An Investigation Into Crouzeix\u27s Conjecture

We will explore Crouzeix’s Conjecture, an upper bound on the norm of a matrix after the application of a polynomial involving the numerical range. More formally, Crouzeix’s Conjecture states that for any n × n matrix A and any polynomial p from C → C,∥p(A)∥ ≤ 2 supz∈W (A) |p(z)|.Where W (A) is a set in C related to A, and ∥·∥ is the matrix norm. We first discuss the conjecture, and prove the simple case when the matrix is normal. We then explore a proof for a class of matrices given by Daeshik Choi. We expand upon the proof where details are left out in the original. We also find and fix a small flaw in one section of the original paper

Modeling AIDS survival after initiation of antiretroviral treatment by Weibull models with changepoints

<p>Abstract</p> <p>Background</p> <p>Mortality of HIV-infected patients initiating antiretroviral therapy in the developing world is very high immediately after the start of ART therapy and drops sharply thereafter. It is necessary to use models of survival time that reflect this change.</p> <p>Methods</p> <p>In this endeavor, parametric models with changepoints such as Weibull models can be useful in order to explicitly model the underlying failure process, even in the case where abrupt changes in the mortality rate are present. Estimation of the temporal location of possible mortality changepoints has important implications on the effective management of these patients. We briefly describe these models and apply them to the case of estimating survival among HIV-infected patients who are initiating antiretroviral therapy in a care and treatment programme in sub-Saharan Africa.</p> <p>Results</p> <p>As a first reported data-driven estimate of the existence and location of early mortality changepoints after antiretroviral therapy initiation, we show that there is an early change in risk of death at three months, followed by an intermediate risk period lasting up to 10 months after therapy.</p> <p>Conclusion</p> <p>By explicitly modelling the underlying abrupt changes in mortality risk after initiation of antiretroviral therapy we are able to estimate their number and location in a rigorous, data-driven manner. The existence of a high early risk of death after initiation of antiretroviral therapy and the determination of its duration has direct implications for the optimal management of patients initiating therapy in this setting.</p

Wall Crossing from Dirac Zeromodes

We explore the physics of two-body decay of BPS states using semiclassical analysis to construct explicit solutions that illustrate the main features of wall crossing, for both ordinary and framed BPS states. In particular we recover the primitive wall-crossing formula from an asymptotic analysis of certain Dirac-type operators on monopole moduli spaces. Along the way we give an asymptotic metric for the moduli space of singular monopoles, analogous to the Gibbons-Manton and Lee-Weinberg-Yi metrics for the moduli space of smooth monopoles, and we find evidence for the existence of stable non-BPS boundstates. Our discussion applies to four-dimensional N = 2 super-Yang-Mills theories with general gauge group and general 't Hooft defects.Comment: 32 pages plus appendices; 1 figure. v2: references added, typos fixed. v3: references added, published versio

A Comparison of the Ovulation Method With the CUE Ovulation Predictor in Determining the Fertile Period

The purpose of this study was to compare the CUE Ovulation Predictor with the ovulation method in determining the fertile period. Eleven regularly ovulating women measured their salivary and vaginal electrical resistance (ER) with the CUE, observed their cervical-vaginal mucus, and measured their urine for a luteinizing hormone (LH) surge on a daily basis. Data from 21 menstrual cycles showed no statistical difference (T= 0.33, p= 0.63) between the CUE fertile period, which ranged from 5 to 10 days (mean = 6.7 days, SD = 1.6), and the fertile period of the ovulation method, which ranged from 4 to 9 days (mean = 6.5 days, SD = 2.0). The CUE has potential as an adjunctive device in the learning and use of natural family planning methods

A flavour of omics approaches for the detection of food fraud

Food fraud has been identified as an increasing problem on a global scale with wide-ranging economic, social, health and environmental impacts. Omics and their related techniques, approaches, and bioanalytical platforms incorporate a significant number of scientific areas which have the potential to be applied to and significantly reduce food fraud and its negative impacts. In this overview we consider a selected number of very recent studies where omics techniques were applied to detect food authenticity and could be implemented to ensure food integrity. We postulate that significant reductions in food fraud, with the assistance of omics technologies and other approaches, will result in less food waste, decreases in energy use as well as greenhouse gas emissions, and as a direct consequence of this, increases in quality, productivity, yields, and the ability of food systems to be more resilient and able to withstand future food shocks

Vibratory response modeling and verification of a high precision optical positioning system.

