scholarly journals Stabilization of Stochastic Fluctuations in Hyperbolic Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 7223-7227
Author(s):  
Stephan Gerster
2000 ◽  
Vol 32 (12) ◽  
pp. 23-36 ◽  
Author(s):  
Sergey I. Lyashko ◽  
Vladimir V. Semenov ◽  
Ivan I. Lyashko
Keyword(s):  

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Alain R. Bonny ◽  
João Pedro Fonseca ◽  
Jesslyn E. Park ◽  
Hana El-Samad

AbstractStochastic fluctuations at the transcriptional level contribute to isogenic cell-to-cell heterogeneity in mammalian cell populations. However, we still have no clear understanding of the repercussions of this heterogeneity, given the lack of tools to independently control mean expression and variability of a gene. Here, we engineer a synthetic circuit to modulate mean expression and heterogeneity of transgenes and endogenous human genes. The circuit, a Tunable Noise Rheostat (TuNR), consists of a transcriptional cascade of two inducible transcriptional activators, where the output mean and variance can be modulated by two orthogonal small molecule inputs. In this fashion, different combinations of the inputs can achieve the same mean but with different population variability. With TuNR, we achieve low basal expression, over 1000-fold expression of a transgene product, and up to 7-fold induction of the endogenous gene NGFR. Importantly, for the same mean expression level, we are able to establish varying degrees of heterogeneity in expression within an isogenic population, thereby decoupling gene expression noise from its mean. TuNR is therefore a modular tool that can be used in mammalian cells to enable direct interrogation of the implications of cell-to-cell variability.


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