A stochastic model for heart rate fluctuations

Normal human heart rate shows complex fluctuations in time, which is natural, since heart rate is controlled by a large number of different feedback control loops. These unpredictable fluctuations have been shown to display fractal dynamics, long-term correlations, and 1/f noise. These characterizations are statistical and they have been widely studied and used, but much less is known about the detailed time evolution (dynamics) of the heart rate control mechanism. Here we show that a simple one-dimensional Langevin-type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical to Gaussian noise, and both parts can be directly determined from the measured heart rate data. Studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems: there are two stable fixed points and one unstable one.Comment: 8 pages in PDF, Revtex style. Added more dat

Multiple post-domestication origins of kabuli chickpea through allelic variation in a diversification-associated transcription factor

Chickpea (Cicer arietinum) is among the founder crops domesticated in the Fertile Crescent. One of two major forms of chickpea, the so-called kabuli type, has white flowers and light-colored seed coats, properties not known to exist in the wild progenitor. The origin of the kabuli form has been enigmatic. We genotyped a collection of wild and cultivated chickpea genotypes with 538 single nucleotide polymorphisms (SNPs) and examined patterns of molecular diversity relative to geographical sources and market types. In addition, we examined sequence and expression variation in candidate anthocyanin biosynthetic pathway genes. A reduction in genetic diversity and extensive genetic admixture distinguish cultivated chickpea from its wild progenitor species. Among germplasm, the kabuli form is polyphyletic. We identified a basic helix-loop-helix (bHLH) transcription factor at chickpea\u27s B locus that conditions flower and seed colors, orthologous to Mendel\u27s A gene of garden pea, whose loss of function is associated invariantly with the kabuli type of chickpea. From the polyphyletic distribution of the kabuli form in germplasm, an absence of nested variation within the bHLH gene and invariant association of loss of function of bHLH among the kabuli type, we conclude that the kabuli form arose multiple times during the phase of phenotypic diversification after initial domestication of cultivated chickpea

Origin and Evolution of Saturn's Ring System

The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini Division, B, C), the F Ring, and the diffuse rings (E and G). During the Voyager era, models of evolutionary processes affecting the rings on long time scales (erosion, viscous spreading, accretion, ballistic transport, etc.) had suggested that Saturn's rings are not older than 100 My. In addition, Saturn's large system of diffuse rings has been thought to be the result of material loss from one or more of Saturn's satellites. In the Cassini era, high spatial and spectral resolution data have allowed progress to be made on some of these questions. Discoveries such as the ''propellers'' in the A ring, the shape of ring-embedded moonlets, the clumps in the F Ring, and Enceladus' plume provide new constraints on evolutionary processes in Saturn's rings. At the same time, advances in numerical simulations over the last 20 years have opened the way to realistic models of the rings's fine scale structure, and progress in our understanding of the formation of the Solar System provides a better-defined historical context in which to understand ring formation. All these elements have important implications for the origin and long-term evolution of Saturn's rings. They strengthen the idea that Saturn's rings are very dynamical and rapidly evolving, while new arguments suggest that the rings could be older than previously believed, provided that they are regularly renewed. Key evolutionary processes, timescales and possible scenarios for the rings's origin are reviewed in the light of tComment: Chapter 17 of the book ''Saturn After Cassini-Huygens'' Saturn from Cassini-Huygens, Dougherty, M.K.; Esposito, L.W.; Krimigis, S.M. (Ed.) (2009) 537-57