A generic vibratory-response modeling program has been developed as a tool for designing high-precision optical positioning systems. Based on multibody dynamics theory, the system is modeled as rigid-body structures connected by linear elastic elements, such as complex actuators and bearings. The full dynamic properties of each element are determined experimentally or theoretically, then integrated into the program as inertial and stiffness matrices. Utilizing this program, the theoretical and experimental verification of the vibratory behavior of a double-multilayer monochromator support and positioning system is presented. Results of parametric design studies that investigate the influence of support floor dynamics and highlight important design issues are also presented. Overall, good matches between theory and experiment demonstrate the effectiveness of the program as a dynamic modeling tool

Deposition of platinum clusters on surface-modified tobacco mosaic virus

Nanoscaled Pt conductors were prepared from genetically engineered Tobacco mosaic virus (TMV) templates through Pt cluster deposition on the outer surface of the TMV. Pt clusters were synthesized and deposited on the engineered TMV with surface-exposed cysteine via the in situ mineralization of hexachloroplatinate anions. This deposition was driven by the specific binding between thiols and the solid metal clusters. In addition, Pt-thiolate adducts are suggested to form on the engineered TMV in aqueous solutions that work as nucleation sites for the formation of the Pt clusters. The specific binding between Pt clusters and the engineered TMV template was investigated using UV/vis spectrophotometry and quartz crystal microbalance (QCM) analysis. The electric conductance of Pt-deposited TMV was greater than that of the uncoated TMV virion particles. This result suggests the application of metal cluster-deposited engineered TMV in future electrical devices such as rapid response sensors

Efficacy of RTS,S malaria vaccines: individual-participant pooled analysis of phase 2 data.

BACKGROUND: The efficacy of RTS,S/AS01 as a vaccine for malaria is being tested in a phase 3 clinical trial. Early results show significant, albeit partial, protection against clinical malaria and severe malaria. To ascertain variations in vaccine efficacy according to covariates such as transmission intensity, choice of adjuvant, age at vaccination, and bednet use, we did an individual-participant pooled analysis of phase 2 clinical data. METHODS: We analysed data from 11 different sites in Africa, including 4453 participants. We measured heterogeneity in vaccine efficacy by estimating the interactions between covariates and vaccination in pooled multivariable Cox regression and Poisson regression analyses. Endpoints for measurement of vaccine efficacy were infection, clinical malaria, severe malaria, and death. We defined transmission intensity levels according to the estimated local parasite prevalence in children aged 2-10 years (PrP₂₋₁₀), ranging from 5% to 80%. Choice of adjuvant was either AS01 or AS02. FINDINGS: Vaccine efficacy against all episodes of clinical malaria varied by transmission intensity (p=0·001). At low transmission (PrP₂₋₁₀ 10%) vaccine efficacy was 60% (95% CI 54 to 67), at moderate transmission (PrP₂₋₁₀ 20%) it was 41% (21 to 57), and at high transmission (PrP₂₋₁₀ 70%) the efficacy was 4% (-10 to 22). Vaccine efficacy also varied by adjuvant choice (p<0·0001)--eg, at low transmission (PrP₂₋₁₀ 10%), efficacy varied from 60% (95% CI 54 to 67) for AS01 to 47% (14 to 75) for AS02. Variations in efficacy by age at vaccination were of borderline significance (p=0·038), and bednet use and sex were not significant covariates. Vaccine efficacy (pooled across adjuvant choice and transmission intensity) varied significantly (p<0·0001) according to time since vaccination, from 36% efficacy (95% CI 24 to 45) at time of vaccination to 0% (-38 to 38) after 3 years. INTERPRETATION: Vaccine efficacy against clinical disease was of limited duration and was not detectable 3 years after vaccination. Furthermore, efficacy fell with increasing transmission intensity. Outcomes after vaccination cannot be gauged accurately on the basis of one pooled efficacy figure. However, predictions of public-health outcomes of vaccination will need to take account of variations in efficacy by transmission intensity and by time since vaccination. FUNDING: Medical Research Council (UK); Bill & Melinda Gates Foundation Vaccine Modelling Initiative; Wellcome Trust

Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Background: Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures. Methods: Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies. Results: Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated. Conclusion: The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies