On a problem of A. Weil

A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant is complete, i.e. the geodesic lamination can be recovered from the invariant. The continuous part of the invariant has geometric meaning of a slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

Consumer Bankruptcy Update

Materials from the Consumer Bankruptcy Update presentations held by UK/CLE in December 2000

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

The CHEK2 Variant C.349A>G Is Associated with Prostate Cancer Risk and Carriers Share a Common Ancestor.

The identification of recurrent founder variants in cancer predisposing genes may have important implications for implementing cost-effective targeted genetic screening strategies. In this study, we evaluated the prevalence and relative risk of the CHEK2 recurrent variant c.349A>G in a series of 462 Portuguese patients with early-onset and/or familial/hereditary prostate cancer (PrCa), as well as in the large multicentre PRACTICAL case-control study comprising 55,162 prostate cancer cases and 36,147 controls. Additionally, we investigated the potential shared ancestry of the carriers by performing identity-by-descent, haplotype and age estimation analyses using high-density SNP data from 70 variant carriers belonging to 11 different populations included in the PRACTICAL consortium. The CHEK2 missense variant c.349A>G was found significantly associated with an increased risk for PrCa (OR 1.9; 95% CI: 1.1-3.2). A shared haplotype flanking the variant in all carriers was identified, strongly suggesting a common founder of European origin. Additionally, using two independent statistical algorithms, implemented by DMLE+2.3 and ESTIAGE, we were able to estimate the age of the variant between 2300 and 3125 years. By extending the haplotype analysis to 14 additional carrier families, a shared core haplotype was revealed among all carriers matching the conserved region previously identified in the high-density SNP analysis. These findings are consistent with CHEK2 c.349A>G being a founder variant associated with increased PrCa risk, suggesting its potential usefulness for cost-effective targeted genetic screening in PrCa families

Simian Immunodeficiency Virus Infection of Chimpanzees (Pan troglodytes) Shares Features of Both Pathogenic and Non-pathogenic Lentiviral Infections.

The virus-host relationship in simian immunodeficiency virus (SIV) infected chimpanzees is thought to be different from that found in other SIV infected African primates. However, studies of captive SIVcpz infected chimpanzees are limited. Previously, the natural SIVcpz infection of one chimpanzee, and the experimental infection of six chimpanzees was reported, with limited follow-up. Here, we present a long-term study of these seven animals, with a retrospective re-examination of the early stages of infection. The only clinical signs consistent with AIDS or AIDS associated disease was thrombocytopenia in two cases, associated with the development of anti-platelet antibodies. However, compared to uninfected and HIV-1 infected animals, SIVcpz infected animals had significantly lower levels of peripheral blood CD4+ T-cells. Despite this, levels of T-cell activation in chronic infection were not significantly elevated. In addition, while plasma levels of β2 microglobulin, neopterin and soluble TNF-related apoptosis inducing ligand (sTRAIL) were elevated in acute infection, these markers returned to near-normal levels in chronic infection, reminiscent of immune activation patterns in 'natural host' species. Furthermore, plasma soluble CD14 was not elevated in chronic infection. However, examination of the secondary lymphoid environment revealed persistent changes to the lymphoid structure, including follicular hyperplasia in SIVcpz infected animals. In addition, both SIV and HIV-1 infected chimpanzees showed increased levels of deposition of collagen and increased levels of Mx1 expression in the T-cell zones of the lymph node. The outcome of SIVcpz infection of captive chimpanzees therefore shares features of both non-pathogenic and pathogenic lentivirus infections.This work was supported by the Biotechnology and Biological Sciences Research Council and by the Wellcome Trust.This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.ppat.100514

Polygenic hazard score is associated with prostate cancer in multi-ethnic populations.

Genetic models for cancer have been evaluated using almost exclusively European data, which could exacerbate health disparities. A polygenic hazard score (PHS1) is associated with age at prostate cancer diagnosis and improves screening accuracy in Europeans. Here, we evaluate performance of PHS2 (PHS1, adapted for OncoArray) in a multi-ethnic dataset of 80,491 men (49,916 cases, 30,575 controls). PHS2 is associated with age at diagnosis of any and aggressive (Gleason score ≥ 7, stage T3-T4, PSA ≥ 10 ng/mL, or nodal/distant metastasis) cancer and prostate-cancer-specific death. Associations with cancer are significant within European (n = 71,856), Asian (n = 2,382), and African (n = 6,253) genetic ancestries (p < 10-180). Comparing the 80th/20th PHS2 percentiles, hazard ratios for prostate cancer, aggressive cancer, and prostate-cancer-specific death are 5.32, 5.88, and 5.68, respectively. Within European, Asian, and African ancestries, hazard ratios for prostate cancer are: 5.54, 4.49, and 2.54, respectively. PHS2 risk-stratifies men for any, aggressive, and fatal prostate cancer in a multi-ethnic dataset