Discrete Dynamical Systems: A Brief Survey

Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization

Solar type II radio bursts associated with CME expansions as shown by EUV waves

We investigate the physical conditions of the sources of two metric Type-II bursts associated with CME expansions with the aim of verifying the relationship between the shocks and the CMEs, comparing the heights of the radio sources and the heights of the EUV waves associated with the CMEs. The heights of the EUV waves associated with the events were determined in relation to the wave fronts. The heights of the shocks were estimated by applying two different density models to the frequencies of the Type-II emissions and compared with the heights of the EUV waves. For the 13 June 2010 event, with band-splitting, the shock speed was estimated from the frequency drifts of the upper and lower branches of the harmonic lane, taking into account the H/F frequency ratio fH/fF = 2. Exponential fits on the intensity maxima of the branches revealed to be more consistent with the morphology of the spectrum of this event. For the 6 June 2012 event, with no band-splitting and with a clear fundamental lane on the spectrum, the shock speed was estimated directly from the frequency drift of the fundamental emission, determined by linear fit on the intensity maxima of the lane. For each event, the most appropriate density model was adopted to estimate the physical parameters of the radio source. The 13 June 2010 event presented a shock speed of 664-719 km/s, consistent with the average speed of the EUV wave fronts of 609 km/s. The 6 June 2012 event was related to a shock of speed of 211-461 km/s, also consistent with the average speed of the EUV wave fronts of 418 km/s. For both events, the heights of the EUV wave revealed to be compatible with the heights of the radio source, assuming a radial propagation of the shock.Comment: Accepted for publication in Astronomy and Astrophysic

Assessing individual differences in genome-wide gene expression in human whole blood: reliability over four hours and stability over 10 months.

Studying the causes and correlates of natural variation in gene expression in healthy populations assumes that individual differences in gene expression can be reliably and stably assessed across time. However, this is yet to be established. We examined 4-hour test-retest reliability and 10 month test-retest stability of individual differences in gene expression in ten 12-year-old children. Blood was collected on four occasions: 10 a.m. and 2 p.m. on Day 1 and 10 months later at 10 a.m. and 2 p.m. Total RNA was hybridized to Affymetrix-U133 plus 2.0 arrays. For each probeset, the correlation across individuals between 10 a.m. and 2 p.m. on Day 1 estimates test-retest reliability. We identified 3,414 variable and abundantly expressed probesets whose 4-hour test-retest reliability exceeded .70, a conventionally accepted level of reliability, which we had 80% power to detect. Of the 3,414 reliable probesets, 1,752 were also significantly reliable 10 months later. We assessed the long-term stability of individual differences in gene expression by correlating the average expression level for each probe-set across the two 4-hour assessments on Day 1 with the average level of each probe-set across the two 4-hour assessments 10 months later. 1,291 (73.7%) of the 1,752 probe-sets that reliably detected individual differences across 4 hours on two occasions, 10 months apart, also stably detected individual differences across 10 months. Heritability, as estimated from the MZ twin intraclass correlations, is twice as high for the 1,752 reliable probesets versus all present probesets on the array (0.68 vs 0.34), and is even higher (0.76) for the 1,291 reliable probesets that are also stable across 10 months. The 1,291 probesets that reliably detect individual differences from a single peripheral blood collection and stably detect individual differences over 10 months are promising targets for research on the causes (e.g., eQTLs) and correlates (e.g., psychopathology) of individual differences in gene expression

Scotin, a novel p53-inducible proapoptotic protein located in the ER and the nuclear membrane

p53 is a transcription factor that induces growth arrest or apoptosis in response to cellular stress. To identify new p53-inducible proapoptotic genes, we compared, by differential display, the expression of genes in spleen or thymus of normal and p53 nullizygote mice after γ-irradiation of whole animals. We report the identification and characterization of human and mouse Scotin homologues, a novel gene directly transactivated by p53. The Scotin protein is localized to the ER and the nuclear membrane. Scotin can induce apoptosis in a caspase-dependent manner. Inhibition of endogenous Scotin expression increases resistance to p53-dependent apoptosis induced by DNA damage, suggesting that Scotin plays a role in p53-dependent apoptosis. The discovery of Scotin brings to light a role of the ER in p53-dependent apoptosis