SQCD: A Geometric Apercu

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur

Interactions Among Western Corn Rootworm (Coleoptera: Chrysomelidae), Yellow Foxtail, and Corn

Field studies at sites with two contrasting soil types investigated effects from the presence of yellow foxtail [Setaria pumila (Poir.) Roem. and Schult.], established in bands parallel to corn rows, on western corn rootworm (Diabrotica virgifera virgifera LeConte) survival, corn root injury, lodging, biomass production, and yield. Results suggested that the presence of foxtail as an alternate host inßuenced the degree and progression of corn rootworm damage and adult emergence in a givenlocality. Rootworm adults emergedlater from foxtail band areas and had smaller head capsule size than did individuals from areas without foxtail, consistent with earlier Þndings that foxtail in the diet of western corn rootworm was a poor nutritional substitute for corn. Lodging was reduced in the presence of yellow foxtail in some cases, but corn stover biomass and yield also were lower. Inßuences, if any, of soil type on rootworm survival were unclear because of differences in planting date between the two sites. Foxtail may function as a buffer to reduce rootworm damage to corn and serves as an alternate host that should be considered in the development of resistance management strategies for transgenic corn modiÞed for rootworm resistance

Lung volume reduction reoperations

BACKGROUND: Optimal management of emphysematous patients who have lost the benefits achieved after lung volume reduction surgery is a clinical dilemma. We have hypothesized that in stringently selected instances, lung volume reduction reoperations might be considered as a salvage surgical treatment. We sought to analyze the results of a series of patients undergoing lung volume reduction reoperations after successful bilateral lung volume reduction surgery. METHODS: Between January 2000 and April 2006, 17 patients (mean age, 66 +/- 3 years) with radiologic evidence of distinct regional lung hyperinflation underwent lung volume reduction reoperations. Surgical procedures entailed completion lobectomy in 7 patients, nonanatomic resection of lung target areas were performed in 5 patients under general anesthesia with one-lung ventilation, and awake lung plication was performed in 5 patients under sole epidural anesthesia. Follow-up at 6 and 12 months was complete in all survivors. RESULTS: Mean operative time was 100 +/- 12 minutes. Two patients (11.7%) died perioperatively of adult respiratory distress syndrome. Hospital stay was 9 +/- 2 days. Significant improvements occurred for up to 12 months in forced expiratory volume in 1 second (FEV(1); p < 0.001), forced vital capacity (p < 0.002), residual volume (p < 0.001), 6-minute walk test (p < 0.001), and modified Medical Research Council dyspnea index (p < 0.001). At 6-months, improvements in FEV(1) were greater than 200 mL in 11 patients and correlated with the postoperative reduction in residual volume (r = -0.62, p = 0.01); baseline residual volume was inversely correlated with the degree of improvement in the dyspnea index (r = -0.54, p = 0.03). CONCLUSIONS: Lung volume reduction reoperations can offer significant clinical improvement to stringently selected patients who have lost the clinical benefit achieved after lung volume reduction surgery

Growth and Fecundity of Several Weed Species in Corn and Soybean

Do weeds that emerge later in the season justify additional control costs\u27? If crop yield is not reduced or few or no seeds arc added to the soil seed hank, then no control may he needed. Eight weed species were sown in corn (Zea mays L.) and soybean I Glycine max (L.) Mcrr.l (i) before crop emergence, (ii) at crop emergence, (iii) at V-1, and (iv) at V-2 stages of crop growth in 2002 and 2003. Weed seed was sown close to the crop row and thinned to 1.3 plants m 2• Weed growth and fecundity were influenced by species, time of planting, and year. Only barnyarclgrass (Echinochloa crus-galli L.), rcclroot pigwced (Amaranthus retniflexus L.), and vclvetlcaf (Abutilon theophrasti L.) survived to produce seed. Plants from the pre-emergence seeding had the largest canopy and produced the most seeds. Harnyardgrass had maximum canopy cover in early .July in corn and late .Inly in soybean hut only produced seed in corn. Rcclroot pigweecl and vclvctleaf had maximum canopy cover in late August or midSeptember, and some plants from most seeding elates survived and produced seed in both corn and soybean. However, plants that grew from seed sown at V-1 and V-2 crnp grnwth stages did not reduce yield or biomass of adjacent crop plants, had low fecundity, and may not warrant treatment. Control may be necessary, however, to prevent yield losses if weeds arc present at high densities or to prevent establishment of uncommon species

