Dynamical models for circle covering: Brownian motion and Poisson updating

We consider two dynamical variants of Dvoretzky's classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length $\ell$ is updated at rate $\ell^{-\alpha}$ where $\alpha \ge0$ is a parameter. For the model with Brownian motions, a special case of our results is that if the length of the $n$th interval is $c/n$, then there are times at which a fixed point is not covered if and only if $c<2$ and there are times at which the circle is not fully covered if and only if $c<3$. For the Poisson updating model, we obtain analogous results with $c<\alpha$ and $c<\alpha+1$ instead. We also compute the Hausdorff dimension of the set of exceptional times for some of these questions.Comment: Published in at http://dx.doi.org/10.1214/07-AOP340 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Why Our Next President May Keep His or her Senate Seat: A Conjecture on the Constitution’s Incompatibility Clause

Heart diseases are common and significant contributors to worldwide mortality and morbidity. During recent years complement mediated inflammation has been shown to be an important player in a variety of heart diseases. Despite some negative results from clinical trials using complement inhibitors, emerging evidence points to an association between the complement system and heart diseases. Thus, complement seems to be important in coronary heart disease as well as in heart failure, where several studies underscore the prognostic importance of complement activation. Furthermore, patients with atrial fibrillation often share risk factors both with coronary heart disease and heart failure, and there is some evidence implicating complement activation in atrial fibrillation. Moreover, Chagas heart disease, a protozoal infection, is an important cause of heart failure in Latin America, and the complement system is crucial for the protozoa-host interaction. Thus, complement activation appears to be involved in the pathophysiology of a diverse range of cardiac conditions. Determination of the exact role of complement in the various heart diseases will hopefully help to identify patients that might benefit from therapeutic complement intervention

Reconstruction of Random Colourings

Reconstruction problems have been studied in a number of contexts including biology, information theory and and statistical physics. We consider the reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for large $k$. Bhatnagar et. al. showed non-reconstruction when $\Delta \leq \frac12 k\log k - o(k\log k)$ and reconstruction when $\Delta \geq k\log k + o(k\log k)$. We tighten this result and show non-reconstruction when $\Delta \leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$ and reconstruction when $\Delta \geq k[\log k + \log \log k + 1+o(1)]$.Comment: Added references, updated notatio

Design and development of a low temperature, inductance based high frequency ac susceptometer

We report on the development of an induction based low temperature high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration have allowed a sample magnetic moment resolution of $5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and characterization of the susceptometer, and explain the calibration process. We also include some example measurements on the spin ice material CdEr$_2$S$_4$ and iron oxide based nanoparticles to illustrate functionality

Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201

BRCA2 mutation carriers, reproductive factors and breast cancer risk

BACKGROUND: Germline mutations in the BRCA genes dramatically increase the risk of breast cancer. In the general population, breast cancer risk is affected by age at menarche, by age at first birth, by the number of births and by the duration of breast feeding. Whether this is true for mutation carriers is not clear. METHODS: In a case–control study, nested in a population-based cohort of the Icelandic Cancer Detection Clinic, two groups of cases were defined, matched on year of birth, on age at diagnosis and on age when giving information on reproductive factors: 100 carriers of the Icelandic founder BRCA2 mutation 999del5, and 361 BRCA2-negative cases. The mean age at diagnosis was 48 years. There were 1000 women in a matched group of unaffected controls. Conditional logistic regression was used for the analysis. RESULTS: An increased number of births was associated with a decreased risk of breast cancer in BRCA2-negative cases but not in BRCA2-positive cases. A negative association between risk and duration of breast feeding was observed only in the mutation carriers. These associations were not statistically significant, but the effects of the two variables differed significantly according to mutation status (P = 0.007 and P = 0.045 for interaction with number of births and with duration of breast feeding, respectively). This was maintained when limiting the analysis to women diagnosed older than the age of 40 years. CONCLUSION: The association between breast cancer and the number of pregnancies and between breast cancer and the duration of breast feeding was not the same for carriers and noncarriers of a detrimental BRCA2 mutation. In the context of other epidemiological and laboratory studies, this may indicate that the product of the BRCA2 gene has a function relating to the differentiation of epithelial tissue in the breast