On computational complexity of Siegel Julia sets

It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.Comment: Updated version, to appear in Commun. Math. Phy

The Elimination of Low-Molecular-Weight Proteins in Patients with Isolated Acute Renal Failure

Objective: to study the effectiveness of some types of semipermeable dialysis membranes and replacement therapy techniques in patients with isolated acute renal failure (iARF). Subjects and methods: Eighty-nine patients aged 24 to 67 years, who received intensive and replacement/maintenance therapy, were examined. The patients were divided into 3 groups in accordance with their condition rated by the APACHE III scale, from the used dialysis membranes and renal replacement/maintenance therapy options. Results. By varying the permeability of a membrane, its area and the volume of convection, we can control the rate of substance elimination, which is similar to that of test markers having a molecular weight of 100 to 15000 Da. Conclusion. Adequate replacement therapy for iARF is possible only when high-flux, high-permeability dia-lyzers are applied. The indices of hemodialysis/hemodiafiltration adequacy in terms of urea cannot be determinants in patients with iARF. The achievement of elimination of low-molecular-weight proteins — markers of uremic intoxication to 30—35% and/or an increase in effective albumin concentrations as a summary marker of toxicity by 16—20% is of much more importance. Key words: isolated acute renal failure, uremic toxins, hemodialysis, hemodiafiltration

Warming Overcomes Dispersal-Limitation to Promote Non-native Expansion in Lake Baikal

Non-native species and climate change pose serious threats to global biodiversity. However, the roles of climate, dispersal, and competition are difficult to disentangle in heterogeneous landscapes. We combine empirical data and theory to examine how these forces influence the spread of non-native species in Lake Baikal. We analyze the potential for Daphnia longispina to establish in Lake Baikal, potentially threatening an endemic, cryophillic copepod Epischurella baikalensis. We collected field samples to establish current community composition and compared them to model predictions informed by flow rates, present-day temperatures, and temperature projections. Our data and model agree that expansion is currently limited by dispersal. However, projected increases in temperature reverse this effect, allowing D. longispina to establish in Lake Baikal’s main basin. A strong negative impact emerges from the interaction between climate change and dispersal, outweighing their independent effects. Climate, dispersal, and competition have complex, interactive effects on expansion with important implications for global biodiversity