Versatile analysis of single-molecule tracking data by comprehensive testing against Monte Carlo simulations
S Wieser, M Axmann, GJ Schütz - Biophysical journal, 2008 - cell.com
We propose here an approach for the analysis of single-molecule trajectories which is
based on a comprehensive comparison of an experimental data set with multiple Monte …
based on a comprehensive comparison of an experimental data set with multiple Monte …
Asymptotic exponentiality of exit times
F Marchetti - Statistics & Probability Letters, 1983 - Elsevier
This paper is concerned with sufficient conditions to insure that certain diffusion exit times
have, asymptotically, an exponential distribution. We also show that our requirements are …
have, asymptotically, an exponential distribution. We also show that our requirements are …
[引用][C] Approximation of the first passage time density of a Brownian motion to an exponentially decaying threshold by two-piecewise linear threshold. Application to …
M Tamborrino - Mathematical Biosciences and Engineering, 2016
Estimation of the diffusion coefficient from crossings
D Florens - Statistical Inference for Stochastic Processes, 1998 - Springer
In a previous work we proposed a kernel method for estimating the value of a state‐
dependent diffusion coefficient σ (x) from discrete time observations. We propose an …
dependent diffusion coefficient σ (x) from discrete time observations. We propose an …
Stochastic narrow escape in molecular and cellular biology
D Holcman, Z Schuss - Analysis and Applications. Springer, New York, 2015 - Springer
This monograph consists of two main parts, mathematical and biological. The mathematical
part, which is quite sophisticated involving advanced asymptotic methods in partial …
part, which is quite sophisticated involving advanced asymptotic methods in partial …
Effective diffusion constant for inhomogeneous diffusion
S Revathi, V Balakrishnan - Journal of Physics A: Mathematical …, 1993 - iopscience.iop.org
We consider the problem of determining analytically the effective diffusion constant D eff for
diffusion in an inhomogeneous medium, described by the diffusion equation delta t P= delta …
diffusion in an inhomogeneous medium, described by the diffusion equation delta t P= delta …
Diffusion models with time-dependent parameters: An analysis of computational effort and accuracy of different numerical methods
Drift-diffusion models have become valuable tools in many fields of contemporary
psychology and the neurosciences. The present study compares and analyzes different …
psychology and the neurosciences. The present study compares and analyzes different …
Towards dead time inclusion in neuronal modeling
A Buonocore, G Esposito, V Giorno… - arXiv preprint math …, 2003 - arxiv.org
A mathematical description of the refractoriness period in neuronal diffusion modeling is
given and its moments are explicitly obtained in a form that is suitable for quantitative …
given and its moments are explicitly obtained in a form that is suitable for quantitative …
A transformation approach to modelling multi-modal diffusions
JL Forman, M Sørensen - Journal of Statistical Planning and Inference, 2014 - Elsevier
This paper demonstrates that flexible and statistically tractable multi-modal diffusion models
can be attained by transformation of simple well-known diffusion models such as the …
can be attained by transformation of simple well-known diffusion models such as the …
Non-parametric estimation of the diffusion coefficient from noisy data
E Schmisser - Statistical inference for stochastic processes, 2012 - Springer
We consider a diffusion process (X t) t≥ 0, with drift b (x) and diffusion coefficient σ (x). At
discrete times tk= k δ for k from 1 to M, we observe noisy data of the sample path, Y_ k δ= X …
discrete times tk= k δ for k from 1 to M, we observe noisy data of the sample path, Y_ k δ= X …