Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in \F_{p^m}[x] of degree $d$ over the finite field \F_{p^m}, one can view it as a map from \F_{p^m} to \F_{p^m}, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}

The critical group of the Kneser graph on 22-subsets of an nn-element set

In this paper we compute the critical group of the Kneser graph $KG(n,2)$. This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph.Comment: 16 pages, minor change

Incommensurate chirality density wave transition in a hybrid molecular framework

Using single-crystal X-ray diffraction we characterise the 235\,K incommensurate phase transition in the hybrid molecular framework tetraethylammonium silver(I) dicyanoargentate, [NEt$_4$]Ag$_3$(CN)$_4$. We demonstrate the transition to involve spontaneous resolution of chiral [NEt$_4$]$^+$ conformations, giving rise to a state in which molecular chirality is incommensurately modulated throughout the crystal lattice. We refer to this state as an incommensurate chirality density wave (XDW) phase, which represents a fundamentally new type of chiral symmetry breaking in the solid state. Drawing on parallels to the incommensurate ferroelectric transition of NaNO$_2$ we suggest the XDW state arises through coupling between acoustic (shear) and molecular rotoinversion modes. Such coupling is symmetry-forbidden at the Brillouin zone centre but symmetry-allowed for small but finite modulation vectors $\mathbf q=[0,0,q_z]^\ast$. The importance of long-wavelength chirality modulations in the physics of this hybrid framework may have implications for the generation of mesoscale chiral textures, as required for advanced photonic materials.Comment: 5 pages, 3 figure

Postgraduate Medical Trainees at a Ugandan University Perceive Their Clinical Learning Environment Positively but Differentially Despite Challenging Circumstances: A Cross-sectional Study

Purpose The clinical learning environment is an essential component in health professions’ education. Data are scant on how postgraduate trainees in sub-Saharan Africa perceive their medical school learning environments, and how those perceptions contribute to their engagement during training, their emotional wellbeing, and career aspirations. This study examined perceptions of postgraduate medical trainees (residents) in a resource-limited setting, regarding their learning environment and explored perceptual contributions to their career engagement during training. The data reported contribute to understanding how clinical learning environments can be improved in low-resource settings in Uganda and elsewhere. Methods This study was done at the Faculty of Medicine of Mbarara University of Science and Technology in Uganda. We used a descriptive cross-sectional design involving sequential mixed methods. Quantitative data were collected using the Postgraduate Hospital Educational Environment Measure (PHEEM). Qualitative data were collected using focus group discussions. Results Ninety of the 113 eligible residents responded (79.6%). Of these, 62 (68.9%) were males, 51 (56.7%) were third-year trainees, and the majority (40%) of the residents were aged between 30 and 34 years. Overall PHEEM scored 98.22 ± 38.09; Role Autonomy scored 34.25 ± 13.69, Teaching scored 39.7 ± 13.81, and Social Support scored 24.27 ± 10.59. Gender differences occurred in the perceptions of teaching and social support. Cronbach’s alpha coefficient was 0.94 for the overall PHEEM. Five major themes were identified from the qualitative data (trainee support, supervision environment, engagement with overall learning environment, preparation for future practice, and challenges that impede training). Conclusions Overall, this study suggests that postgraduate trainees at the institution perceived the clinical learning environment positively amidst challenges of limited resources. Trainees’ insights provided data that propose improvements on a number of domains in the learning environment

The behavioral immune system: Current concerns and future directions

The behavioral immune system is a motivational system that helps minimize infection risk by changing cognition, affect, and behavior in ways that promote pathogen avoidance. In the current paper, we review foundational concepts of the behavioral immune system and provide a brief summary of recent social psychological research on this topic. Next, we highlight current conceptual and empirical limitations of this work and delineate important questions that have the potential to drive major advances in the field. These questions include predicting the ontological development of the behavioral immune system, specifying the relationship between this system and the physiological immune system, and distinguishing conditions that elicit direct effects of situational pathogen threats versus effects that occur only in interaction with dispositional disease concerns. This discussion highlights significant challenges and underexplored topics to be addressed by the next generation of behavioral immune system research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142457/1/spc312371.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142457/2/spc312371_am.pd

Dwarf Galaxy Dark Matter Density Profiles Inferred from Stellar and Gas Kinematics

