Majorana Zero-modes and Topological Phases of Multi-flavored Jackiw-Rebbi model

Motivated by the recent Kitaev's K-theory analysis of topological insulators and superconductors, we adopt the same framework to study the topological phase structure of Jackiw-Rebbi model in 3+1 dimensions. According to the K-theory analysis based on the properties of the charge conjugation and time reversal symmetries, we classify the topological phases of the model. In particular, we find that there exist $\mathbf{Z}$ Majorana zero-modes hosted by the hedgehogs/t'Hooft-Polyakov monopoles, if the model has a $T^2=1$ time reversal symmetry. Guided by the K-theory results, we then explicitly show that a single Majorana zero mode solution exists for the SU(2) doublet fermions in some co-dimensional one planes of the mass parameter space. It turns out we can see the existence of none or a single zero mode when the fermion doublet is only two. We then take a step further to consider four-fermion case and find there can be zero, one or two normalizable zero mode in some particular choices of mass matrices. Our results also indicate that a single normalizable Majorana zero mode can be compatible with the cancellation of SU(2) Witten anomaly.Comment: 29 pages, 3 figures; v2, typos correcte

Selecting patients for randomized trials: a systematic approach based on risk group

BACKGROUND: A key aspect of randomized trial design is the choice of risk group. Some trials include patients from the entire at-risk population, others accrue only patients deemed to be at increased risk. We present a simple statistical approach for choosing between these approaches. The method is easily adapted to determine which of several competing definitions of high risk is optimal. METHOD: We treat eligibility criteria for a trial, such as a smoking history, as a prediction rule associated with a certain sensitivity (the number of patients who have the event and who are classified as high risk divided by the total number patients who have an event) and specificity (the number of patients who do not have an event and who do not meet criteria for high risk divided by the total number of patients who do not have an event). We then derive simple formulae to determine the proportion of patients receiving intervention, and the proportion who experience an event, where either all patients or only those at high risk are treated. We assume that the relative risk associated with intervention is the same over all choices of risk group. The proportion of events and interventions are combined using a net benefit approach and net benefit compared between strategies. RESULTS: We applied our method to design a trial of adjuvant therapy after prostatectomy. We were able to demonstrate that treating a high risk group was superior to treating all patients; choose the optimal definition of high risk; test the robustness of our results by sensitivity analysis. Our results had a ready clinical interpretation that could immediately aid trial design. CONCLUSION: The choice of risk group in randomized trials is usually based on rather informal methods. Our simple method demonstrates that this decision can be informed by simple statistical analyses

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_\mu j^{\mu}(x)= 0$ where $j^\mu(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A] j^{\mu a}(x)= 0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(\tau_0)=f^{abd}q^d(\tau_0)$, ~~$r=|{\vec x}-{\vec X}(\tau_0)|$, ~~$\tau_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(\tau_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $\Phi^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $\Phi(x)=\frac{e}{r}$.Comment: Final version, two more sections added, 45 pages latex, accepted for publication in JHE

Comparing the frequency of common genetic variants and haplotypes between carriers and non-carriers of BRCA1 and BRCA2 deleterious mutations in Australian women diagnosed with breast cancer before 40 years of age

BACKGROUND: BRCA1 and BRCA2 mutations are found in a proportion of families with multiple early-onset breast cancers. There are a large number of different deleterious mutations in both genes, none of which would be detectable using standard genetic association studies. Single common variants and haplotypes of common variants may capture groups of deleterious mutations since some low prevalence haplotypes of common variants occur more frequently among chromosomes that carry rare, deleterious mutations than chromosomes that do not. METHODS: DNA sequence data for BRCA1 and BRCA2 was obtained from 571 participants from the Australian Breast Cancer Family Study. Genetic variants were classified as either deleterious mutations or common genetic variants. Variants tagging common polymorphisms were selected and haplotypes resolved using Haploview. Their frequency was compared to those with and without deleterious mutations using a permutation test. RESULTS: A common genetic variant in BRCA1 (3232A > G) was found to be over-represented in deleterious mutation carriers (p = 0.05), whereas a common genetic variant in BRCA2 (1342A > C) occurred less frequently in deleterious mutation carriers (p = 0.04). All four of the common BRCA1 variants used to form haplotypes occurred more frequently in the deleterious mutation carriers when compared to the non-carriers, but there was no evidence of a difference in the distributions between the two groups (p = 0.34). In BRCA2, all four common variants were found to occur less frequently in the deleterious mutation carriers when compared to non-carriers, but the evidence for difference in the distribution between the two groups was weak (p = 0.16). Several less common haplotypes of common BRCA1 variants were found to be over-represented among deleterious mutation carriers but there was no evidence for this at the population level. In BRCA2, only the most common haplotype was found to occur more frequently in deleterious mutation carriers, with again no evidence at the population level. CONCLUSIONS: We observed differences in the frequency of common genetic variants of the BRCA1 and BRCA2 and their haplotypes between early-onset breast cancer cases who did and did not carry deleterious mutations in these genes. Although our data provide only weak evidence for a difference in frequencies at the population level, the number of deleterious mutation carriers was low and the results may yet be substantiated in a larger study using pooled data

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Percentile reference values for anthropometric body composition indices in European children from the IDEFICS study

