Classifying matchbox manifolds

Matchbox manifolds are foliated spaces with totally disconnected transversals. Two matchbox manifolds which are homeomorphic have return equivalent dynamics, so that invariants of return equivalence can be applied to distinguish non-homeomorphic matchbox manifolds. In this work we study the problem of showing the converse implication: when does return equivalence imply homeomorphism? For the class of weak solenoidal matchbox manifolds, we show that if the base manifolds satisfy a strong form of the Borel Conjecture, then return equivalence for the dynamics of their foliations implies the total spaces are homeomorphic. In particular, we show that two equicontinuous \mT^n--like matchbox manifolds of the same dimension are homeomorphic if and only if their corresponding restricted pseudogroups are return equivalent. At the same time, we show that these results cannot be extended to include the "\emph{adic}-surfaces", which are a class of weak solenoids fibering over a closed surface of genus 2.Comment: This work is an extensive revision of the previous version on the arXi

Manifold-like matchbox manifolds

A matchbox manifold is a generalized lamination, and is a continuum whose arc-components define the leaves of a foliation of the space. The main result of this paper implies that a matchbox manifold which is manifold-like must be homeomorphic to a weak solenoid.Comment: Various text edits in version

Dissipation time and decay of correlations

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit

Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

Bone mineral density in breast cancer patients treated with adjuvant letrozole, tamoxifen, or sequences of letrozole and tamoxifen in the BIG 1-98 study (SAKK 21/07)

Background: The risk of osteoporosis and fracture influences the selection of adjuvant endocrine therapy. We analyzed bone mineral density (BMD) in Swiss patients of the Breast International Group (BIG) 1-98 trial [treatment arms: A, tamoxifen (T) for 5 years; B, letrozole (L) for 5 years; C, 2 years of T followed by 3 years of L; D, 2 years of L followed by 3 years of T]. Patients and methods: Dual-energy X-ray absorptiometry (DXA) results were retrospectively collected. Patients without DXA served as control group. Repeated measures models using covariance structures allowing for different times between DXA were used to estimate changes in BMD. Prospectively defined covariates were considered as fixed effects in the multivariable models. Results: Two hundred and sixty-one of 546 patients had one or more DXA with 577 lumbar and 550 hip measurements. Weight, height, prior hormone replacement therapy, and hysterectomy were positively correlated with BMD; the correlation was negative for letrozole arms (B/C/D versus A), known osteoporosis, time on trial, age, chemotherapy, and smoking. Treatment did not influence the occurrence of osteoporosis (T score < −2.5 standard deviation). Conclusions: All aromatase inhibitor regimens reduced BMD. The sequential schedules were as detrimental for bone density as L monotherap

Secondary LS category of measured laminations

In the author's Ph.D., a version of the tangential LS category for foliated spaces depending on a transverse invariant measure, called the measured category, was introduced. Unfortunately, the measured category vanishes easily. When it is zero, the rate of convergence to zero of the quantity involved in the definition, by taking arbitrarily large homotopies, gives a new invariant, called the secondary measured category. Several versions of classical results are proved for the secondary measured category. It is also shown that the secondary measured category is a transverse invariant related to the growth of (pseudo)groups. The equality between secondary category and the growth of a group is done in the case of free suspensions by Rohlin groups.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1112.500

Outcomes of special histotypes of breast cancer after adjuvant endocrine therapy with letrozole or tamoxifen in the monotherapy cohort of the BIG 1-98 trial

In the BIG 1-98 clinical trial of 4922 postmenopausal women treated with 5 years of letrozole or tamoxifen for endocrine-responsive breast cancer, 183 had the rare histotypes mucinous or tubular/cribriform. These women had better outcomes than those with other histotypes. The magnitude of the letrozole advantage compared with tamoxifen may not be as large in patients with these rare histotype

Clinical activity of ipilimumab for metastatic uveal melanoma: a retrospective review of the Dana-Farber Cancer Institute, Massachusetts General Hospital, Memorial Sloan-Kettering Cancer Center, and University Hospital of Lausanne experience.

BACKGROUND: Uveal melanoma exhibits a high incidence of metastases; and, to date, there is no systemic therapy that clearly improves outcomes. The anticytotoxic T-lymphocyte-associated protein 4 (anti-CTLA-4) antibody ipilimumab is a standard of care for metastatic melanoma; however, the clinical activity of CTLA-4 inhibition in patients with metastatic uveal melanoma is poorly defined. METHODS: To assess ipilimumab in this setting, the authors performed a multicenter, retrospective analysis of 4 hospitals in the United States and Europe. Clinical characteristics, toxicities, and radiographic disease burden, as determined by central, blinded radiology review, were evaluated. RESULTS: Thirty-nine patients with uveal melanoma were identified, including 34 patients who received 3 mg/kg ipilimumab and 5 who received 10 mg/kg ipilimumab. Immune-related response criteria and modified World Health Organization criteria were used to assess the response rate (RR) and the combined response plus stable disease (SD) rate after 12 weeks, after 23 weeks, and overall (median follow-up, 50.4 weeks [12.6 months]). At week 12, the RR was 2.6%, and the response plus SD rate was 46.%; at week 23, the RR was 2.6%, and the response plus SD rate was 28.2%. There was 1 complete response and 1 late partial response (at 100 weeks after initial SD) for an immune-related RR of 5.1%. Immune-related adverse events were observed in 28 patients (71.8%) and included 7 (17.9%) grade 3 and 4 events. Immune-related adverse events were more frequent in patients who received 10 mg/kg ipilimumab than in those who received 3 mg/kg ipilimumab. The median overall survival from the first dose of ipilimumab was 9.6 months (95% confidence interval, 6.3-13.4 months; range, 1.6-41.6 months). Performance status, lactate dehydrogenase level, and an absolute lymphocyte count ≥ 1000 cells/μL at week 7 were associated significantly with survival. CONCLUSIONS: In this multicenter, retrospective analysis of 4 hospitals in the United States and Europe of patients with uveal melanoma, durable responses to ipilimumab and manageable toxicity were observed

Adverse prognostic value of peritumoral vascular invasion: is it abrogated by adequate endocrine adjuvant therapy? Results from two International Breast Cancer Study Group randomized trials of chemoendocrine adjuvant therapy for early breast cancer

Background: Peritumoral vascular invasion (PVI) may assist in assigning optimal adjuvant systemic therapy for women with early breast cancer. Patients and methods: Patients participated in two International Breast Cancer Study Group randomized trials testing chemoendocrine adjuvant therapies in premenopausal (trial VIII) or postmenopausal (trial IX) node-negative breast cancer. PVI was assessed by institutional pathologists and/or central review on hematoxylin-eosin-stained slides in 99% of patients (analysis cohort 2754 patients, median follow-up >9 years). Results: PVI, present in 23% of the tumors, was associated with higher grade tumors and larger tumor size (trial IX only). Presence of PVI increased locoregional and distant recurrence and was significantly associated with poorer disease-free survival. The adverse prognostic impact of PVI in trial VIII was limited to premenopausal patients with endocrine-responsive tumors randomized to therapies not containing goserelin, and conversely the beneficial effect of goserelin was limited to patients whose tumors showed PVI. In trial IX, all patients received tamoxifen: the adverse prognostic impact of PVI was limited to patients with receptor-negative tumors regardless of chemotherapy. Conclusion: Adequate endocrine adjuvant therapy appears to abrogate the adverse impact of PVI in node-negative disease, while PVI may identify patients who will benefit particularly from adjuvant therap