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

Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems

The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one of us is elucidated with the help of examples, using the geometry of shear transformations and rotations. For non-interacting particles in a magnetic field, there are several ways to derive the result (even at non-zero temperature), including standard linear response theory. Arguments for the quantization, and the robustness of Hall viscosity to small changes in the Hamiltonian that preserve rotational invariance, are given. Numerical calculations of adiabatic transport are performed to check the predictions for quantum Hall systems, with excellent agreement for trial states. The coefficient of k^4 in the static structure factor is also considered, and shown to be exactly related to the orbital spin and robust to perturbations in rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry; some other improvements; no change in result

Two successful natural pregnancies in a patient with severe uterine prolapse: A case report

<p>Abstract</p> <p>Introduction</p> <p>Uterine prolapse is a common gynecologic condition that is rare during or before pregnancy. We report an exceptional case of two pregnancies in a totally prolapsed uterus.</p> <p>Case presentation</p> <p>A 36-year-old Caucasian woman with a history of uterine prolapse presented with pregnancy. A vaginal pessary was applied to keep her uterus inside the pelvis after manual reposition. The pessary was removed at the 24th week. The gravid uterus persisted in the abdominal cavity because of its increased volume.</p> <p>Conclusion</p> <p>Our case shows that pregnancy during uterine prolapse is possible and that careful assessment is required to prevent complications during delivery. According to our experience, an elective caesarean section near term could be the safest mode of delivery.</p

Analytic representations with theta functions for systems on ℤ(d) and on .

yesAn analytic representation with Theta functions on a torus, for systems with variables in ℤ(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied

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

The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

Generalized Involution Models for Wreath Products

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gelfand model for wreath products of the form $A \wr S_n$ with $A$ abelian, and give an alternate proof of a recent result due to Adin, Postnikov, and Roichman describing a particularly elegant Gelfand model for the wreath product \ZZ_r \wr S_n. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Roichman, and Postnikov's.Comment: 29 page

Bladder neck mobility in continent nulliparous women

To evaluate the mobility of the vesical neck during coughing and valsalva in healthy nulliparous volunteers and to test the reliability of the technique applied. Design Clinical observational study. Setting Department of Obstetrics and Gynaecology, Cantonal Hospital Lucerne, Switzerland. Population Thirty-nine nulliparous volunteers. Methods Vesical neck motion was assessed with perineal ultrasound. Intra–abdominal pressure was controlled for with an intrarectal probe. Intra-rater reliability was evaluated. Results Vesical neck mobility was significantly lower during coughing (8 mm, SD 4 mm) than during valsalva (15 mm, SD 10 mm) ( P < 0.005 ). Between individuals mobility varied from 4 mm to 32 mm during coughing and from 2 mm to 31 mm during valsalva. Test-retest-studies showed a maximum difference between to tests during coughing of 4 mm and during valsalva of 5 mm. Conclusion The bladder neck is mobile in normal continent women and bladder neck mobility is lower during coughing than during Valsalva.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74987/1/j.1471-0528.2001.00066.x.pd