Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets

In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation $$\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,$$ where $K$ is a p.c.f. set and $\Delta$ its Laplacian given by a regular harmonic structure. In particular, we prove the existence of nontangential limits of the corresponding Poisson integrals, and the analogous results of the classical Fatou theorems for bounded and nontangentially bounded harmonic functions.Comment: 22 page

Transition from Diffusive to Localized Regimes in Surface Corrugated Optical Waveguides

Exact calculations of the transmittance of surface corrugated optical waveguides are presented. The elastic scattering of diffuse light or other electromagnetic waves from a rough surface induces a diffusive transport along the waveguide axis. As the length of the corrugated part of the waveguide increases, a transition from the diffusive to the localized regime is observed. This involves an analogy with electron conduction in nanowires, and hence, a concept analogous to that of ``resistance'' can be introduced. We show an oscillatory behavior of both the elastic mean free path and the localization length versus the wavelength.Comment: 3 pages, REVTEX, 3 PS figure

Hypocholesterolemic and Hepatoprotective Effects of “Triguero” Asparagus from Andalusia in Rats Fed a High Cholesterol Diet

The cultivated species of the wild autochthonous Asparagus officinalis in Andalusia in Spain is commonly called “triguero” asparagus. This vegetable has traditionally been very much appreciated for its organoleptic and nutritional characteristics. This study has been designed to evaluate the potential effect of different concentrations of freeze-dried asparagus (500, 250, and 125 mg/Kg of body weight/day) on oxidative status and lipid profile in rats fed a cholesterol-rich diet. After five weeks of treatment, doses of 250 and 500 mg/Kg of asparagus were able to significantly reduce total cholesterol and LDL cholesterol levels. Atherogenic index was also significantly reduced in a dose-dependent manner by administrating freeze-dried asparagus. A beneficial effect was observed in the HDL cholesterol levels in asparagus-fed groups although the increase was not significant. Consumption of asparagus also improved antioxidant status, assayed superoxide dismutase (SOD) and catalase (CAT) enzymes, and protected against lipid peroxidation. These results show that the intake of green asparagus from Andalusia (Spain) helps to regulate plasma lipid levels and prevents oxidative damage in hypercholesterolemic conditions

Global field observations of tree die-off reveal hotter-drought fingerprint for Earth’s forests

Earth's forests face grave challenges in the Anthropocene, including hotter droughts increasingly associated with widespread forest die-off events. But despite the vital importance of forests to global ecosystem services, their fates in a warming world remain highly uncertain. Lacking is quantitative determination of commonality in climate anomalies associated with pulses of tree mortality-from published, field-documented mortality events-required for understanding the role of extreme climate events in overall global tree die-off patterns. Here we established a geo-referenced global database documenting climate-induced mortality events spanning all tree-supporting biomes and continents, from 154 peer-reviewed studies since 1970. Our analysis quantifies a global "hotter-drought fingerprint" from these tree-mortality sites-effectively a hotter and drier climate signal for tree mortality-across 675 locations encompassing 1,303 plots. Frequency of these observed mortality-year climate conditions strongly increases nonlinearly under projected warming. Our database also provides initial footing for further community-developed, quantitative, ground-based monitoring of global tree mortality

Snap evaporation of droplets on smooth topographies

Droplet evaporation on solid surfaces is important in many applications including printing, micro-patterning and cooling. While seemingly simple, the configuration of evaporating droplets on solids is difficult to predict and control. This is because evaporation typically proceeds as a “stick-slip” sequence—a combination of pinning and de-pinning events dominated by static friction or “pinning”, caused by microscopic surface roughness. Here we show how smooth, pinning-free, solid surfaces of non-planar topography promote a different process called snap evaporation. During snap evaporation a droplet follows a reproducible sequence of configurations, consisting of a quasi-static phase-change controlled by mass diffusion interrupted by out-of-equilibrium snaps. Snaps are triggered by bifurcations of the equilibrium droplet shape mediated by the underlying non-planar solid. Because the evolution of droplets during snap evaporation is controlled by a smooth topography, and not by surface roughness, our ideas can inspire programmable surfaces that manage liquids in heat- and mass-transfer applications

Quantum Conductance in Semimetallic Bismuth Nanocontacts

Electronic transport properties of bismuth nanocontacts are analyzed by means of a low temperature scanning tunneling microscope. The subquantum steps observed in the conductance versus elongation curves give evidence of atomic rearrangements in the contact. The underlying quantum nature of the conductance reveals itself through peaks in the conductance histograms. The shape of the conductance curves at 77 K is well described by a simple gliding mechanism for the contact evolution during elongation. The strikingly different behaviour at 4 K suggests a charge carrier transition from light to heavy ones as the contact cross section becomes sufficiently small.Comment: 5 pages including 4 figures. Accepted for publication in Phys. Rev. Let