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

Relating Spatial Patterns of Stream Metabolism to Distributions of Juveniles Salmonids at the River Network Scale

Understanding the factors that drive spatial patterns in stream ecosystem processes and the distribution of aquatic biota is important to effective management of these systems and the conservation of biota at the network scale. In this study, we conducted field surveys throughout an extensive river network in NE Oregon that supports diminishing populations of wild salmonids. We collected data on physical habitat, nutrient concentrations, biofilm standing stocks, stream metabolism (gross primary production [GPP] and ecosystem respiration [ER]), and ESA‐listed juvenile salmonid density from approximately 50 sites across two sub‐basins. Our goals were to (1) to evaluate network patterns in these metrics, and (2) determine network‐scale linkages among these metrics, thus providing inference of processes driving observed patterns. Ambient nitrate‐N and phosphate‐P concentrations were low across both sub‐basins (\u3c40 μg/L). Nitrate‐N decreased with watershed area in both sub‐basins, but phosphate‐P only decreased in one sub‐basin. These spatial patterns suggest co‐limitation in one sub‐basin but N limitation in the other; experimental results using nutrient diffusing substrates across both sub‐basins supported these predictions. Solar exposure, temperature, GPP, ER, and GPP:ER increased with watershed area, but biofilm Chl a and ash‐free dry mass (AFDM) did not. Spatial statistical network (SSN) models explained between 70% and 75% of the total variation in biofilm Chl a, AFDM, and GPP, but only 21% of the variation in ER. Temperature and nutrient concentrations were the most supported predictors of Chl aand AFDM standing stocks, but these variables explained little of the total variation compared to spatial autocorrelation. In contrast, solar exposure and temperature were the most supported variables explaining GPP, and these variables explained far more variation than autocorrelation. Solar exposure, temperature, and nutrient concentrations explained almost none of the variation in ER. Juvenile salmonids—a key management focus in these sub‐basins—were most abundant in cool stream sections where rates of GPP were low, suggesting temperature constraints on these species restrict their distribution to oligotrophic areas where energy production at the base of the food web may be limited

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Retinopathy in old persons with and without diabetes mellitus: the Age, Gene/Environment Susceptibility--Reykjavik Study (AGES-R).

To access full text version of this article. Please click on the hyperlink "View/open" at the bottom of this pageWe aimed to describe the prevalence of retinopathy in an aged cohort of Icelanders with and without diabetes mellitus. The study population consisted of 4,994 persons aged ≥ 67 years, who participated in the Age, Gene/Environment Susceptibility-Reykjavik Study (AGES-R). Type 2 diabetes mellitus was defined as HbA(1c) ≥ 6.5% (>48 mmol/mol). Retinopathy was assessed by grading fundus photographs using the modified Airlie House adaptation of the Early Treatment Diabetic Retinopathy Study protocol. Associations between retinopathy and risk factors were estimated using odds ratios obtained from multivariate analyses. The overall prevalence of retinopathy in AGES-R was 12.4%. Diabetes mellitus was present in 516 persons (10.3%), for 512 of whom gradable fundus photos were available, including 138 persons (27.0%, 95% CI 23.2, 31.0) with any retinopathy. Five persons (1.0%, 95% CI 0.3, 2.3) had proliferative retinopathy. Clinically significant macular oedema was present in five persons (1.0%, 95% CI 0.3, 2.3). Independent risk factors for retinopathy in diabetic patients in a multivariate model included HbA(1c), insulin use and use of oral hypoglycaemic agents, the last two being indicators of longer disease duration. In 4478 participants without diabetes mellitus, gradable fundus photos were available for 4,453 participants, with retinopathy present in 476 (10.7%, 95% CI 9.8, 11.6) and clinically significant macular oedema in three persons. Independent risk factors included increasing age and microalbuminuria. Over three-quarters (78%) of retinopathy cases were found in persons without diabetes and a strong association between microalbuminuria and non-diabetic retinopathy was found. These results may have implications for patient management of the aged.NIH N01-AG-12100 NIH/NIA, National Eye Institute (NEI) of the NIH ZIAEY000401, Hjartavernd (the Icelandic Heart Association), Althingi (the Icelandic Parliament), University of Iceland

Immunogenetic studies of juvenile dermatomyositis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66141/1/j.1399-0039.1983.tb00371.x.pd