10 research outputs found
On distributions of functionals of anomalous diffusion paths
Functionals of Brownian motion have diverse applications in physics,
mathematics, and other fields. The probability density function (PDF) of
Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger
equation in imaginary time. In recent years there is a growing interest in
particular functionals of non-Brownian motion, or anomalous diffusion, but no
equation existed for their PDF. Here, we derive a fractional generalization of
the Feynman-Kac equation for functionals of anomalous paths based on
sub-diffusive continuous-time random walk. We also derive a backward equation
and a generalization to Levy flights. Solutions are presented for a wide number
of applications including the occupation time in half space and in an interval,
the first passage time, the maximal displacement, and the hitting probability.
We briefly discuss other fractional Schrodinger equations that recently
appeared in the literature.Comment: 25 pages, 4 figure
On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967
The problem of “1∕ƒ” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕ƒ” noise and LRD, concepts which are often treated as equivalent
Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020
We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe
Quantification of photoinduced and spontaneous quantum-dot luminescence blinking
10.1103/PhysRevB.72.125304Physical Review B - Condensed Matter and Materials Physics7212-PRBM
Publisher Correction: Global site-specific neddylation profiling reveals that NEDDylated cofilin regulates actin dynamics (Nature Structural & Molecular Biology, (2020), 27, 2, (210-220), 10.1038/s41594-019-0370-3).
In the version of this article initially published online, in Fig. 6d, the third and fourth bars were incorrectly labeled “DMSO + cytochrome D” and “MLN4924 + cytochrome D,” respectively. They should have been labeled “DMSO + cytochalasin D” and “MLN4924 + cytochalasin D,” respectively. The errors have been corrected in the print, PDF and HTML versions of the article
Effects on generalized growth models driven by a non-Poissonian dichotomic noise
In this paper we consider a general growth model with stochastic growth rate modelled via
a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its
probability distribution. We consider the, as yet, unexplored case where the deterministic
growth rate is perturbed by a dichotomic noise characterized by a waiting time
distribution in the two state that is a power law with
power 1 < μ < 2. We
apply the results to two well-known growth models; Malthus-Verhulst and Gompertz