Modular symbols and Hecke operators

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.Comment: 11 pp, 2 figures, uses psfrag.st

A modified operation for Hirschsprung's disease: Posterior longitudinal anorectal split with a “heart-shaped” anastomosis

A variety of complications can arise after the definitive pull-through operation for Hirschsprung's disease. Among these are constipation and soiling, which may be due to mismanagement of the internal anal sphincter. In order to prevent these complications, we developed an improved operative procedure based on preservation of the anterior anorectum that utilizes a posterior longitudinal split with an oblique anastomosis. Forty patients underwent this procedure over a 4-year period; adequate follow-up was obtained in 34 cases. Mean age at operation was 13 months (range 3 months to 7 years). A primary pull-through without a colostomy was performed in 38 of the 40 patients. The results showed excellent preservation of function, with a mean follow-up of 5 years and 7 months. There was no occurrence of spastic stenosis of the internal sphincter, no incontinence, and minimal constipation or soiling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47153/1/383_2004_Article_BF00178428.pd

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Recurrence after laparoscopic and open Nissen fundoplication

Background: Laparoscopic Nissen fundoplication as treatment for gastroesophageal reflux disease (GERD) in adults has a reported recurrence rate of 2–17%. We investigated the rates and mechanisms of failure after laparoscopic Nissen fundoplication in children. Methods: All patients who underwent a laparoscopic Nissen fundoplication for GERD and who subsequently required a redo Nissen were reviewed ( n = 15). The control group consisted of the most recent 15 patients who developed recurrent GER after an open Nissen, fundoplication. Results: Between 1994 and 2000, laparoscopic Nissen fundoplication was performed in 179 patients. Fifteen patients (8.7%) underwent revision. The mechanisms of failure were herniation in four patients, wrap dehiscence in four, a too-short wrap in three, a loosened wrap in two, and other reasons in two. The reoperation was performed laparoscopically in five patients (33%). The failure mechanisms were different in the open patients: eight were due to slipped wraps; three to dehiscences; and two to herniations. Conclusion: The failure rate after laparoscopic Nissen is acceptably low. A redo laparoscopic Nissen can be performed safely after an initial laparoscopic approach.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41361/1/464_2002_Article_8515.pd

Mesoscopic phase separation in La2CuO4.02 - a 139La NQR study

In crystals of La2CuO4.02 oxygen diffusion can be limited to such small length scales, that the resulting phase separation is invisible for neutrons. Decomposition of the 139La NQR spectra shows the existence of three different regions, of which one orders antiferromagnetically below 17K concomitantly with the onset of a weak superconductivity in the crystal. These regions are compared to the macroscopic phases seen previously in the title compound and the cluster-glass and striped phases reported for the underdoped Sr-doped cuprates.Comment: 4 pages, RevTeX, 5 figures, to be published in PR

Multipolar Interactions in the Anderson Lattice with Orbital Degeneracy

Microscopic investigation is performed for intersite multipolar interactions in the orbitally degenerate Anderson lattice, with CeB$_6$ taken as an exemplary target. In addition to the $f^0$ intermediate state, $f^2$ Hund's-rule ground states are included as intermediate states for the interactions. The conduction-band states are taken as plane waves and the hybridization as spherically symmetric. The spatial dependences of multipolar interactions are given by the relative weight of partial wave components along the pair of sites. It is clarified how the the anisotropy arises in the interactions depending on the orbital degeneracy and the spatial configuration. The stability of the $\Gamma_5$ antiferro-quadrupole order in the phase II of CeB$_6$ is consistent with our model. Moreover, the pseudo-dipole interactions follow a tendency required by the phenomenological model for the phase III.Comment: 30 pages, 4 figure

Charged Particle Production in Proton-, Deuteron-, Oxygen- and Sulphur-Nucleus Collisions at 200 GeV per Nucleon

The transverse momentum and rapidity distributions of net protons and negatively charged hadrons have been measured for minimum bias proton-nucleus and deuteron-gold interactions, as well as central oxygen-gold and sulphur-nucleus collisions at 200 GeV per nucleon. The rapidity density of net protons at midrapidity in central nucleus-nucleus collisions increases both with target mass for sulphur projectiles and with the projectile mass for a gold target. The shape of the rapidity distributions of net protons forward of midrapidity for d+Au and central S+Au collisions is similar. The average rapidity loss is larger than 2 units of rapidity for reactions with the gold target. The transverse momentum spectra of net protons for all reactions can be described by a thermal distribution with `temperatures' between 145 +- 11 MeV (p+S interactions) and 244 +- 43 MeV (central S+Au collisions). The multiplicity of negatively charged hadrons increases with the mass of the colliding system. The shape of the transverse momentum spectra of negatively charged hadrons changes from minimum bias p+p and p+S interactions to p+Au and central nucleus-nucleus collisions. The mean transverse momentum is almost constant in the vicinity of midrapidity and shows little variation with the target and projectile masses. The average number of produced negatively charged hadrons per participant baryon increases slightly from p+p, p+A to central S+S,Ag collisions.Comment: 47 pages, submitted to Z. Phys.

Transgenic Mice for a Tamoxifen-Induced, Conditional Expression of the Cre Recombinase in Osteoclasts

Background: Studies on osteoclasts, the bone resorbing cells, have remained limited due to the lack of transgenic mice allowing the conditional knockout of genes in osteoclasts at any time during development or adulthood. Methodology/Principal Finding: We report here on the generation of transgenic mice which specifically express a tamoxifen-inducible Cre recombinase in osteoclasts. These mice, generated on C57BL/6 and FVB background, express a fusion Cre recombinase-ERT2 protein whose expression is driven by the promoter of cathepsin K (CtsK), a gene highly expressed in osteoclasts. We tested the cellular specificity of Cre activity in CtsKCreERT2 strains by breeding with Rosa26LacZ reporter mice. PCR and histological analyses of the CtsKCreERT2LacZ positive adult mice and E17.5 embryos show that Cre activity is restricted largely to bone tissue. In vitro, primary osteoclasts derived from the bone marrow of CtsKCreERT2+/2LacZ+/2 adult mice show a Cre-dependent b-galactosidase activity after tamoxifen stimulation