The eigenvalue problem for the ∞-Bilaplacian

We consider the problem of finding and describing minimisers of the Rayleigh quotient Λ∞:=infu∈W2,∞(Ω)∖{0}∥Δu∥L∞(Ω)∥u∥L∞(Ω), Λ∞:=infu∈W2,∞(Ω)∖{0}‖Δu‖L∞(Ω)‖u‖L∞(Ω), where Ω⊆RnΩ⊆Rn is a bounded C1,1C1,1 domain and W2,∞(Ω)W2,∞(Ω) is a class of weakly twice differentiable functions satisfying either u=0u=0 on ∂Ω∂Ω or u=|Du|=0u=|Du|=0 on ∂Ω∂Ω . Our first main result, obtained through approximation by LpLp -problems as p→∞p→∞ , is the existence of a minimiser u∞∈W2,∞(Ω)u∞∈W2,∞(Ω) satisfying {Δu∞∈Λ∞Sgn(f∞)Δf∞=μ∞ a.e. in Ω, in D′(Ω), {Δu∞∈Λ∞Sgn(f∞) a.e. in Ω,Δf∞=μ∞ in D′(Ω), for some f∞∈L1(Ω)∩BVloc(Ω)f∞∈L1(Ω)∩BVloc(Ω) and a measure μ∞∈M(Ω)μ∞∈M(Ω) , for either choice of boundary conditions. Here Sgn is the multi-valued sign function. We also study the dependence of the eigenvalue Λ∞Λ∞ on the domain, establishing the validity of a Faber–Krahn type inequality: among all C1,1C1,1 domains with fixed measure, the ball is a strict minimiser of Ω↦Λ∞(Ω)Ω↦Λ∞(Ω) . This result is shown to hold true for either choice of boundary conditions and in every dimension

Modal analysis of holey fiber mode-selective couplers

Mode Division Multiplexing is currently investigated as a possible way to increase fiber system capacity. With this approach, different modes of the same fiber carry distinct information. One of the problems to be solved in these systems concerns coupling/decoupling of the various modes to/from the same fiber. In this presentation, the mode features of a mode mux/demux based on holey fibers are investigated, with particular emphasis on optimal device design. Some preliminary experimental results will also be presented

Sex Dimorphism of Nonalcoholic Fatty Liver Disease (NAFLD) in Pparg-Null Mice.

Men with nonalcoholic fatty liver disease (NAFLD) are more exposed to nonalcoholic steatohepatitis (NASH) and liver fibrosis than women. However, the underlying molecular mechanisms of NALFD sex dimorphism are unclear. We combined gene expression, histological and lipidomic analyses to systematically compare male and female liver steatosis. We characterized hepatosteatosis in three independent mouse models of NAFLD, ob/ob and lipodystrophic fat-specific (PpargF <sup>Δ/Δ</sup> ) and whole-body PPARγ-null (Pparg <sup>Δ/Δ</sup> ) mice. We identified a clear sex dimorphism occurring only in Pparg <sup>Δ/Δ</sup> mice, with females showing macro- and microvesicular hepatosteatosis throughout their entire life, while males had fewer lipid droplets starting from 20 weeks. This sex dimorphism in hepatosteatosis was lost in gonadectomized Pparg <sup>Δ/Δ</sup> mice. Lipidomics revealed hepatic accumulation of short and highly saturated TGs in females, while TGs were enriched in long and unsaturated hydrocarbon chains in males. Strikingly, sex-biased genes were particularly perturbed in both sexes, affecting lipid metabolism, drug metabolism, inflammatory and cellular stress response pathways. Most importantly, we found that the expression of key sex-biased genes was severely affected in all the NAFLD models we tested. Thus, hepatosteatosis strongly affects hepatic sex-biased gene expression. With NAFLD increasing in prevalence, this emphasizes the urgent need to specifically address the consequences of this deregulation in humans

Intestinal PPARγ signalling is required for sympathetic nervous system activation in response to caloric restriction.

Nuclear receptor PPARγ has been proven to affect metabolism in multiple tissues, and has received considerable attention for its involvement in colon cancer and inflammatory disease. However, its role in intestinal metabolism has been largely ignored. To investigate this potential aspect of PPARγ function, we submitted intestinal epithelium-specific PPARγ knockout mice (iePPARγKO) to a two-week period of 25% caloric restriction (CR), following which iePPARγKO mice retained more fat than their wild type littermates. In attempting to explain this discrepancy, we analysed the liver, skeletal muscle, intestinal lipid trafficking, and the microbiome, none of which appeared to contribute to the adiposity phenotype. Interestingly, under conditions of CR, iePPARγKO mice failed to activate their sympathetic nervous system (SNS) and increase CR-specific locomotor activity. These KO mice also manifested a defective control of their body temperature, which was overly reduced. Furthermore, the white adipose tissue of iePPARγKO CR mice showed lower levels of both hormone-sensitive lipase, and its phosphorylated form. This would result from impaired SNS signalling and possibly cause reduced lipolysis. We conclude that intestinal epithelium PPARγ plays an essential role in increasing SNS activity under CR conditions, thereby contributing to energy mobilization during metabolically stressful episodes

A chemotaxonomic investigation on Vitis vinifera L. II. Comparison among ssp. sativa traditional cultivars and wild biotypes of ssp. silvestris from various Italian regions

An extensive screening on regional representatives of Vitis vinifera ssp. sativa and silvestris was carried out to look for relationships and differences between different taxa. Total proteins in the pH range 4.0-5.5, and the enzymes AcP, ADH, EST, G-6-PDH, MDH, PGM and POD were recorded. Only patterns of storage protein subunits, AcP, EST and G-6-PDH were taxonomically informative. Dendrograms were computerized on the basis of presence/absence of individual bands; these always distinguish at different levels in homogeneous groups between ssp. sativa and ssp. silvestris. The acidic subunits showed a dichotomy from the first branching of the cladogram. These observations are a demonstration that neither hypotheses of direct or indirect origin of the Italian ssp. sativa from Italian ssp. silvestris via domestication is tenanble. The authors suggest that, the morphological, the ecological and the biochemical differences between the two taxa support the hypothesis that V. sativa and V. silvestris should be regarded as two separate taxa that have had reciprocal interactions such a long period of time that a precise location of origin is no longer possible