INTRODUCTION: To characterise the nutritional status in children with obesity or wasting conditions, European anthropometric reference values for body composition measures beyond the body mass index (BMI) are needed. Differentiated assessment of body composition in children has long been hampered by the lack of appropriate references. OBJECTIVES: The aim of our study is to provide percentiles for body composition indices in normal weight European children, based on the IDEFICS cohort (Identification and prevention of Dietary-and lifestyle-induced health Effects in Children and infantS). METHODS: Overall 18 745 2.0-10.9-year-old children from eight countries participated in the study. Children classified as overweight/obese or underweight according to IOTF (N = 5915) were excluded from the analysis. Anthropometric measurements (BMI (N = 12 830); triceps, subscapular, fat mass and fat mass index (N = 11 845-11 901); biceps, suprailiac skinfolds, sum of skinfolds calculated from skinfold thicknesses (N = 8129-8205), neck circumference (N = 12 241); waist circumference and waist-to-height ratio (N = 12 381)) were analysed stratified by sex and smoothed 1st, 3rd, 10th, 25th, 50th, 75th, 90th, 97th and 99th percentile curves were calculated using GAMLSS. RESULTS: Percentile values of the most important anthropometric measures related to the degree of adiposity are depicted for European girls and boys. Age-and sex-specific differences were investigated for all measures. As an example, the 50th and 99th percentile values of waist circumference ranged from 50.7-59.2 cm and from 51.3-58.7 cm in 4.5-to < 5.0-year-old girls and boys, respectively, to 60.6-74.5 cm in girls and to 59.9-76.7 cm in boys at the age of 10.5-10.9 years. CONCLUSION: The presented percentile curves may aid a differentiated assessment of total and abdominal adiposity in European children

The Distances of the Magellanic Clouds

The present status of our knowledge of the distances to the Magellanic Clouds is evaluated from a post-Hipparcos perspective. After a brief summary of the effects of structure, reddening, age and metallicity, the primary distance indicators for the Large Magellanic Cloud are reviewed: The SN 1987A ring, Cepheids, RR Lyraes, Mira variables, and Eclipsing Binaries. Distances derived via these methods are weighted and combined to produce final "best" estimates for the Magellanic Clouds distance moduli.Comment: Invited review article to appear in ``Post Hipparcos Cosmic Candles'', F. Caputo & A. Heck (Eds.), Kluwer Academic Publ., Dordrecht, in pres

A functional approach to estimation of the parameters of generalized negative binomial and gamma distributions

The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and embraces Poisson distributions, negative binomial distributions, Sichel distributions, Weibull--Poisson distributions and many other types of distributions supplying descriptive statistics with many flexible models. These distributions seem to be very promising for the statistical description of many real phenomena. GG distributions are widely applied in signal and image processing and other practical problems. The statistical estimation of the parameters of GNB and GG distributions is quite complicated. To find estimates, the methods of moments or maximum likelihood can be used as well as two-stage grid EM-algorithms. The paper presents a methodology based on the search for the best distribution using the minimization of $\ell^p$-distances and $L^p$-metrics for GNB and GG distributions, respectively. This approach, first, allows to obtain parameter estimates without using grid methods and solving systems of nonlinear equations and, second, yields not point estimates as the methods of moments or maximum likelihood do, but the estimate for the density function. In other words, within this approach the set of decisions is not a Euclidean space, but a functional space.Comment: 13 pages, 6 figures, The XXI International Conference on Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2018

Efficient Utilization of Rare Variants for Detection of Disease-Related Genomic Regions

When testing association between rare variants and diseases, an efficient analytical approach involves considering a set of variants in a genomic region as the unit of analysis. One factor complicating this approach is that the vast majority of rare variants in practical applications are believed to represent background neutral variation. As a result, analyzing a single set with all variants may not represent a powerful approach. Here, we propose two alternative strategies. In the first, we analyze the subsets of rare variants exhaustively. In the second, we categorize variants selectively into two subsets: one in which variants are overrepresented in cases, and the other in which variants are overrepresented in controls. When the proportion of neutral variants is moderate to large we show, by simulations, that the both proposed strategies improve the statistical power over methods analyzing a single set with total variants. When applied to a real sequencing association study, the proposed methods consistently produce smaller p-values than their competitors. When applied to another real sequencing dataset to study the difference of rare allele distributions between ethnic populations, the proposed methods detect the overrepresentation of variants between the CHB (Chinese Han in Beijing) and YRI (Yoruba people of Ibadan) populations with small p-values. Additional analyses suggest that there is no difference between the CHB and CHD (Chinese Han in Denver) datasets, as expected. Finally, when applied to the CHB and JPT (Japanese people in Tokyo) populations, existing methods fail to detect any difference, while it is detected by the proposed methods in several regions

Financial crises and the attainment of the SDGs: an adjusted multidimensional poverty approach

This paper analyses the impact of financial crises on the Sustainable Development Goal of eradicating poverty. To do so, we develop an adjusted Multidimensional Poverty Framework (MPF) that includes 15 indicators that span across key poverty aspects related to income, basic needs, health, education and the environment. We then use an econometric model that allows us to examine the impact of financial crises on these indicators in 150 countries over the period 1980–2015. Our analysis produces new estimates on the impact of financial crises on poverty’s multiple social, economic and environmental aspects and equally important captures dynamic linkages between these aspects. Thus, we offer a better understanding of the potential impact of current debt dynamics on Multidimensional Poverty and demonstrate the need to move beyond the boundaries of SDG1, if we are to meet the target of eradicating poverty. Our results indicate that the current financial distress experienced by many low-income countries may reverse the progress that has been made hitherto in reducing poverty. We find that financial crises are associated with an approximately 10% increase of extreme poor in low-income countries. The impact is even stronger in some other poverty aspects. For instance, crises are associated with an average decrease of government spending in education by 17.72% in low-income countries. The dynamic linkages between most of the Multidimensional Poverty indicators, warn of a negative domino effect on a number of SDGs related to poverty, if there is a financial crisis shock. To pre-empt such a domino effect, the specific SDG target 17.4 on attaining long-term debt sustainability through coordinated policies plays a key role and requires urgent attention by the international community