Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Lateralization of cognitive functions after stroke in childhood

A child's brain shows a remarkable ability to recover from adverse events such as stroke. Language functions recover particularly well, while visuo-spatial skills are more affected by brain damage, regardless of its localization. This study investigated the lateralization of language and visual search after childhood stroke.

A differential concentration-dependent effect of IVIg on neutrophil functions: relevance for anti-microbial and anti-inflammatory mechanisms

Background Polymorphonuclear neutrophils (PMN) play a key role in host defences against invading microorganisms but can also potentiate detrimental inflammatory reactions in case of excessive or misdirected responses. Intravenous immunoglobulins (IVIg) are used to treat patients with immune deficiencies and, at higher doses, in autoimmune, allergic and systemic inflammatory disorders. Methodology/Principal Findings We used flow cytometry to examine the effects of IVIg on PMN functions and survival, using whole-blood conditions in order to avoid artifacts due to isolation procedures. IVIg at low concentrations induced PMN activation, as reflected by decreased L-selectin and increased CD11b expression at the PMN surface, oxidative burst enhancement, and prolonged cell survival. In contrast, IVIg at higher concentrations inhibited LPS-induced CD11b degranulation and oxidative burst priming, and counteracted LPS-induced PMN lifespan prolongation. Conclusions/Significance IVIg appears to have differential, concentration-dependent effects on PMN, possibly supporting the use of IVIg as either an anti-microbial or an anti-inflammatory agent.

CX3CR1 defines functionally distinct intestinal mononuclear phagocyte subsets which maintain their respective functions during homeostatic and inflammatory conditions

Intestinal mononuclear phagocytes (iMNP) are critically involved in mucosal immunity and tissue homeostasis. Two major non-overlapping populations of iMNP have been identified in mice. CD103(+) iMNP represent a migratory population capable of inducing tolerogenic responses, whereas CX3CR1(+) iMNP are resident cells with disease-promoting potential. CX3CR1(+) iMNP can further be subdivided based on differential expression of CX3CR1. Using CX3CR1(GFP/+) ×RAG2(-/-) mice, we demonstrate that CX3CR1(hi) and CX3CR1(lo) iMNP clearly differ with respect to their morphological and functional properties. Compared with CX3CR1(hi) iMNP, CX3CR1(lo) iMNP are polarised towards pro-inflammatory responses already under homeostatic conditions. During a CD4(+) T-cell-induced colitis, CX3CR1(lo) cells accumulate in the inflamed mucosa and upregulate the expression of pro-inflammatory cytokines and triggering receptor expressed on myeloid cells-1 (TREM-1). In contrast, CX3CR1(hi) iMNP retain their non-inflammatory profile even during intestinal inflammation. These findings identify two functionally distinct iMNP subsets based on differential expression of CX3CR1 and indicate an unanticipated stability of iMNP.