Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs

We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of "magical" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.Comment: 20 page

The Catalan butterfly monitoring scheme has the capacity to detect effects of modifying agricultural practices

Impacts of agricultural management practices on the receiving environment are seldom suitably assessed because environmental monitoring is costly. In this regard, data generated by already existing environmental survey networks (ESNs) may have sufficient capacity to detect effects. Here, we study the capacity of the Catalan butterfly monitoring scheme (CBMS) to detect differences in butterfly abundance due to changes in agricultural practices. As a model, we compared butterfly abundance across two landscape types according to agricultural intensification. A 2 km diameter buffer area was centered on the CBMS transect, the control group were transects located in areas where intensive agriculture represented <20% of the area; a treated group was simulated by selecting transects located in areas where intensive agriculture occupied an area over 40%. The Welch t‐test (α = 0.05 and 80% power) was used to compare butterfly abundance per section across landscape types. The capacity of the t‐test to detect changes in mean butterfly abundance, of 12 butterfly indicators relevant to farmland, was calculated annually and for 5‐, 10‐, and 15‐yr periods. Detection capacity of the t‐test depended mainly on butterfly data sample size and variability; difference in butterfly abundance was less important. The t‐test would be capable of detecting acceptably small population changes across years and sites. For instance, considering a 15‐yr period, it would be possible to detect a change in abundance below 10% of the multispecies indicators (all butterfly species, open habitat species, mobile species, and grassland indicators) and two single species (Lasiommata megera and Lycaena phlaeas). When comparisons were carried out within each year, the t‐test would only be capable of detecting a change below 30% for all butterfly species, mobile species, and L. megera. However, detection capacity rapidly improved with the addition of further years, and with 5 yr of monitoring, all indicators but Thymelicus acteon had a detection capacity below 30%. We therefore conclude that, from a statistical point of view, the CBMS data “as is” are sensitive enough for monitoring effects of changes in agricultural practices. It could be used, for instance, for the general surveillance of genetically modified crops.This work was partially supported by the Spanish Government‐funded project AGL2011‐23996 and a FI‐DGR scholarship to M. Lee from the Catalan Government

Fusarium Mycotoxins and Metabolites that Modulate Their Production

The genus Fusarium is a group of fungi producing several types of toxins with toxicological effect in both humans and animals. Such fungi are commonly found in soils so it can contaminate various types of crops, preferably cereals, leading to significant economic losses. Relative humidity, storage temperature and various handling in cereales increase the possibility of contamination by Fusarium toxins. Cereals naturally have secondary metabolites that may help attenuate contamination by these toxins, but it is necessary to know strategies and mechanisms that generate inactivation mycotoxins. This chapter reviews relevant information about cereal mycotoxin contamination, as well as the production of cereal secondary metabolites as a strategy to reduce the possibility of mycotoxin contamination

A Study of the Near-Ultraviolet Spectrum of Vega

UV, optical, and near-IR spectra of Vega have been combined to test our understanding of stellar atmospheric opacities, and to examine the possibility of constraining chemical abundances from low-resolution UV fluxes. We have carried out a detailed analysis assuming Local Thermodynamic Equilibrium (LTE) to identify the most important contributors to the UV continuous opacity: H, H$^{-}$, C I, and Si II. Our analysis also assumes that Vega is spherically symmetric and its atmosphere is well described with the plane parallel approximation. Comparing observations and computed fluxes we have been able to discriminate between two different flux scales that have been proposed, the IUE-INES and the HST scales, favoring the latter. The effective temperature and angular diameter derived from the analysis of observed optical and near-UV spectra are in very good agreement with previous determinations based on different techniques. The silicon abundance is poorly constrained by the UV observations of the continuum and strong lines, but the situation is more favorable for carbon and the abundances inferred from the UV continuum and optical absorption lines are in good agreement. Some spectral intervals in the UV spectrum of Vega that the calculations do not reproduce well are likely affected by deviations from LTE, but we conclude that our understanding of UV atmospheric opacities is fairly complete for early A-type stars.Comment: 13 pages, 9 figures, to be published in Ap