Scattering Amplitudes and Toric Geometry

In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of well defined finite objects called on-shell diagrams drawn on disks. Furthermore it has been shown that the physical information of on-shell diagrams is encoded in the geometry of auxiliary algebraic varieties called the totally non negative Grassmannians. In this new formulation the infinite dimensional symmetry of the theory is manifest and many results, that are quite tricky to obtain in terms of the standard Lagrangian formulation of the theory, are instead manifest. In this paper, elaborating on previous results, we provide another picture of the scattering amplitudes in terms of toric geometry. In particular we describe in detail the toric varieties associated to an on-shell diagram, how the singularities of the amplitudes are encoded in some subspaces of the toric variety, and how this picture maps onto the Grassmannian description. Eventually we discuss the action of cluster transformations on the toric varieties. The hope is to provide an alternative description of the scattering amplitudes that could contribute in the developing of this very interesting field of research.Comment: 58 pages, 25 figures, typos corrected, a reference added, to be published in JHE

Crop Species Diversity Changes in the United States: 1978-2012

Citation: Aguilar, J., Gramig, G. G., Hendrickson, J. R., Archer, D. W., Forcella, F., & Liebig, M. A. (2015). Crop Species Diversity Changes in the United States: 1978-2012. Plos One, 10(8), 14. doi:10.1371/journal.pone.0136580Anecdotal accounts regarding reduced US cropping system diversity have raised concerns about negative impacts of increasingly homogeneous cropping systems. However, formal analyses to document such changes are lacking. Using US Agriculture Census data, which are collected every five years, we quantified crop species diversity from 1978 to 2012, for the contiguous US on a county level basis. We used Shannon diversity indices expressed as effective number of crop species (ENCS) to quantify crop diversity. We then evaluated changes in county-level crop diversity both nationally and for each of the eight Farm Resource Regions developed by the National Agriculture Statistics Service. During the 34 years we considered in our analyses, both national and regional ENCS changed. Nationally, crop diversity was lower in 2012 than in 1978. However, our analyses also revealed interesting trends between and within different Resource Regions. Overall, the Heartland Resource Region had the lowest crop diversity whereas the Fruitful Rim and Northern Crescent had the highest. In contrast to the other Resource Regions, the Mississippi Portal had significantly higher crop diversity in 2012 than in 1978. Also, within regions there were differences between counties in crop diversity. Spatial autocorrelation revealed clustering of low and high ENCS and this trend became stronger over time. These results show that, nationally counties have been clustering into areas of either low diversity or high diversity. Moreover, a significant trend of more counties shifting to lower rather than to higher crop diversity was detected. The clustering and shifting demonstrates a trend toward crop diversity loss and attendant homogenization of agricultural production systems, which could have far-reaching consequences for provision of ecosystem system services associated with agricultural systems as well as food system sustainability

Influence of Yellow Foxtail on Corn Growth and Yield

Yellow foxtail [Setaria pumila syn. Setaria glauca (L.) Beauv.] competitive influence on corn (Zea mays L.) growth and yield was investigated at Brookings, South Dakota, and Morris, Minnesota, in 1995 and 1996. Yellow foxtail was seeded at different densities, and at Morris, two levels of nitrogen (N) were applied. Corn biomass measured at V‐6 or V‐8, silking, and harvest and grain yield were correlated negatively to foxtail biomass and density, but the loss differed between years and sites. Nitrogen increased corn growth and decreased yield loss. Defining a single foxtail density or biomass that resulted in a maximum yield loss of 10% was not possible. The most conservative estimate was 3 yellow foxtail plants m−2 or 24 g m−2 of yellow foxtail biomass, but ranged up to 55 plants m−2 and 256 g m−2 when weather conditions and N were optimal

New results for the SQCD Hilbert series

We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of unstable D-branes: expansions using Schur polynomials, and the log-gas approach related to random matrix theory.Comment: 33 pages, 2 figures; v2: references and comments on the 3rd order phase transition added; v3: refs. correcte

On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials

We study the algebraic and geometric structures that underly the space of vacua of N=1 super Yang-Mills theories at the non-perturbative level. Chiral operators are shown to satisfy polynomial equations over appropriate rings, and the phase structure of the theory can be elegantly described by the factorization of these polynomials into irreducible pieces. In particular, this idea yields a powerful method to analyse the possible smooth interpolations between different classical limits in the gauge theory. As an application in U(Nc) theories, we provide a simple and completely general proof of the fact that confining and Higgs vacua are in the same phase when fundamental flavors are present, by finding an irreducible polynomial equation satisfied by the glueball operator. We also derive the full phase diagram for the theory with one adjoint when Nc is less than or equal to 7 using computational algebraic geometry programs.Comment: 87 pages; v2: typos and eq. (4.44) correcte