The Forest City Landslide

A large and complex landslide in marine shales is impacting the approach roadway and a 4600-ft long bridge carrying U.S. Route 212 over the Oahe Reservoir at Forest City, South Dakota. After extensive investigation and analyses it was determined that the main landslide could be remediated by unloading the slide using a large cut through the escarpment located upslope from the bridge. Although moving with the main slide, the 900- foot long approach embankment is failing in directions differing from the main slide. Preliminary study indicates that the independent slides within the approach embankment can be stabilized by stone columns or reinforced concrete dowels. Partial remediation has been achieved by the installation of stone columns around the embankment toe

Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function

Zooming in on local level statistics by supersymmetric extension of free probability

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner-Efetov supersymmetry method of integration over commuting and anti-commuting variables. This insight leads to a potent new technique for the study of local statistics, e.g., level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section

Unitary designs and codes

A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a unitary code - a subset of U(d) in which the trace inner product of any pair of matrices is restricted to only a small number of distinct values - and give an upper bound for the size of a code of degree s in U(d) for any d and s. These bounds can be strengthened when the particular inner product values that occur in the code or design are known. Finally, we describe some constructions of designs: we give an upper bound on the size of the smallest weighted unitary t-design in U(d), and we catalogue some t-designs that arise from finite groups.Comment: 25 pages, no figure

Automorphic Instanton Partition Functions on Calabi-Yau Threefolds

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that whenever the low-energy theory in D=3 exhibits an arithmetic "U-duality" symmetry G(Z) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function can be realized as a holomorphic section on the twistor space Z over M. We also offer some comments on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra, Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201

Higgs Bundles, Gauge Theories and Quantum Groups

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed.Comment: 48 pages, typos corrected, one reference adde

Nifedipin ublažava djelovanje kokaina na enzimsku aktivnost u mozgu i jetri te smanjuje njegovo izlučivanje putem mokraće

The aim of this study was to see how nifedipine counters the effects of cocaine on hepatic and brain enzymatic activity in rats and whether it affects urinary excretion of cocaine. Male Wistar rats were divided in four groups of six: control, nifedipine group (5 mg kg-1 i.p. a day for five days); cocaine group (15 mg kg-1 i.p. a day for five days), and the nifedipine+cocaine group. Twenty-four hours after the last administration, we measured neuronal nitric oxide synthase (nNOS) activity in the brain and cytochrome P450 quantity, ethylmorphine-N-demethylase, and anilinehydroxylase activity in the liver. Urine samples were collected 24 h after the last cocaine and cocaine+nifedipine administration. Urinary cocaine concentration was determined using the GC/MS method. Cocaine administration increased brain nNOS activity by 55 % (p<0.05) in respect to control, which indicates the development of tolerance and dependence. In the combination group, nifedipine decreased the nNOS activity in respect to the cocaine-only group. In the liver, cocaine significantly decreased and nifedipine significantly increased cytochrome P450, ethylmorphine-N-demethylase, and anilinehydroxylase in respect to control. In combination, nifedipine successfully countered cocaine effects on these enzymes. Urine cocaine excretion in the cocaine+nifedipine group significantly dropped (by 35 %) compared to the cocaine-only group. Our results have confirmed the effects of nifedipine against cocaine tolerance and development of dependence, most likely due to metabolic interactions between them.Cilj je ovoga istraživanja bio utvrditi kako nifedipin ublažava djelovanje kokaina na enzimsku aktivnost u mozgu i jetri Wistar štakora te utječe li na njegovo izlučivanje putem mokraće. Mužjaci su podijeljeni u četiri skupine po šest jedinki: kontrolnu skupinu, nifedipinsku skupinu koja je pet dana intraperitonealno primala nifedipin u dozi od 5 mg kg-1; skupinu koja je pet dana primala kokain u dozi od 15 mg kg-1 na dan te skupinu koja je zajedno primala nifedipin i kokain u odgovarajućim dozama. Dvadeset i četiri sata nakon posljednje doze izmjerena je enzimska aktivnost sintaze dušičnoga oksida (nNOS) u mozgu, razina citokroma P450 te aktivnosti enzima etilmorfi n-N-demetilaze i anilinhidroksilaze u jetri štakora. Uzorci mokraće prikupljeni su 24 sata nakon posljednje doze kokaina odnosno kombinacije nifedipina i kokaina. Koncentracija kokaina u mokraći izmjerena je s pomoću vezanog sustava plinske kromatografi je i spektrometrije masa. Kokain je povećao aktivnost nNOS-a u mozgu za 55 % (p<0,05) u odnosu na kontrolnu skupinu, što upućuje na stvaranje tolerancije i ovisnosti. U kombiniranoj skupini nifedipin je značajno smanjio aktivnost nNOS-a u odnosu na skupinu koja je primila samo kokain. Kokain je značajno snizio, a nifedipin značajno povisio razinu citokroma P450 u jetri te aktivnost etilmorfi n-N-demetilaze i anilinhidroksilaze u odnosu na kontrolnu skupinu. U kombiniranoj skupini nifedipin je uspješno ublažio djelovanje kokaina na aktivnost spomenutih enzima. Izlučivanje kokaina putem mokraće u kombiniranoj skupini bilo je značajno manje (35 %) nego u skupini koja je primala samo kokain. Ovi rezultati potvrđuju da nifedipin štiti od djelovanja kokaina i stvaranja ovisnosti, najvjerojatnije zbog interakcija u metabolizmu dvaju spojeva

