A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred. This paper presents another method, different from [7] and [8], to determine the sigh (unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones with odd order in the non-cyclic index 4 case. And we note that the method in this paper are more succinct and effective than [8] and [7]

Properties of dense partially random graphs

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small World Graphs (SWGs). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWGs, which are sparse). This allows us to calculate the mean distance and clustering, that are qualitatively similar (although not in such a dramatic scale range) to the case of SWGs. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review

Quantifying the prediction accuracy of a 1-D SVAT model at a range of ecosystems in the USA and Australia: evidence towards its use as a tool to study Earth's system interactions

This paper describes the validation of the SimSphere SVAT (Soil–Vegetation–Atmosphere Transfer) model conducted at a range of US and Australian ecosystem types. Specific focus was given to examining the models' ability in predicting shortwave incoming solar radiation (Rg), net radiation (Rnet), latent heat (LE), sensible heat (H), air temperature at 1.3 m (Tair 1.3 m) and air temperature at 50 m (Tair 50 m). Model predictions were compared against corresponding in situ measurements acquired for a total of 72 selected days of the year 2011 obtained from eight sites belonging to the AmeriFlux (USA) and OzFlux (Australia) monitoring networks. Selected sites were representative of a variety of environmental, biome and climatic conditions, to allow for the inclusion of contrasting conditions in the model evaluation. Overall, results showed a good agreement between the model predictions and the in situ measurements, particularly so for the Rg, Rnet, Tair 1.3 m and Tair 50 m parameters. The simulated Rg parameter exhibited a root mean square deviation (RMSD) within 25 % of the observed fluxes for 58 of the 72 selected days, whereas an RMSD within ~ 24 % of the observed fluxes was reported for the Rnet parameter for all days of study (RMSD = 58.69 W m−2). A systematic underestimation of Rg and Rnet (mean bias error (MBE) = −19.48 and −16.46 W m−2) was also found. Simulations for the Tair 1.3 m and Tair 50 m showed good agreement with the in situ observations, exhibiting RMSDs of 3.23 and 3.77 °C (within ~ 15 and ~ 18 % of the observed) for all days of analysis, respectively. Comparable, yet slightly less satisfactory simulation accuracies were exhibited for the H and LE parameters (RMSDs = 38.47 and 55.06 W m−2, ~ 34 and ~ 28 % of the observed). Highest simulation accuracies were obtained for the open woodland savannah and mulga woodland sites for most of the compared parameters. The Nash–Sutcliffe efficiency index for all parameters ranges from 0.720 to 0.998, suggesting a very good model representation of the observations. To our knowledge, this study presents the most detailed evaluation of SimSphere done so far, and the first validation of it conducted in Australian ecosystem types. Findings are important and timely, given the expanding use of the model both as an educational and research tool today. This includes ongoing research by different space agencies examining its synergistic use with Earth observation data towards the development of global operational products

Quantum Theory and Galois Fields

We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one. The paper has been prepared as a presentation to the ICSSUR' 2005 conference (Besancon, France, May 2-6, 2005).Comment: Latex, 24 pages, 1 figur

Associations between e-cigarette access and smoking and drinking behaviours in teenagers

Background: Public health concerns regarding e-cigarettes and debate on appropriate regulatory responses are focusing on the need to prevent child access to these devices. However, little is currently known about the characteristics of those young people that are accessing e-cigarettes. Methods: Using a cross-sectional survey of 14-17 year old school students in North West England (n = 16,193) we examined associations between e-cigarette access and demographics, conventional smoking behaviours, alcohol consumption, and methods of accessing cigarettes and alcohol. Access to e-cigarettes was identified through a question asking students if they had ever tried or purchased e-cigarettes. Results: One in five participants reported having accessed e-cigarettes (19.2%). Prevalence was highest among\ud smokers (rising to 75.8% in those smoking >5 per day), although 15.8% of teenagers that had accessed e-cigarettes had never smoked conventional cigarettes (v.13.6% being ex-smokers). E-cigarette access was independently associated with male gender, having parents/guardians that smoke and students’ alcohol use. Compared with non-drinkers, teenagers that drank alcohol at least weekly and binge drank were more likely to have accessed e-cigarettes (adjusted odds ratio [AOR] 1.89, P < 0.001), with this association particularly strong among never-smokers (AOR 4.59, P < 0.001). Among drinkers, e-cigarette access was related to: drinking to get drunk, alcohol-related violence, consumption of spirits; self-purchase of alcohol from shops or supermarkets; and accessing alcohol by recruiting adult proxy purchasers outside shops. Conclusions: There is an urgent need for controls on the promotion and sale of e-cigarettes to children. Findings suggest that e-cigarettes are being accessed by teenagers more for experimentation than smoking cessation. Those most likely to access e-cigarettes may already be familiar with illicit methods of accessing age-restricted substances

Abundances in intermediate-mass AGB stars undergoing third dredge-up and hot-bottom burning

