Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

On the 2015 outburst of the EXor variable star V1118 Ori

After a long-lasting period of quiescence of about a decade, the source V1118 Ori, one of the most representative members of the EXor variables, is now outbursting. Since the initial increase of the near-infrared flux of about 1 mag (JHK bands) registered on 2015 September 22, the source brightness has remained fairly stable. We estimate DeltaV about 3 mag with respect to the quiescence phase. An optical/near-IR low-resolution spectrum has been obtained with the Large Binocular Telescope instruments MODS and LUCI2, and compared with a spectrum of similar spectral resolution and sensitivity level taken during quiescence. Together with the enhancement of the continuum, the outburst spectrum presents a definitely higher number of emission lines, in particular HI recombination lines of the Balmer, Paschen, and Brackett series, along with bright permitted lines of several species, forbidden atomic lines, and CO ro-vibrational lines. Both mass accretion and mass loss rates have significantly increased (by to about an order of magnitude, mass accretion rate = 1.2-4.8 10^-8 M_sun/yr, mass loss rate = 0.8-2 10^-9 M_sun/yr) with respect to the quiescence phase. If compared with previous outbursts, the present one appears less energetic. Alternatively, it could already be in the fading phase (with the maximum brightness level reached when the source was not visible), or, viceversa, still in the rising phase.Comment: Accepted ApJ Letter

GALNT2 as a novel modulator of adipogenesis and adipocyte insulin signaling

Background/objectives: A better understanding of adipose tissue biology is crucial to tackle insulin resistance and eventually coronary heart disease and diabetes, leading causes of morbidity and mortality worldwide. GALNT2, a GalNAc-transferase, positively modulates insulin signaling in human liver cells by down-regulating ENPP1, an insulin signaling inhibitor. GALNT2 expression is increased in adipose tissue of obese as compared to that of non-obese individuals. Whether this association is secondary to a GALNT2-insulin sensitizing effect exerted also in adipocytes is unknown. We then investigated in mouse 3T3-L1 adipocytes the GALNT2 effect on adipogenesis, insulin signaling and expression levels of both Enpp1 and 72 adipogenesis-related genes. Methods: Stable over-expressing GALNT2 and GFP preadipocytes (T 0 ) were generated. Adipogenesis was induced with (R+) or without (R−) rosiglitazone and investigated after 15 days (T 15 ). Lipid accumulation (by Oil Red-O staining) and intracellular triglycerides (by fluorimetric assay) were measured. Lipid droplets (LD) measures were analyzed at confocal microscope. Gene expression was assessed by RT-PCR and insulin-induced insulin receptor (IR), IRS1, JNK and AKT phosphorylation by Western blot. Results: Lipid accumulation, triglycerides and LD measures progressively increased from T 0 to T 15 R- and furthermore to T 15 R+. Such increases were significantly higher in GALNT2 than in GFP cells so that, as compared to T 15 R+GFP, T 15 R- GALNT2 cells showed similar (intracellular lipid and triglycerides accumulation) or even higher (LD measures, p < 0.01) values. In GALNT2 preadipocytes, insulin-induced IR, IRS1 and AKT activation was higher than that in GFP cells. GALNT2 effect was totally abolished during adipocyte maturation and completely reversed at late stage maturation. Such GALNT2 effect trajectory was paralleled by coordinated changes in the expression of Enpp1 and adipocyte-maturation key genes. Conclusions: GALNT2 is a novel modulator of adipogenesis and related cellular phenotypes, thus becoming a potential target for tackling the obesity epidemics and its devastating sequelae

Mechanically-based approach to non-local elasticity: Variational principles

AbstractThe mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Moreover, the Euler–Lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations. Numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approach