The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

Determination of the photodisintegration reaction rates involving charged particles: systematical calculations and proposed measurements based on Extreme Light Infrastructure - Nuclear Physics (ELI-NP)

Photodisintegration reaction rates involving charged particles are of relevance to the p-process nucleosynthesis that aims at explaining the production of the stable neutron-deficient nuclides heavier than iron. In this study, the cross sections and astrophysical rates of (g,p) and (g,a) reactions for about 3000 target nuclei with 10<Z<100 ranging from stable to proton dripline nuclei are computed. To study the sensitivity of the calculations to the optical model potentials (OMPs), both the phenomenological Woods-Saxon and the microscopic folding OMPs are taken into account. The systematic comparisons show that the reaction rates, especially for the (g,a) reaction, are dramatically influenced by the OMPs. Thus the better determination of the OMP is crucial to reduce the uncertainties of the photodisintegration reaction rates involving charged particles. Meanwhile, a gamma-beam facility at ELI-NP is being developed, which will open new opportunities to experimentally study the photodisintegration reactions of astrophysics interest. Considering both the important reactions identified by the nucleosynthesis studies and the purpose of complementing the experimental results for the reactions involving p-nuclei, the measurements of six (g,p) and eight (g,a) reactions based on the gamma-beam facility at ELI-NP and the ELISSA detector for the charged particles detection are proposed, and the GEANT4 simulations are correspondingly performed. The minimum required energies of the gamma-beam to measure these reactions are estimated. It is shown that the direct measurements of these photonuclear reactions within the Gamow windows at T_9=2.5 for p-process are fairly feasible and promising at ELI-NP. The expected experimental results will be used to constrain the OMPs of the charged particles, which can eventually reduce the uncertainties of the reaction rates for the p-process nucleosynthesis.Comment: 14 pages, 8 figures, Phys. Rev. C accepte

Morbilliviruses in aquatic mammals: report on round table discussion.

A workshop was organised to ascertain the current situation with regard to morbillivirus infections in aquatic animals. The great interest generated by the discovery of these new virus infections in 1988 has to some extent abated but much high quality research has continued in this field as the workshop showed. There is some serological evidence that the viruses have continued to circulate in most areas since the initial epizootics. As to their origin, it appears that the most likely source of the European seal morbillivirus (PDV-1) is the North Atlantic and Artic seal populations. As to the origin of the Mediterranean dolphin morbillivirus and the morbilliviruses isolated from porpoises, there is serological evidence that the viruses are widespread in many cetacean species in the Atlantic and 93% of long-finned pilot whales (Globicephala melas) which mass stranded between 1982 and 1993 were morbillivirus seropositive. The epizootic in freshwater seals in Lake Baikal was unrelated to events in the European marine mammal populations. The virus which infected these animals (PDV-2) is indistinguishable from canine distemper field strains. Serological and molecular biological studies provided evidence for the presence of the virus in the seals, at least as late as the Summer of 1992 when the animals were last sampled

Detecting QTLs and putative candidate genes involved in budbreak and flowering time in an apple multiparental population

UMR AGAP - équipe AFEF - Architecture et fonctionnement des espèces fruitièresIn temperate trees, growth resumption in spring time results from chilling and heat requirements, and is an adaptive trait under global warming. Here, the genetic determinism of budbreak and flowering time was deciphered using five related full-sib apple families. Both traits were observed over 3 years and two sites and expressed in calendar and degree-days. Best linear unbiased predictors of genotypic effect or interaction with climatic year were extracted from mixed linear models and used for quantitative trait locus (QTL) mapping, performed with an integrated genetic map containing 6849 single nucleotide polymorphisms (SNPs), grouped into haplotypes, and with a Bayesian pedigree-based analysis. Four major regions, on linkage group (LG) 7, LG10, LG12, and LG9, the latter being the most stable across families, sites, and years, explained 5.6–21.3% of trait variance. Co-localizations for traits in calendar days or growing degree hours (GDH) suggested common genetic determinism for chilling and heating requirements. Homologs of two major flowering genes, AGL24 and FT, were predicted close to LG9 and LG12 QTLs, respectively, whereas Dormancy Associated MADs-box (DAM) genes were near additional QTLs on LG8 and LG15. This suggests that chilling perception mechanisms could be common among perennial and annual plants. Progenitors with favorable alleles depending on trait and LG were identified and could benefit new breeding strategies for apple adaptation to temperature increase

Emerging and recurring diseases in cetaceans worldwide and the role of environmental stressors. Scientific Committee Document SC/60/DW5, International Whaling Commission, June 2008, Santiago, Chile

Emerging and recurring infectious diseases known or suspected to have the potential to significantly impact cetacean populations, and possible synergistic effects of environmental factors are reviewed. Cetacean morbilliviruses and papillomaviruses and brucellosis may affect population densities through high mortality rates or interference with reproduction. Evidence is available for the role of environmental factors in the emergence/recurrence and severity of at least six infectious conditions i.e. lobomycosis, toxoplasmosis, tattoo skin disease, generalized bacterial infections, miscellaneous skin diseases and morbillivirus epizootics. Other micro-parasites of potential importance include rhabdo-, herpes- and parainfluenza-viruses as well as Helicobacter spp., Streptococcus spp., Salmonella spp. and Mycobacterium marinum. The population impact and aetiology of newly emerging skin diseases in South America are unknown and represent a cause of concern