Sun, 27 Jul 2008 11:05:48 BST CiteULike: dchen statistics http://www.citeulike.org/user/dchen/tag/statistics CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/dchen/article/2759260 <i>(2008)</i><br /><br />The time needed for a particle to exit a confining domain through a small window, called the narrow-escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean NET for a given geometric environment is therefore a requisite step to quantify the reaction rate constant of such processes, which has raised a growing interest in the past few years. In this Letter, we determine explicitly the scaling dependence of the mean NET on both the volume of the confining domain and the starting point to aperture distance. We show that this analytical approach is applicable to a very wide range of stochastic processes, including anomalous diffusion or diffusion in the presence of an external force field, which cover situations of biological relevance. Narrow-Escape Time Problem: Time Needed for a Particle to Exit a Confining Domain through a Small Windowb O Bénichou R Voituriez (2008) 2008-05-05T21:45:19-00:00 2008 2008 diffusion statistics http://www.citeulike.org/user/dchen/article/1711726 <i>Physical Review Letters, Vol. 99, No. 13. (2007)</i><br /><br />We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression. Universal Scaling Law in Human Behavioral Organization Toru Nakamura Ken Kiyono Kazuhiro Yoshiuchi Rika Nakahara Zbigniew Struzik Yoshiharu Yamamoto doi:10.1103/PhysRevLett.99.138103 Physical Review Letters, Vol. 99, No. 13. (2007) 2007-09-30T16:11:00-00:00 2007 Physical Review Letters 99 13 APS 2007 statistics system