Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [Masoller and Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes

Statistics of finite-time Lyapunov exponents in the Ulam map

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the calculation of the variance of exponents computed over time intervals of length $n$. The variance anomalously decays as $1/n^2$. The probability density of finite-time exponents noticeably deviates from the Gaussian shape, decaying with exponential tails and presenting $2^{n-1}$ spikes that narrow and accumulate close to the mean value with increasing $n$. The asymptotic expression for this probability distribution function is derived. It provides an adequate smooth approximation to describe numerical histograms built for not too small $n$, where the finiteness of bin size trimmes the sharp peaks.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Invasion genetics of the Pacific oyster Crassostrea gigas in the British Isles inferred from microsatellite and mitochondrial markers

The Pacific oyster, Crassostrea gigas, native to northeast Asia, is one of the most important cultured shellfish species. In Europe, Pacific oysters first settled along the Atlantic coasts of France at the end of the 1960s but rapidly spread and are now widely established. Twenty-two sites in the United Kingdom (UK), Ireland, Denmark, France and Spain were sampled to assess genetic diversity and differentiation. Hatchery-propagated stocks from two hatcheries located in the UK also were included. Two main genetic clusters were identified from pairwise genetic differentiation indexes, Bayesian clustering methods or neighbour-joining analysis, based on 7 microsatellite loci: (1) a Northeast cluster (including feral samples from East England, Ireland and Denmark as well as UK hatchery stocks) and (2) a Southwest cluster (including samples from South Wales, South West England, France and Spain). The Southwest cluster had significantly higher allelic richness (A) and expected heterozygosity (He) (A: 45.68, He: 0.928) than in the Northeast (A: 26.58, He: 0.883); the two diverging by a small but significant FST value (FST=0.017, 95% CI: 0.014-0.021). A 739-bp fragment of the major noncoding region of the mitochondrial genome was sequenced in 248 oysters from 12 of the studied samples in Europe and in 25 oysters from Miyagi prefecture (Japan). A total of 81 haplotypes were found. Haplotype frequency analyses identified the same two clusters observed using microsatellites. This study highlights how the number and size of introduction events, aquaculture practices, genetic bottlenecks followed by genetic drift and natural dispersal can act concurrently to shape the genetic diversity and structure of introduced populations

Modulation of peritoneal macrophage activity by the saturation state of the fatty acid moiety of phosphatidylcholine

To determine the effects of saturated and unsaturated fatty acids in phosphatidylcholine (PC) on macrophage activity, peritoneal lavage cells were cultured in the presence of phosphatidylcholine rich in saturated or unsaturated fatty acids (sat PC and unsat PC, respectively), both used at concentrations of 32 and 64 µM. The treatment of peritoneal macrophages with 64 µM unsat PC increased the production of hydrogen peroxide by 48.3% compared to control (148.3 ± 16.3 vs 100.0 ± 1.8%, N = 15), and both doses of unsat PC increased adhesion capacity by nearly 50%. Moreover, 64 µM unsat PC decreased neutral red uptake by lysosomes by 32.5% compared to the untreated group (67.5 ± 6.8 vs 100.0 ± 5.5%, N = 15), while both 32 and 64 µM unsat PC decreased the production of lipopolysaccharide-elicited nitric oxide by 30.4% (13.5 ± 2.6 vs 19.4 ± 2.5 µM) and 46.4% (10.4 ± 3.1 vs 19.4 ± 2.5 µM), respectively. Unsat PC did not affect anion production in non-stimulated cells or phagocytosis of unopsonized zymosan particles. A different result pattern was obtained for macrophages treated with sat PC. Phorbol 12-miristate 13-acetate-elicited superoxide production and neutral red uptake were decreased by nearly 25% by 32 and 64 µM sat PC, respectively. Sat PC did not affect nitric oxide or hydrogen peroxide production, adhesion capacity or zymosan phagocytosis. Thus, PC modifies macrophage activity, but this effect depends on cell activation state, fatty acid saturation and esterification to PC molecule and PC concentration. Taken together, these results indicate that the fatty acid moiety of PC modulates macrophage activity and, consequently, is likely to affect immune system regulation in vivo.Fundação Araucári