Description: This article discusses correlation function and generalized master equation of arbitrary age. Abstract: We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J. Stat. Phys. 104, 489 (2001)]. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations fo ...

Description: This article discusses root architecture and nodulation. Abstract: The Medicago truncatula LATD/NIP gene is essential for the development of lateral and primary root and nitrogen-fixing nodule meristems as well as for rhizobial invasion of nodules. LATD/NIP encodes a member of the NRT1(PTR1) nitrate and di-and tri-peptide transporter family, suggesting that its function is to transport one of these or another compound(s). Because latd/nip mutants can have their lateral and primary root defects rescued by ABA, ABA is a potential substrate for transport. LATD/NIP expression in the root meristem was demonstrated to be regulated by auxin, cytokinin and abscisic acid, but not by nitrate. LATD/NIP's potential function and its role in coordinating root architecture and nodule formation are discussed.

Description: This article discusses linear response and 1/f optimal information transport. Article: Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. The authors show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

Description: This article discusses dynamics of electroencephalogram entropy and pitfalls of scaling detection. Abstract: In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein the authors study the time evolution of diffusion entropy to elucidate the scaling of EGG time series. For a cohort of 20 awake healthy volunteers with closed eyes, the authors find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in ...

Description: This article discusses LIN, a Medicago truncatula gene. Ethyl methanesulfonate mutagenesis of the model legume Medicago truncatula has previously identified several genes required for early steps in nodulation. Here, the authors describe a new mutant that is defective in intermediate steps of nodule differentiation. The lin (lumpy infections) mutant is characterized by a 4-fold reduction in the number of infections, all of which arrest in the root epidermis, and by nodule primordia that initiate normally but fail to mature. Genetic analyses indicate that the symbiotic phenotype is conferred by a single gene that maps to the lower arm of linkage group 1. Transcriptional markers for early Nod factor responses (RIP1 and ENOD40) are induced in lin, as is another early nodulin, ENOD20, a gene expressed during the differentiation of nodule primordia. By contrast, other markers correlated with primordium differentiation (CCS52A), infection progression (MtN6), or nodule morphogenesis (ENOD2 and ENOD8) show reduced or no induction in homozygous lin individuals. Taken together, these results suggest that LIN functions in maintenance of rhizobial infections and differentiation of nodules from nodule primordia.