Supercharacters, Exponential Sums, and the Uncertainty Principle

The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases

Oxygen abundances in unevolved metal-poor stars from near-UV OH lines

We have performed a detailed oxygen abundance analysis of 23 metal-poor (-3.0<[Fe/H]<-0.3) unevolved halo stars and one giant through the OH bands in the near UV, using high-resolution echelle spectra. Oxygen is found to be overabundant with respect to iron in these stars, with the [O/Fe] ratio increasing from 0.6 to 1 between [Fe/H]=-1.5 and -3.0. The behavior of the oxygen overabundance with respect to [Fe/H] is similar to that seen in previous works based on OI IR triplet data (Abia and Rebolo 1989; Tomkin et al. 1992; Cavallo, Pilachowski, and Rebolo 1997). Contrary to the previously accepted picture, our oxygen abundances, derived from low-excitation OH lines, agree well with those derived from high-excitation lines of the triplet. For nine stars in common with Tomkin et al. we obtain a mean difference of 0.00+/-0.11 dex with respect to the abundances determined from the triplet using the same stellar parameters and model photospheres. For four stars in our sample we have found measurements of the [OI] 6300 A line in the literature, from which we derive oxygen abundances consistent (average difference 0.09 dex) with those based on OH lines, showing that the long standing controversy between oxygen abundances from forbidden and permitted lines in metal-poor unevolved stars can be resolved. Our new oxygen abundances show a smooth extension of the Edvardsson et al.'s (1993) [O/Fe] versus metallicity curve to much lower abundances, with a slope -0.31+/- 0.11 (taking into account the error bars in both oxygen abundances and metallicities) in the range -3<[Fe/H]<-1.Comment: 17 pages, 8 figures, 3 table

Spectroscopic Observations of Convective Patterns in the Atmospheres of Metal-Poor Stars

Convective line asymmetries in the optical spectrum of two metal-poor stars, Gmb1830 and HD140283, are compared to those observed for solar metallicity stars. The line bisectors of the most metal-poor star, the subgiant HD140283, show a significantly larger velocity span that the expectations for a solar-metallicity star of the same spectral type and luminosity class. The enhanced line asymmetries are interpreted as the signature of the lower metal content, and therefore opacity, in the convective photospheric patterns. These findings point out the importance of three-dimensional convective velocity fields in the interpretation of the observed line asymmetries in metal-poor stars, and in particular, urge for caution when deriving isotopic ratios from observed line shapes and shifts using one-dimensional model atmospheres. The mean line bisector of the photospheric atomic lines is compared with those measured for the strong Mg I b1 and b2 features. The upper part of the bisectors are similar, and assuming they overlap, the bottom end of the stronger lines, which are formed higher in the atmosphere, goes much further to the red. This is in agreement with the expected decreasing of the convective blue-shifts in upper atmospheric layers, and compatible with the high velocity redshifts observed in the chromosphere, transition region, and corona of late-type stars.Comment: 27 pages, LaTeX; 10 Figures (14 PostScript files); to be published in The Astrophysical Journa

Chronic kidney disease in Ecuador : an epidemiological and health system analysis of an emerging public health crisis

Funding: IT, AMSI, ML, SN, KB and RS were supported by a grant from Dialysis Clinic, Inc (DCI), award number 84232.The absence of a chronic kidney disease (CKD) registry in Ecuador makes it difficult to assess the burden of disease, but there is an anticipated increase in the incidence of CKD along with increasing diabetes, hypertension and population age. From 2012, augmented funding for renal replacement therapy expanded dialysis clinics and patient coverage. We conducted 73 in-depth sociological interviews with healthcare providers in eight provinces and collected quantitative epidemiological data on patients with CKD diagnoses from six national-level databases between 2015 and 2018. Datasets show a total of 17,484 dialysis patients in 2018, or 567 patients per million population (pmp), with an annual cost exceeding 11% of Ecuador’s public health budget. Each year, there were 139–162 pmp new dialysis patients, while doctors reported waiting lists. The number of patients on peritoneal dialysis was static; those on hemodialysis increased over time. Only 13 of 24 provinces were found to have dialysis services, and nephrologists were clustered in major cities, which limits access, delays medical attention, and adds a travel burden on patients. Prevention and screening programs are scarce, while hospitalization is an important reality for CKD patients. CKD is an emerging public health crisis that has increased dramatically over the last decade in Ecuador and is expected to continue, making coverage for all patients impossible and the current structure, unsustainable. A patient registry would help health policymakers and administrators estimate the demand and progression of patients with consideration for comorbidities, disease stage, requirements and costs, mortality and follow-up. This should be used to help identify where to focus prevention and improved treatment efforts. Organized monitoring of CKD patients would benefit from improvements in patient referral. Community-based education and prevention programs, the strengthening of primary healthcare capacity (including basic routine tests) and improved nephrology services are also urgently needed.Publisher PDFPeer reviewe