High dispersion near-infrared spectra have been taken of seven highly-evolved, variable, intermediate-mass (4-6 Msun) AGB stars in the LMC and SMC in order to look for C, N and O variations that are expected to arise from third dredge-up and hot-bottom burning. The pulsation of the objects has been modelled, yielding stellar masses, and spectral synthesis calculations have been performed in order to derive abundances from the observed spectra. For two stars, abundances of C, N, O, Na, Al, Ti, Sc and Fe were derived and compared with the abundances predicted by detailed AGB models. Both stars show very large N enhancements and C deficiencies. These results provide the first observational confirmation of the long-predicted production of primary nitrogen by the combination of third dredge-up and hot-bottom burning in intermediate-mass AGB stars. It was not possible to derive abundances for the remaining five stars: three were too cool to model, while another two had strong shocks in their atmospheres which caused strong emission to fill the line cores and made abundance determination impossible. The latter occurrence allows us to predict the pulsation phase interval during which observations should be made if successful abundance analysis is to be possible.Comment: Accepted for publication in MNRA

Regulation and Regulatory Role of WNT Signaling in Potentiating FSH Action during Bovine Dominant Follicle Selection

Follicular development occurs in wave like patterns in monotocous species such as cattle and humans and is regulated by a complex interaction of gonadotropins with local intrafollicular regulatory molecules. To further elucidate potential mechanisms controlling dominant follicle selection, granulosa cell RNA harvested from F1 (largest) and F2 (second largest) follicles isolated at predeviation (PD) and onset of diameter deviation (OD) stages of the first follicular wave was subjected to preliminary RNA transcriptome analysis. Expression of numerous WNT system components was observed. Hence experiments were performed to test the hypothesis that WNT signaling modulates FSH action on granulosa cells during follicular waves. Abundance of mRNA for WNT pathway members was evaluated in granulosa cells harvested from follicles at emergence (EM), PD, OD and early dominance (ED) stages of the first follicular wave. In F1 follicles, abundance of CTNNB1 and DVL1 mRNAs was higher and AXIN2 mRNA was lower at ED versus EM stages and DVL1 and FZD6 mRNAs were higher and AXIN2mRNA was lower in F1 versus F2 follicle at the ED stage. Bovine granulosa cells were treated in vitro with increasing doses of the WNT inhibitor IWR-1+/− maximal stimulatory dose of FSH. IWR-1 treatment blocked the FSH-induced increase in granulosa cell numbers and reduced the FSH-induced increase in estradiol. Granulosa cells were also cultured in the presence or absence of FSH +/− IWR-1 and hormonal regulation of mRNA for WNT pathway members and known FSH targets determined. FSH treatment increased CYP19A1, CCND2, CTNNB1, AXIN2and FZD6 mRNAs and the stimulatory effect on CYP19A1 mRNA was reduced by IWR-1. In contrast, FSH reduced CARTPT mRNA and IWR-1 partially reversed the inhibitory effect of FSH. Results support temporal and hormonal regulation and a potential role for WNT signaling in potentiating FSH action during dominant follicle selection

Inhomogeneities in molecular layers of Mira atmospheres

We obtained K-band spectro-interferometric observations of the Miras R Cnc, X Hya, W Vel, and RW Vel with a spectral resolution of 1500 using the VLTI/AMBER instrument. We obtained concurrent JHKL photometry using the the Mk II instrument at the SAAO. Our sources have wavelength-dependent visibility values that are consistent with earlier low-resolution AMBER observations of S Ori and with the predictions of dynamic model atmosphere series based on self-excited pulsation models. The wavelength-dependent UD diameters show a minimum near the near-continuum bandpass at 2.25 um. They increase by up to 30% toward the H2O band at 2.0 um and by up to 70% at the CO bandheads. The dynamic model atmosphere series show a consistent wavelength-dependence, and their parameters such as the visual phase, effective temperature, and distances are consistent with independent estimates. The closure phases have significantly wavelength-dependent non-zero values indicating deviations from point symmetry. For example, the R Cnc closure phase is 110 degr in the 2.0 um H2O band, corresponding for instance to an additional unresolved spot contributing 3% of the total flux at a separation of ~4 mas. Our observations are consistent with the predictions of the latest dynamic model atmosphere series based on self-excited pulsation models. The wavelength-dependent radius variations are interpreted as the effect of molecular layers. The wavelength-dependent closure phase values are indicative of deviations from point symmetry at all wavelengths, thus a complex non-spherical stratification of the extended atmosphere. In particular, the significant deviation from point symmetry in the H2O band is interpreted as a signature on large scales of inhomogeneities or clumps in the water vapor layer. The observed inhomogeneities might be caused by pulsation- and shock-induced chaotic motion in the extended atmosphere.Comment: 5 pages, 2 figures, accepted for publication as a Letter in Astronomy and Astrophysic

Principles And Practices Fostering Inclusive Excellence: Lessons From The Howard Hughes Medical Institute’s Capstone Institutions

Best-practices pedagogy in science, technology, engineering, and mathematics (STEM) aims for inclusive excellence that fosters student persistence. This paper describes principles of inclusivity across 11 primarily undergraduate institutions designated as Capstone Awardees in Howard Hughes Medical Institute’s (HHMI) 2012 competition. The Capstones represent a range of institutional missions, student profiles, and geographical locations. Each successfully directed activities toward persistence of STEM students, especially those from traditionally underrepresented groups, through a set of common elements: mentoring programs to build community; research experiences to strengthen scientific skill/identity; attention to quantitative skills; and outreach/bridge programs to broaden the student pool. This paper grounds these program elements in learning theory, emphasizing their essential principles with examples of how they were implemented within institutional contexts. We also describe common assessment approaches that in many cases informed programming and created traction for stakeholder buy-in. The lessons learned from our shared experiences in pursuit of inclusive excellence, including the resources housed on our companion website, can inform others’ efforts to increase access to and persistence in STEM in higher education