Positivity of Chern Classes for Reflexive Sheaves on P^N

It is well known that the Chern classes $c_i$ of a rank $n$ vector bundle on \PP^N, generated by global sections, are non-negative if $i\leq n$ and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers $c_i$ with $i\geq 4$ can be arbitrarily negative for reflexive sheaves of any rank; on the contrary for $i\leq 3$ we show positivity of the $c_i$ with weaker hypothesis. We obtain lower bounds for $c_1$, $c_2$ and $c_3$ for every reflexive sheaf \FF which is generated by H^0\FF on some non-empty open subset and completely classify sheaves for which either of them reach the minimum allowed, or some value close to it.Comment: 16 pages, no figure

Conchoidal transform of two plane curves

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in \PP^2 \times \PP^2. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng., Commun. Comput

Documenting and modeling the accretion of surface and subsoil organic carbon in agricultural Inceptisols reclaimed from Mediterranean sea marshes in Sardinia

High input agriculture in productive Inceptisols that were reclaimed from sea marshes offers an opportunity to study the increase of soil organic carbon (SOC) in soils with originally low SOC. We documented the current SOC content and its distribution with depth for several soil profiles

Rotation of Low-mass Stars in Taurus with K2

We present an analysis of K2 light curves (LCs) from Campaigns 4 and 13 for members of the young (~3 Myr) Taurus association, in addition to an older (~30 Myr) population of stars that is largely in the foreground of the Taurus molecular clouds. Out of 156 of the highest-confidence Taurus members, we find that 81% are periodic. Our sample of young foreground stars is biased and incomplete, but nearly all stars (37/38) are periodic. The overall distribution of rotation rates as a function of color (a proxy for mass) is similar to that found in other clusters: the slowest rotators are among the early M spectral types, with faster rotation toward both earlier FGK and later M types. The relationship between period and color/mass exhibited by older clusters such as the Pleiades is already in place by Taurus age. The foreground population has very few stars but is consistent with the USco and Pleiades period distributions. As found in other young clusters, stars with disks rotate on average slower, and few with disks are found rotating faster than ~2 days. The overall amplitude of the LCs decreases with age, and higher-mass stars have generally lower amplitudes than lower-mass stars. Stars with disks have on average larger amplitudes than stars without disks, though the physical mechanisms driving the variability and the resulting LC morphologies are also different between these two classes

Preventive Effect of Cow's Milk Fermented with Lactobacillus paracasei CBA L74 on Common Infectious Diseases in Children: A Multicenter Randomized Controlled Trial

Background: Fermented foods have been proposed to prevent common infectious diseases (CIDs) in children attending day care or preschool

Using the right words or using the words right? Re-conceptualizing Living Labs for systemic innovation in socio-ecological systems

Mediterranean rural systems, understood as socio-ecological systems (SES), often face complex sustainability challenges arising from the structural coupling of ecological and socioeconomic processes, climatic pressures, and weak adaptive capacities. Living labs are gradually gaining ground as an approach to tackling complex sustainability challenges. However, the existing literature is urban-focused and little attention has been paid to the implementation of living labs in rural contexts. This study fills this gap by addressing whether the increasingly popular living lab approach is suitable for pursuing systemic innovation for sustainable development in rural SES. Through a systematic review of the existing literature, this paper offers a contemporary perspective on living labs as models to support systemic innovation and governance of rural SES, while also accounting for previous interpretations of the concept. The paper then moves to a critical discussion of the main constraints on living lab conceptualisation and operationalisation and provides several recommendations for more effective and transparent use of living labs in rural SES. We argue that it is paramount to recognise living labs not solely as laboratories to validate techno-scientific solutions, but also as living systems that can be designed as social learning spaces to improve situations of complexity and uncertainty. In this sense, the success of living labs is contingent upon the willingness and capacity of both stakeholders and researchers to remain actively engaged in social learning and co-creation processes

Restricted Boltzmann Machines Propagators for Auxiliary Field Diffusion Monte Carlo

The auxiliary field diffusion Monte Carlo method uses imaginary-time projection techniques to accurately solve the ground-state wave function of atomic nuclei and infinite nuclear matter. In this work, we present a novel representation of the imaginary-time propagator based on restricted Boltzmann machines. We test its accuracy against the routinely employed Hubbard-Stratonovich transformations by evaluating ground-state energies and single-particle densities of selected light nuclei. This analysis paves the way for incorporating more realistic nuclear potentials in the auxiliary field diffusion Monte Carlo method, including isospin-dependent spin-orbit terms and cubic spin-isospin operators, which characterize accurate phenomenological and chiral effective field theory Hamiltonians.Comment: 8 pages, 3 figure

The Genome of the Toluene-Degrading Pseudomonas veronii Strain 1YdBTEX2 and Its Differential Gene Expression in Contaminated Sand.

The natural restoration of soils polluted by aromatic hydrocarbons such as benzene, toluene, ethylbenzene and m- and p-xylene (BTEX) may be accelerated by inoculation of specific biodegraders (bioaugmentation). Bioaugmentation mainly involves introducing bacteria that deploy their metabolic properties and adaptation potential to survive and propagate in the contaminated environment by degrading the pollutant. In order to better understand the adaptive response of cells during a transition to contaminated material, we analyzed here the genome and short-term (1 h) changes in genome-wide gene expression of the BTEX-degrading bacterium Pseudomonas veronii 1YdBTEX2 in non-sterile soil and liquid medium, both in presence or absence of toluene. We obtained a gapless genome sequence of P. veronii 1YdBTEX2 covering three individual replicons with a total size of 8 Mb, two of which are largely unrelated to current known bacterial replicons. One-hour exposure to toluene, both in soil and liquid, triggered massive transcription (up to 208-fold induction) of multiple gene clusters, such as toluene degradation pathway(s), chemotaxis and toluene efflux pumps. This clearly underlines their key role in the adaptive response to toluene. In comparison to liquid medium, cells in soil drastically changed expression of genes involved in membrane functioning (e.g., lipid composition, lipid metabolism, cell fatty acid synthesis), osmotic stress response (e.g., polyamine or trehalose synthesis, uptake of potassium) and putrescine metabolism, highlighting the immediate response mechanisms of P. veronii 1YdBTEX2 for successful establishment in polluted soil