Open AccessBook
Stochastic Processes in Cell Biology
TLDR
Self-Organization in Cells I: Active Processes and Reaction-Diffusion Models: The WKB Method and Large Deviation Theory and Probability Theory and Martingales are used.Abstract:
Introduction- Diffusion in Cells: Random walks and Brownian Motion- Stochastic Ion Channels- Polymers and Molecular Motors- Sensing the Environment: Adaptation and Amplification in Cells- Stochastic Gene Expression and Regulatory Networks- Transport Processes in Cells- Self-Organization in Cells I: Active Processes- Self-Organization in Cells II: Reaction-Diffusion Models- The WKB Method and Large Deviation Theory- Probability Theory and Martingalesread more
Citations
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Journal ArticleDOI
WKB theory of large deviations in stochastic populations
Michael Assaf,Baruch Meerson +1 more
TL;DR: In this article, the authors review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems.
Journal ArticleDOI
Unreasonable Effectiveness of Learning Neural Networks: From Accessible States and Robust Ensembles to Basic Algorithmic Schemes
Carlo Baldassi,Christian Borgs,Jennifer Chayes,Alessandro Ingrosso,Carlo Lucibello,Luca Saglietti,Riccardo Zecchina +6 more
TL;DR: It is shown that there are regions of the optimization landscape that are both robust and accessible and that their existence is crucial to achieve good performance on a class of particularly difficult learning problems, and an explanation of this good performance is proposed in terms of a nonequilibrium statistical physics framework.
Book
Fractional Diffusion Equations and Anomalous Diffusion
TL;DR: Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids.
Journal ArticleDOI
Single-Particle Diffusion Characterization by Deep Learning
Naor Granik,Lucien E. Weiss,Elias Nehme,Maayan Levin,Michael Chein,Eran Perlson,Yael Roichman,Yoav Shechtman +7 more
TL;DR: A neural network is implemented to classify single-particle trajectories by diffusion type: Brownian motion, fractional BrownianMotion and continuous time random walk, and the applicability of the network architecture for estimating the Hurst exponent for fractionalBrownian motion and the diffusion coefficient for Brownianmotion on both simulated and experimental data is demonstrated.
Journal ArticleDOI
Uncertainty relations in stochastic processes: An information inequality approach
Yoshihiko Hasegawa,Tan Van Vu +1 more
TL;DR: It is found that the thermodynamic uncertainty relation is a particular case of the Cramér-Rao inequality, in which the Fisher information is the total entropy production, and the stochastictotal entropy production is the only quantity that can attain equality in the thermodynamics uncertainty relation.
References
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Book ChapterDOI
Self-Organization in Cells II: Reaction-Diffusion Models
TL;DR: This chapter focuses on the role of active processes such as polymerization on the self-organization of cytoskeletal structures and the interplay between diffusion and nonlinear chemical reactions in this area.
Book ChapterDOI
Self-Organization in Cells I: Active Processes
TL;DR: In order to address questions about how cellular and subcellular structures are formed and maintained given their particular molecular components, the theory of self-organizing non-equilibrium systems is considered.