Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

Predicting Broccoli Development: I. Development Is Predominantly Determined By Temperature Rather Than Photoperiod

Predictive models of broccoli (Brassica oleracea L. var. italica Plenck) ontogeny will aid farmers who need to forecast changes in crop maturity arising from variable climatic conditions so that their forward marketing arrangements can match their anticipated supply. The objective of this study was to quantify the temperature and photoperiod responses of development in a sub-tropical environment from emergence to floral initiation (EFI), and from floral initiation to harvest maturity (FIHM). Three cultivars, ('Fiesta', 'Greenbelt' and 'Marathon') were sown on eight dates from 11 March to 22 May 1997 and grown under natural and extended (16 h) photoperiods at Gatton College, south-east Queensland, under non-limiting conditions of water and nutrient supply. Climatic data, dates of emergence, floral initiation and harvest maturity were obtained. The estimated base (Tbase) and optimum (Topt) temperatures of 0 and 20 degrees C, respectively were consistent across cultivars, but thermal time requirements were cultivar specific. Differences in thermal time between cultivars during FIHM were small and of little practical importance, but differences in thermal time during EFI were large. Sensitivity to photoperiod and solar radiation was low in the three cultivars used. When the thermal time models were tested on independent data for five cultivars ('Fiesta', 'Greenbelt', 'Marathon', 'CMS Liberty' and 'Triathlon') grown as commercial crops over two years, they adequately predicted floral initiation and harvest maturity

Corneal Biomechanics in Ectatic Diseases: Refractive Surgery Implications.

BACKGROUND: Ectasia development occurs due to a chronic corneal biomechanical decompensation or weakness, resulting in stromal thinning and corneal protrusion. This leads to corneal steepening, increase in astigmatism, and irregularity. In corneal refractive surgery, the detection of mild forms of ectasia pre-operatively is essential to avoid post-operative progressive ectasia, which also depends on the impact of the procedure on the cornea. METHOD: The advent of 3D tomography is proven as a significant advancement to further characterize corneal shape beyond front surface topography, which is still relevant. While screening tests for ectasia had been limited to corneal shape (geometry) assessment, clinical biomechanical assessment has been possible since the introduction of the Ocular Response Analyzer (Reichert Ophthalmic Instruments, Buffalo, USA) in 2005 and the Corvis ST (Oculus Optikgerate GmbH, Wetzlar, Germany) in 2010. Direct clinical biomechanical evaluation is recognized as paramount, especially in detection of mild ectatic cases and characterization of the susceptibility for ectasia progression for any cornea. CONCLUSIONS: The purpose of this review is to describe the current state of clinical evaluation of corneal biomechanics, focusing on the most recent advances of commercially available instruments and also on future developments, such as Brillouin microscopy.(undefined)info:eu-repo/semantics/publishedVersio

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Predicting stroke through genetic risk functions: the CHARGE Risk Score Project.

BACKGROUND AND PURPOSE: Beyond the Framingham Stroke Risk Score, prediction of future stroke may improve with a genetic risk score (GRS) based on single-nucleotide polymorphisms associated with stroke and its risk factors. METHODS: The study includes 4 population-based cohorts with 2047 first incident strokes from 22,720 initially stroke-free European origin participants aged ≥55 years, who were followed for up to 20 years. GRSs were constructed with 324 single-nucleotide polymorphisms implicated in stroke and 9 risk factors. The association of the GRS to first incident stroke was tested using Cox regression; the GRS predictive properties were assessed with area under the curve statistics comparing the GRS with age and sex, Framingham Stroke Risk Score models, and reclassification statistics. These analyses were performed per cohort and in a meta-analysis of pooled data. Replication was sought in a case-control study of ischemic stroke. RESULTS: In the meta-analysis, adding the GRS to the Framingham Stroke Risk Score, age and sex model resulted in a significant improvement in discrimination (all stroke: Δjoint area under the curve=0.016, P=2.3×10(-6); ischemic stroke: Δjoint area under the curve=0.021, P=3.7×10(-7)), although the overall area under the curve remained low. In all the studies, there was a highly significantly improved net reclassification index (P&lt;10(-4)). CONCLUSIONS: The single-nucleotide polymorphisms associated with stroke and its risk factors result only in a small improvement in prediction of future stroke compared with the classical epidemiological risk factors for stroke