B\"acklund transformations for the rational Lagrange chain

We consider a long--range homogeneous chain where the local variables are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain'' showing how one can obtain it starting from $\mathfrak{su}(2)$ rational Gaudin models. Moreover we construct one- and two--point integrable maps (B\"acklund transformations).Comment: 12 page

Obesity, Diabetes, and Gut Microbiota: The hygiene hypothesis expanded?

The connection between gut microbiota and energy homeostasis and inflammation and its role in the pathogenesis of obesity-related disorders are increasingly recognized. Animals models of obesity connect an altered microbiota composition to the development of obesity, insulin resistance, and diabetes in the host through several mechanisms: increased energy harvest from the diet, altered fatty acid metabolism and composition in adipose tissue and liver, modulation of gut peptide YY and glucagon-like peptide (GLP)-1 secretion, activation of the lipopolysaccharide toll-like receptor-4 axis, and modulation of intestinal barrier integrity by GLP-2. Instrumental for gut microbiota manipulation is the understanding of mechanisms regulating gut microbiota composition. Several factors shape the gut microflora during infancy: mode of delivery, type of infant feeding, hospitalization, and prematurity. Furthermore, the key importance of antibiotic use and dietary nutrient composition are increasingly recognized. The role of the Western diet in promoting an obesogenic gut microbiota is being confirmation in subjects. Following encouraging results in animals, several short-term randomized controlled trials showed the benefit of prebiotics and probiotics on insulin sensitivity, inflammatory markers, postprandial incretins, and glucose tolerance. Future research is needed to unravel the hormonal, immunomodulatory, and metabolic mechanisms underlying microbe-microbe and microbiota-host interactions and the specific genes that determine the health benefit derived from probiotics. While awaiting further randomized trials assessing long-term safety and benefits on clinical end points, a healthy lifestyle—including breast lactation, appropriate antibiotic use, and the avoidance of excessive dietary fat intake—may ensure a friendly gut microbiota and positively affect prevention and treatment of metabolic disorders

An evolutionary model with Turing machines

The development of a large non-coding fraction in eukaryotic DNA and the phenomenon of the code-bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code can't be attained without maintaining a large inactive fraction. To test this hypothesis we performed computer simulations of an evolutionary toy model for Turing machines, studying the relations among fitness and coding/non-coding ratio while varying mutation and code growth rates. The results suggest that, in our model, having a large reservoir of non-coding states constitutes a great (long term) evolutionary advantage.Comment: 16 pages, 7 figure

Chronic kidney disease (CKD) and NAFLD: Time for awareness and screening

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