Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

A probabilistic description is essential for understanding growth processes in non-stationary states. In this paper, we compute time-dependent probability density functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models. We consider different types of short-correlated multiplicative and additive noise sources and compare the time-dependent PDFs in the two models, elucidating the effects of the additive and multiplicative noises on the form of PDFs. We demonstrate an interesting transition from a unimodal to a bimodal PDF as the multiplicative noise increases for a fixed value of the additive noise. A much weaker (leaky) attractor in the Gompertz model leads to a significant (singular) growth of the population of a very small size. We point out the limitation of using stationary PDFs, mean value and variance in understanding statistical properties of the growth in non-stationary states, highlighting the importance of time-dependent PDFs. We further compare these two models from the perspective of information change that occurs during the growth process. Specifically, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory quantifies the total number of different states that the system undergoes in time, and is called the information length. We show that the time-evolution of the two models become more similar when measured in units of the information length and point out the merit of using the information length in unifying and understanding the dynamic evolution of different growth processes

Two coupled Josephson junctions: dc voltage controlled by biharmonic current

We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junction (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external shunt resistance, a dc voltage across the second junction can be generated. By variation of system parameters like the relative phase or frequency of two harmonics, one can conveniently manipulate both voltages with high efficiency, e.g., changing the dc voltages across the first and second junctions from positive to negative values and vice versa.Comment: 15 pages, 7 figures, to appear in J. Phys. Condens. Matter (2012

Ubiquitination screen using protein microarrays for comprehensive identification of Rsp5 substrates in yeast

Ubiquitin-protein ligases (E3s) are responsible for target recognition and regulate stability, localization or function of their substrates. However, the substrates of most E3 enzymes remain unknown. Here, we describe the development of a novel proteomic in vitro ubiquitination screen using a protein microarray platform that can be utilized for the discovery of substrates for E3 ligases on a global scale. Using the yeast E3 Rsp5 as a test system to identify its substrates on a yeast protein microarray that covers most of the yeast (Saccharomyces cerevisiae) proteome, we identified numerous known and novel ubiquitinated substrates of this E3 ligase. Our enzymatic approach was complemented by a parallel protein microarray protein interaction study. Examination of the substrates identified in the analysis combined with phage display screening allowed exploration of binding mechanisms and substrate specificity of Rsp5. The development of a platform for global discovery of E3 substrates is invaluable for understanding the cellular pathways in which they participate, and could be utilized for the identification of drug targets

Multipoint genome-wide linkage scan for nonword repetition in a multigenerational family further supports chromosome 13q as a locus for verbal trait disorders

Verbal trait disorders encompass a wide range of conditions and are marked by deficits in five domains that impair a person’s ability to communicate: speech, language, reading, spelling, and writing. Nonword repetition is a robust endophenotype for verbal trait disorders that is sensitive to cognitive processes critical to verbal development, including auditory processing, phonological working memory, and motor planning and programming. In the present study, we present a six-generation extended pedigree with a history of verbal trait disorders. Using genome-wide multipoint variance component linkage analysis of nonword repetition, we identified a region spanning chromosome 13q14–q21 with LOD = 4.45 between 52 and 55 cM, spanning approximately 5.5 Mb on chromosome 13. This region overlaps with SLI3, a locus implicated in reading disability in families with a history of specific language impairment. Our study of a large multigenerational family with verbal trait disorders further implicates the SLI3 region in verbal trait disorders. Future studies will further refine the specific causal genetic factors in this locus on chromosome 13q that contribute to language traits. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00439-016-1717-z) contains supplementary material, which is available to authorized users