene expression is defined as the ratio between the observed variance (σ2) and the expected variance given the mean expression level of a given gene over all single cells (Barroso et al. 2018).
The stochastic process { X t, T } defined as the solution to model (1) has a domain I = [ l, r ], where − ∞ ≤ l < r ≤ + ∞.
Mathematically, the objective is defined as a stochastic criterion, belonging to the class of linear quadratic regulator (LQR) optimal control problems.
MDPs are defined as controlled stochastic processes satisfying the Markov property and assigning reward values to state transitions (Bellman 1957; Puterman 1994).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com