Basins of attraction for cascading maps

We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some of the attractors for such systems and prove general results about their basins of attraction. In particular, we show that the basins of attraction have infinitely many path components. We show that these components always accumulate at the corners of the domain of the system. For all threshold parameters above a certain value, we show that they accumulate at a Cantor set in the interior of the domain. For certain ranges of the threshold, we prove that the system has many attractors.Comment: 15 pages, 9 figures. To appear in International Journal of Bifurcations and Chao

Screening in Ionic Systems: Simulations for the Lebowitz Length

Simulations of the Lebowitz length, $\xi_{\text{L}}(T,\rho)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $\rho\lesssim 4\rho_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $\xi_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $\rho > {1/10}\rho_c$ (with $\rho_c a^3 \simeq 0.08$). At highe r densities $\xi_{\text{L}}$ rises above the Debye length, \xi_{\text{D}} \prop to \sqrt{T/\rho}, by 10-30% (upto $\rho\simeq 1.3\rho_c$); the variation is portrayed fairly well by generalized Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $\rho$ or fixed $T$, $\xi_{\text{L}}(T, \rho)$ remains finite with $\xi_{\text{L}}^c \simeq 0.30 a \simeq 1.3 \xi_{\text {D}}^c$ but displays a weak entropy-like singularity.Comment: 4 pages 5 figure

Effects of mammalian herbivore declines on plant communities: observations and experiments in an African savanna

1. Herbivores influence the structure and composition of terrestrial plant communities. However, responses of plant communities to herbivory are variable and depend on environmental conditions, herbivore identity and herbivore abundance. As anthropogenic impacts continue to drive large declines in wild herbivores, understanding the context dependence of herbivore impacts on plant communities becomes increasingly important. 2. Exclosure experiments are frequently used to assess how ecosystems reorganize in the face of large wild herbivore defaunation. Yet in many landscapes, declines in large wildlife are often accompanied by other anthropogenic activities, especially land conversion to livestock production. In such cases, exclosure experiments may not reflect typical outcomes of human-driven extirpations of wild herbivores. 3. Here, we examine how plant community responses to changes in the identity and abundance of large herbivores interact with abiotic factors (rainfall and soil properties). We also explore how effects of wild herbivores on plant communities differ between large-scale herbivore exclosures and landscape sites where anthropogenic activity has caused wildlife declines, often accompanied by livestock increases. 4. Abiotic context modulated the responses of plant communities to herbivore declines with stronger effect sizes in lower-productivity environments. Also, shifts in plant community structure, composition and species richness following wildlife declines differed considerably between exclosure experiments and landscape sites in which wild herbivores had declined and were often replaced by livestock. Plant communities in low wildlife landscape sites were distinct in both composition and physical structure from both exclosure and control sites in experiments. The power of environmental (soil and rainfall) gradients in influencing plant response to herbivores was also greatly dampened or absent in the landscape sites. One likely explanation for these observed differences is the compensatory effect of livestock associated with the depression or extirpation of wildlife. 5. Synthesis. Our results emphasize the importance of abiotic environmental heterogeneity in modulating the effects of mammalian herbivory on plant communities and the importance of such covariation in understanding effects of wild herbivore declines. They also suggest caution when extrapolating results from exclosure experiments to predict the consequences of defaunation as it proceeds in the Anthropocene

Galaxy Cluster Pressure Profiles as Determined by Sunyaev Zel'dovich Effect Observations with MUSTANG and Bolocam I: Joint Analysis Technique

We present a technique to constrain galaxy cluster pressure profiles by jointly fitting Sunyaev-Zel'dovich effect (SZE) data obtained with MUSTANG and Bolocam for the clusters Abell 1835 and MACS0647. Bolocam and MUSTANG probe different angular scales and are thus highly complementary. We find that the addition of the high resolution MUSTANG data can improve constraints on pressure profile parameters relative to those derived solely from Bolocam. In Abell 1835 and MACS0647, we find gNFW inner slopes of $\gamma = 0.36_{-0.21}^{+0.33}$ and $\gamma = 0.38_{-0.25}^{+0.20}$, respectively when $\alpha$ and $\beta$ are constrained to 0.86 and 4.67 respectively. The fitted SZE pressure profiles are in good agreement with X-ray derived pressure profiles.Comment: 12 pages, 12 figures. Submitted to Ap

Contractile force is enhanced in Aortas from pendrin null mice due to stimulation of angiotensin II-dependent signaling.

Pendrin is a Cl-/HCO3- exchanger expressed in the apical regions of renal intercalated cells. Following pendrin gene ablation, blood pressure falls, in part, from reduced renal NaCl absorption. We asked if pendrin is expressed in vascular tissue and if the lower blood pressure observed in pendrin null mice is accompanied by reduced vascular reactivity. Thus, the contractile responses to KCl and phenylephrine (PE) were examined in isometrically mounted thoracic aortas from wild-type and pendrin null mice. Although pendrin expression was not detected in the aorta, pendrin gene ablation changed contractile protein abundance and increased the maximal contractile response to PE when normalized to cross sectional area (CSA). However, the contractile sensitivity to this agent was unchanged. The increase in contractile force/cross sectional area observed in pendrin null mice was due to reduced cross sectional area of the aorta and not from increased contractile force per vessel. The pendrin-dependent increase in maximal contractile response was endothelium- and nitric oxide-independent and did not occur from changes in Ca2+ sensitivity or chronic changes in catecholamine production. However, application of 100 nM angiotensin II increased force/CSA more in aortas from pendrin null than from wild type mice. Moreover, angiotensin type 1 receptor inhibitor (candesartan) treatment in vivo eliminated the pendrin-dependent changes contractile protein abundance and changes in the contractile force/cross sectional area in response to PE. In conclusion, pendrin gene ablation increases aorta contractile force per cross sectional area in response to angiotensin II and PE due to stimulation of angiotensin type 1 receptor-dependent signaling. The angiotensin type 1 receptor-dependent increase in vascular reactivity may mitigate the fall in blood pressure observed with pendrin gene ablation