A multicenter prospective trial evaluating fetal bovine dermal graft (Xenform® Matrix) for pelvic reconstructive surgery

<p>Abstract</p> <p>Background</p> <p>A prospective multicenter clinical study was performed to evaluate the safety and efficacy of a bovine dermal graft (Xenform^®Matrix, Boston Scientific, Natick, MA, USA) during vaginal reconstructive surgery.</p> <p>Methods</p> <p>Forty-five women with ICS stage 2 or higher pelvic organ prolapse (POP) were enrolled at 4 centers. POP-Q, pelvic floor function (PFDI-20), sexual function (PISQ-12), and patient satisfaction tools were used to assess subjects at baseline, and at 2 and 6 weeks, and 3, 6 and 12 months post surgery. The significance of symptom score changes at 6 months and 1 year were determined by the t-test for paired data. Forty-three of the 45 patients completed the 12 month study.</p> <p>Results</p> <p>The majority of the subjects had cystocele (98%) and/or rectocele (84%) defects at study entry. At 12 months, 74% of the defects had improved to a stage 0 or 1. Mean PFDI-20 scores improved by 72% (p < 0.001) at 12 months, and PISQ-12 scores were maintained during the follow-up period indicating no decline in sexual function. Three subjects experienced one serious adverse event each; one of the adverse events (constipation) was deemed by the study physician to be unrelated to Xenform^®. One subject had severe pyelonephritis resulting in dialysis. This subject had a previous history of pyelonephritis, sepsis and acute renal failure. The third subject had a reported recurrent cystocele of moderate severity, possibly related to the device. No graft related erosions or pain lasting more than 30 days were reported. No subjects withdrew due to an adverse event.</p> <p>Conclusion</p> <p>This study is the first to investigate the use of Xenform^®Matrix in vaginal reconstructive surgery among patients with POP. Significant improvement was maintained at 12 months utilizing both objective and subjective assessment tools, confirming the safety and efficacy of this material in vaginal surgery.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov NCT01244165</p

Effect of cytisine on some brain and hepatic biochemical parameters in spontaneously hypertensive rats

Tobacco smoking is a risk factor for variety of cardio-vascular diseases, such as hypertension, myocardial infarction, stroke and many others. It is of great importance for hypertensive patients to stop smoking. One of the medicines widely used for smoking cessation in Bulgaria is the original Bulgarian product Tabex®, which is developed on the basis of natural plant alkaloid cytisine. The aim of the following study was to ivestigate the effects of cytisine on some brain and hepatic biochemical parameters in spontaneously hypertensive rats (SHR), an widely used rodent model for human essential hypertension, and to compare the obtained results with their age-matched normotensive controls Wistar Kyoto (WKY). Multiple cytisine administration did not affect the activity of ethylmorphine-N-demethylase (EMND) and anylinehydroxylase (AH), as well as the quantity of cytochrome P 450, nor in WKY neither in SHR In the liver cytisine increased the MDA quantity both in SHR and in WKY, by 25% (p<0.05) and by 29% (p<0.05) respectively, while the GSH level was not significantly changed by the compound in both strains. In contrast, on the brain level, cytisine administration to SHR caused more prominent toxicity, resulted in GSH depletion and increased MDA quantity, while in WKY strain did not exert any toxicity. Cytisine did not significantly affect ALAT and ASAT activity in both strains. In conclusion, the results of our study suggest higher brain toxicity of cytisine in spontaneously hypertensive rats, that might be due to their pathophysiological characteristics

A few remarks on colour-flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals

The Humboldt Foundation is acknowledged for the financial support of that visit. The research in Nottingham was supported by EPSRC grant EP/C515056/1 'Random Matrices and Polynomials: a tool to understand complexity'