Forgetful maps between Deligne-Mostow ball quotients

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livn\'e fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds

Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.Comment: 4 page

Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Algebraic volume density property of affine algebraic manifolds

We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of \C^n equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.Comment: 35 page

A simple clinical scoring system to improve the sensitivity and standardization of the diagnosis of mycosis fungoides type cutaneous T-cell lymphoma: logistic regression of clinical and laboratory data

Background  The diagnosis of mycosis fungoides (MF) is notoriously difficult to establish because in the early stages, histological features may be nonspecific or merely suggestive. Objectives  To standardize the diagnosis of MF. Methods  We studied 138 patients with suspected MF referred over a 7-year period to a university department of a dermatology-based cutaneous lymphoma clinic. Six diagnostic criteria were evaluated: clinical morphology, clinical distribution, skin biopsy T-cell receptor gene rearrangement (TCR-GR), skin biopsy pan T-cell marker loss ≥ 2, skin biopsy CD4/CD8 ratio ≥ 6, and skin biopsy diffuse epidermal HLA-DR expression. These six clinical and laboratory criteria were compared by logistic regression analysis in patients with histologically diagnosed MF and those with benign disease. Results  Of the 138 patients, 74 had histology of MF, 47 of benign dermatoses and 17 were indeterminate. Close associations were found between a histological diagnosis of MF and TCR-GR (odds ratio 14·4), classical morphology (7·5), classical distribution (2·5) and diffuse epidermal HLA-DR expression (2·8). Logistic regression models were developed depending on the availability of data (either TCR-GR or HLA-DR). Probabilities for correctly diagnosing MF compared with histology as the ‘gold standard’ were derived from these logistic regression models. A scoring system assigning point values based on these probabilities was then created in order to assist the clinician in making the diagnosis. If using TCR-GR data, a positive TCR-GR = 2·5 points, the presence of classical morphology = 2·0 points, and the presence of classical distribution = 1·5 points. A total score of ≥ 3·5 points assigns a high probability (> 85%) of having MF. If using HLA-DR expression, then the presence of classical morphology = 2·5 points, a positive diffuse epidermal HLA-DR expression = 2·0 points, and the presence of classical distribution = 1·5 points. In this case, a total score of ≥ 4·0 points assigns a high probability (> 85%) of MF. Conclusions  The logistic regression models and scoring systems integrate clinical and laboratory assessments, allow rapid probability estimation, and provide a threshold for the diagnosis of MF in an objective, standardized manner.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75520/1/j.1365-2133.2003.05458.x.pd

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page

Compact Hyperbolic Extra Dimensions: Branes, Kaluza-Klein Modes and Cosmology

We reconsider theories with low gravitational (or string) scale M_* where Newton's constant is generated via new large-volume spatial dimensions, while Standard Model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds (CHM's) we show that the spectrum of Kaluza-Klein (KK) modes is radically altered. This allows an early universe cosmology with normal evolution up to substantial temperatures, and completely negates the constraints on M_* arising from astrophysics. Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics can emerge with only order unity coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.Comment: 4 pages, no figure

The No-defect Conjecture: Cosmological Implications

When the topology of the universe is non trivial, it has been shown that there are constraints on the network of domain walls, cosmic strings and monopoles. I generalize these results to textures and study the cosmological implications of such constraints. I conclude that a large class of multi-connected universes with topological defects accounting for structure formation are ruled out by observation of the cosmic microwave background.Comment: 4 pages, 1 figure, accepted for publication as a brief report in Phys. Rev.

Gender differences in local and systemic reactions to inactivated influenza vaccine, established by a meta-analysis of fourteen independent studies

In order to determine whether there is a difference between genders in reported adverse reactions to inactivated influenza vaccine, a computerized database of serological studies was investigated. A standardized questionnaire was used to evaluate vaccine reactogenicity. A total of 1,800 vaccinees in 14 studies were analyzed separately for two age groups ( or = 60 years of age). Females reported significantly more local reactions than males. The pooled odds ratio for the outcome measure "any local reaction" was 0.32 (95% confidence interval, 0.26-0.40, significant) and 0.54 (95% Cl, 0.41-0.70, significant) for young and elderly adults, respectively. Similar results were obtained for the outcome measure "any systemic reaction." Previous exposure to influenza or influenza vaccine had no influence on reactogenicity. There were no gender differences in sero-responses. In conclusion, gender should be regarded as a predictor of reported reactions to influenza vaccine in both young and elderly adults and should be addressed in future study designs