On the generalized Feng-Rao numbers of numerical semigroups generated by intervals

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $r^{th}$ Feng-Rao number is obtained.Comment: 23 pages, 6 figure

Ideal extensions of free commutative monoids

We introduce a new family of monoids, which we call gap absorbing monoids. Every gap absorbing monoid is an ideal extension of a free commutative monoid. For a gap absorbing monoid $S$ we study its set of atoms and Betti elements, which allows us to show that the catenary degree of $S$ is at most four and that the set of lengths of any element in $S$ is an interval. We also give bounds for the $\omega$-primality of any ideal extension of a free commutative monoid. For ideal extensions $S$ of $\mathbb{N}^d$, with $d$ a positive integer, we show that $\omega(S)$ is finite if and only if $S$ has finitely many gaps

The effects of land use and topographic changes on sediment connectivity in mountain catchments

Understanding the evolution of sediment connectivity associated with different land use and topographic changes is a prerequisite for a better understanding of sediment budgets and sediment transport processes. We used the Index of Sediment Connectivity (IC) developed by Cavalli et al. (2013) based on the original approach by Borselli et al. (2008) to study the effects of decadal-scale land use and topographic changes on sediment connectivity in mountain catchments. The input variables of the IC (i.e. land cover and topography) were derived from historical aerial photos using Structure from Motion-Multi View Stereo algorithms (SfM-MVS). The method was applied in different sub-catchments of the Upper River Cinca Catchment (Central Pyrenees), representative of three scenarios: (a) Land cover changes; (b) Topographic changes in agricultural fields (terracing); and (c) Topographic changes associated with infrastructure (road construction). In terms of land cover changes, results show that although connectivity is increased in some areas due to the establishment of new field crops, for most of the study area connectivity decreased due to afforestation caused by rural abandonment. Topographic changes due to the establishment of agricultural terraces affected connectivity to a larger degree than land cover changes. Terracing generally reduced connectivity due to the formation of flat areas in step-slopes, but in certain points, an increase in connectivity caused by the topographic convergence produced by terraces was observed. Finally, topographic changes associated with road construction greatly modified surface flow directions and the drainage network, resulting in changes in connectivity that may affect erosional processes nearby. The methodology used in this paper allows to study the effects of real decadal-scale land use and topographic changes on sediment connectivity and also evaluating and disentangling those changes. Furthermore, this approach can be a useful tool to identify potential risks associated with morphological and land use changes, involving road infrastructures

Calcium phosphate nanoparticles as intrinsic inorganic antimicrobials: In search of the key particle property

One of the main goals of materials science in the 21st century is the development of materials with rationally designed properties as substitutes for traditional pharmacotherapies. At the same time, there is a lack of understanding of the exact material properties that induce therapeutic effects in biological systems, which limits their rational optimization for the related medical applications. This study sets the foundation for a general approach for elucidating nanoparticle properties as determinants of antibacterial activity, with a particular focus on calcium phosphate nanoparticles. To that end, nine physicochemical effects were studied and a number of them were refuted, thus putting an end to frequently erred hypotheses in the literature. Rather than having one key particle property responsible for eliciting the antibacterial effect, a complex synergy of factors is shown to be at work, including (a) nanoscopic size; (b) elevated intracellular free calcium levels due to nanoparticle solubility; (c) diffusivity and favorable electrostatic properties of the nanoparticle surface, primarily low net charge and high charge density; and (d) the dynamics of perpetual exchange of ultrafine clusters across the particle/solution interface. On the positive side, this multifaceted mechanism is less prone to induce bacterial resistance to the therapy and can be a gateway to the sphere of personalized medicine. On a more problematic side, it implies a less intense effect compared to single-target molecular therapies and a difficulty of elucidating the exact mechanisms of action, while also making the rational design of theirs for this type of medical application a challenge

Fermi LAT Search for Photon Lines from 30 to 200 GeV and Dark Matter Implications

Dark matter (DM) particle annihilation or decay can produce monochromatic $\gamma$-rays readily distinguishable from astrophysical sources. $\gamma$-ray line limits from 30 GeV to 200 GeV obtained from 11 months of Fermi Large Area Space Telescope data from 20-300 GeV are presented using a selection based on requirements for a $\gamma$-ray line analysis, and integrated over most of the sky. We obtain $\gamma$-ray line flux upper limits in the range $0.6-4.5\times 10^{-9}\mathrm{cm}^{-2}\mathrm{s}^{-1}$, and give corresponding DM annihilation cross-section and decay lifetime limits. Theoretical implications are briefly discussed.Comment: 6 pages, 1 figure. Accepted for publication by The Physical Review Letter