Donaldson-Thomas invariants and wall-crossing formulas

Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie

Effect of annealing treatments on the anisotropy of a magnesium alloy sheet processed by severe rolling

The effect of annealing treatments on the normal plastic anisotropy (r-value) of a magnesium alloy, AZ61, processed by severe rolling was investigated. The various annealing treatments produce two effects on microstructure: grain coarsening and slight weakening of the texture. In addition, these treatments produce a noticeable decrease of the anisotropy that was correlated with an increase in strain rate sensitivity and a decrease of work hardening rate. It is concluded that an enhanced contribution of basal slip occurs as a consequence of the annealing treatments.The authors acknowledge the financial support from the CICYT grant MAT 2006-02672 awarded by the Spanish Ministry of Education and Science.Peer reviewe

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Renal phenotype of Et-1 transgenic mice is modulated by androgens

<p>Abstract</p> <p>Introduction</p> <p>Activation of the endothelin (ET) system promotes inflammation and fibrosis in various tissues including the kidney. Male ET-1 transgenic mice are characterized by chronic kidney inflammation and renal scarring. We hypothesized that this renal phenotype might be modulated by androgens. Thus the aim of our study was to elucidate the impact of gonadectomy in ET-1 transgenic mice on kidney function and morphology.</p> <p>Methods</p> <p>Male ET-1 transgenic mice at the age of 10 weeks were randomly allocated to the following groups: normal ET transgenic mice (ET; n = 17) and ET transgenic mice that underwent castration (ET+cas; n = 12). Study duration was 9 months. Creatinine clearance and protein excretion was monitored. At study end animals were sacrificed and kidneys were harvested for histology/immunhistochemistry.</p> <p>Results</p> <p>Castration significantly ameliorated glomerulosclerosis in ET-1 transgenic mice (ET glomerulosclerosis-score: 3.0 ± 0.17 vs ET+cas: 2.4 ± 0.17; p < 0.05) as well as renal perivascular fibrosis (ET fibrosis-score: 3.0 ± 0.14 vs ET+cas: 2.2 ± 0.14; p < 0.05). However, interstitial fibrosis and media/lumenratio of renal arteries remained unaffected by castration. Regarding inflammation, castration significantly reduced the number of CD4-positive cells in renal tissue of ET-1 transgenic mice (ET CD4-positive cells/10000 cells: 355 ± 72 vs ET+cas: 147 ± 28; p < 0.05). Renal tissue contents of CD8 positive cells as well as of macrophages were not affected by castration. Regarding kidney function castration significantly reduced proteinuria in ET-1 transgenic mice whereas creatinine clearance did not differ between study groups.</p> <p>Conclusion</p> <p>Our study demonstrates that the renal histopathological phenotype in male ET-1 transgenic mice with regard to glomerulosclerosis, proteinuria, perivascular fibrosis and immune cell immigration is ameliorated by castration. We thus conclude that the effects of ET-1 overexpression on renal tissue injury are modulated by androgens.</p

Spatting restricts ankle motion more effectively than taping during exercise

Ankle injuries, via plantarflexion (PF) and inversion, are commonplace today. To reduce ankle injuries, restrictive appliances such as taping and bracing have been employed. These appliances, however, have the disadvantage of potentially loosening considerably with mild activity. Spatting—applying tape over the shoe and sock—has been suggested as a viable alternative, yet its efficacy has not been researched widely. We examined the effects of taping or spatting the ankles on 17 men (age = 20.7 ± 2.1 years; height = 185.7 ± 5.7 cm; mass = 93.6 ± 16.2 kg) before, during, and after 60 minutes of exercise involving multi-directional activity. Active range of motion (ROM) for PF and inversion was measured via goniometry for each subject\u27s dominant leg to establish baseline values. ROM was measured after the appliances were applied, then following a five-minute warm-up period, and after each of three, 20-minute exercise periods. The subjects also completed a 5-item, 5-point Likert-type scale survey regarding their perceptions of each ankle appliance with respect to comfort, effectiveness, and protective ability. Separate, two-way ANOVAs with repeated measures were used to assess differences in PF and inversion ROM relative to time. A series of Wilcoxon tests were used to assess the Likert-type scale survey. In comparison to spatting, taping loosened by ~5° for PF at 40 minutes and by ~3° for inversion at 20 minutes (both significant interactions, p \u3c 0.01). Thus indicating that spatting is more restrictive than taping after 20 minutes of exercise. Interestingly, taping was perceived as more comfortable than spatting (Z = 2.03, p = 0.04); nonetheless, the perceived protection along with the perceived ability to move before, during, and after exercise was rated similarly between the appliances (p \u3e 0.05). Despite an advantage of restricting PF and inversion during exercise with spatting, it is not known if the loss of tape-skin contact underscores the potential benefits associated with the neuromuscular reactivity that have been reported with taping. Additional research is needed to clarify this issue