We present new constraints on the density profiles of dark matter (DM) halos in seven nearby dwarf galaxies from measurements of their integrated stellar light and gas kinematics. The gas kinematics of low mass galaxies frequently suggest that they contain constant density DM cores, while N-body simulations instead predict a cuspy profile. We present a data set of high resolution integral field spectroscopy on seven galaxies and measure the stellar and gas kinematics simultaneously. Using Jeans modeling on our full sample, we examine whether gas kinematics in general produce shallower density profiles than are derived from the stars. Although 2/7 galaxies show some localized differences in their rotation curves between the two tracers, estimates of the central logarithmic slope of the DM density profile, gamma, are generally robust. The mean and standard deviation of the logarithmic slope for the population are gamma=0.67+/-0.10 when measured in the stars and gamma=0.58+/-0.24 when measured in the gas. We also find that the halos are not under concentrated at the radii of half their maximum velocities. Finally, we search for correlations of the DM density profile with stellar velocity anisotropy and other baryonic properties. Two popular mechanisms to explain cored DM halos are an exotic DM component or feedback models that strongly couple the energy of supernovae into repeatedly driving out gas and dynamically heating the DM halos. We investigate correlations that may eventually be used to test models. We do not find a secondary parameter that strongly correlates with the central DM density slope, but we do find some weak correlations. Determining the importance of these correlations will require further model developments and larger observational samples. (Abridged)Comment: 29 pages, 18 figures, 10 tables, accepted for publication in Ap

Mass production of volume phase holographic gratings for the VIRUS spectrograph array

The Visible Integral-field Replicable Unit Spectrograph (VIRUS) is a baseline array of 150 copies of a simple, fiber-fed integral field spectrograph that will be deployed on the Hobby-Eberly Telescope (HET). VIRUS is the first optical astronomical instrument to be replicated on an industrial scale, and represents a relatively inexpensive solution for carrying out large-area spectroscopic surveys, such as the HET Dark Energy Experiment (HETDEX). Each spectrograph contains a volume phase holographic (VPH) grating with a 138 mm diameter clear aperture as its dispersing element. The instrument utilizes the grating in first-order for 350-550 nm. Including witness samples, a suite of 170 VPH gratings has been mass produced for VIRUS. Here, we present the design of the VIRUS VPH gratings and a discussion of their mass production. We additionally present the design and functionality of a custom apparatus that has been used to rapidly test the first-order diffraction efficiency of the gratings for various discrete wavelengths within the VIRUS spectral range. This device has been used to perform both in-situ tests to monitor the effects of adjustments to the production prescription as well as to carry out the final acceptance tests of the gratings' diffraction efficiency. Finally, we present the as-built performance results for the entire suite of VPH gratings.Comment: 16 pages, 11 figures, 2 tables. To be published in Proc. SPIE, 2014, "Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation", 9151-53. The work presented in this article follows from arXiv:1207:448

Fruit and vegetable knowledge and intake within an Australian population: The ausdiab study

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Understanding the relationship between fruit and vegetable knowledge (FVK) and fruit and vegetable intake (FVI) is an important consideration for improved public health and successful targeting of health promotion messaging. The aim of this study was to investigate the association between FVK and FVI in Australian adults and to identify subgroups most at risk of poor knowledge. Using data from the Australian Diabetes, Obesity, and Lifestyle Study (AusDiab), we investigated associations between FVK and FVI, as well as demographic and lifestyle factors. Baseline FVK was measured using two self-reported questions. FVI was assessed using a validated, self-reported, food frequency questionnaire in 1999/00 (baseline), 2004/05, and 2011/12. Amongst the 8966 participants assessed at baseline, 24.1% had adequate, 73.0% had insufficient, and 2.9% had poor FVK. Using linear regression, those with insufficient or poor FVK reported significantly lower FVI (grams/day) compared to those with adequate FVK: baseline (coefficient (95%CI)): −67.1 (−80.0, −54.3) and −124.0 (−142.9, −105.1), respectively, whilst, at 12 years, the differences were −42.5 (−54.6, −30.5) and −94.6 (−133.8, −55.5) grams/day, respectively (all p \u3c 0.001). Poor FVK was more likely to be reported in males, older individuals (\u3e65 years), socio-economically disadvantaged, smokers, and those with insufficient physical activity/sedentary behavior. We demonstrate that having adequate knowledge of FVI, defined as knowing to consume fruit and vegetables several times a day for a well-balanced diet, is strongly associated with FVI, with several demographic and lifestyle factors predicting FVK. Health promotion messages aimed at increasing FVK should target these subgroups for maximal effect

4D Constructions of Supersymmetric Extra Dimensions and Gaugino Mediation

We present 4D gauge theories which at low energies coincide with higher dimensional supersymmetric (SUSY) gauge theories on a transverse lattice. We show that in the simplest case of pure 5D SUSY Yang-Mills there is an enhancement of SUSY in the continuum limit without fine-tuning. This result no longer holds in the presence of matter fields, in which case fine-tuning is necessary to ensure higher dimensional Lorentz invariance and supersymmetry. We use this construction to generate 4D models which mimic gaugino mediation of SUSY breaking. The way supersymmetry breaking is mediated in these models to the MSSM is by assuming that the physical gauginos are a mixture of a number of gauge eigenstate gauginos: one of these couples to the SUSY breaking sector, while another couples to the MSSM matter fields. The lattice can be as coarse as just two gauge groups while still obtaining the characteristic gaugino-mediated soft breaking terms.Comment: 32 pages LaTeX; missing factor in two-loop gauge-mediated scalar mass estimate fixed, comments on unification revise