Eigenvectors of random matrices: A survey

Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random.Comment: 64 pages, 1 figure; added Section 7 on localized eigenvector

Random perturbation of low rank matrices: Improving classical bounds

Matrix perturbation inequalities, such as Weyl's theorem (concerning the singular values) and the Davis-Kahan theorem (concerning the singular vectors), play essential roles in quantitative science; in particular, these bounds have found application in data analysis as well as related areas of engineering and computer science. In many situations, the perturbation is assumed to be random, and the original matrix has certain structural properties (such as having low rank). We show that, in this scenario, classical perturbation results, such as Weyl and Davis-Kahan, can be improved significantly. We believe many of our new bounds are close to optimal and also discuss some applications.Comment: 28 pages, 1 figure. Updated introduction and reference

Eigenvectors of random matrices: A survey

Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random

'Sink or swim': an evaluation of the clinical characteristics of individuals with high bone mass.

SUMMARY: High bone mineral density on routine dual energy X-ray absorptiometry (DXA) may indicate an underlying skeletal dysplasia. Two hundred fifty-eight individuals with unexplained high bone mass (HBM), 236 relatives (41% with HBM) and 58 spouses were studied. Cases could not float, had mandible enlargement, extra bone, broad frames, larger shoe sizes and increased body mass index (BMI). HBM cases may harbour an underlying genetic disorder. INTRODUCTION: High bone mineral density is a sporadic incidental finding on routine DXA scanning of apparently asymptomatic individuals. Such individuals may have an underlying skeletal dysplasia, as seen in LRP5 mutations. We aimed to characterize unexplained HBM and determine the potential for an underlying skeletal dysplasia. METHODS: Two hundred fifty-eight individuals with unexplained HBM (defined as L1 Z-score ≥ +3.2 plus total hip Z-score ≥ +1.2, or total hip Z-score ≥ +3.2) were recruited from 15 UK centres, by screening 335,115 DXA scans. Unexplained HBM affected 0.181% of DXA scans. Next 236 relatives were recruited of whom 94 (41%) had HBM (defined as L1 Z-score + total hip Z-score ≥ +3.2). Fifty-eight spouses were also recruited together with the unaffected relatives as controls. Phenotypes of cases and controls, obtained from clinical assessment, were compared using random-effects linear and logistic regression models, clustered by family, adjusted for confounders, including age and sex. RESULTS: Individuals with unexplained HBM had an excess of sinking when swimming (7.11 [3.65, 13.84], p < 0.001; adjusted odds ratio with 95% confidence interval shown), mandible enlargement (4.16 [2.34, 7.39], p < 0.001), extra bone at tendon/ligament insertions (2.07 [1.13, 3.78], p = 0.018) and broad frame (3.55 [2.12, 5.95], p < 0.001). HBM cases also had a larger shoe size (mean difference 0.4 [0.1, 0.7] UK sizes, p = 0.009) and increased BMI (mean difference 2.2 [1.3, 3.1] kg/m(2), p < 0.001). CONCLUSION: Individuals with unexplained HBM have an excess of clinical characteristics associated with skeletal dysplasia and their relatives are commonly affected, suggesting many may harbour an underlying genetic disorder affecting bone mass

Acute and Chronic Impact of Dynamic Exercise on Arterial Stiffness in Older Hypertensives

Arterial stiffness increases with ageing and hypertension. Regular physical activity has been recommended as an important management component of hypertension. The purpose of this study was to examine the acute impact of maximal dynamic exercise and the effect of 20 weeks of aerobic exercise on arterial stiffness of the carotid and brachial arteries in older hypertensives. Nine previously sedentary and treated older hypertensives (2 men and 7 women, age 68.2 ± 5.4 yrs) performed maximal treadmill exercise to volitional fatigue while arterial stiffness indices (arterial distensibility and β stiffness index) were measured prior to, immediately (about 10 min) following, and 24 h following maximal exercise. These measurements were repeated following 20 weeks of moderate intensity aerobic exercise training. Maximal exercise had no impact on arterial stiffness indices immediately and 24 h following exercise intervention. Following 20 weeks of training, arterial stiffness indices remained unchanged at rest and following maximal exercise. These data show that, in older hypertensives, 1) acute maximal dynamic exercise had no impact on arterial stiffness of the carotid and brachial arteries, and 2) 20 weeks of moderate intensity aerobic exercise training failed to modify arterial stiffness

Archaeological Support for the Three-Stage Expansion of Modern Humans across Northeastern Eurasia and into the Americas

Background Understanding the dynamics of the human range expansion across northeastern Eurasia during the late Pleistocene is central to establishing empirical temporal constraints on the colonization of the Americas [1]. Opinions vary widely on how and when the Americas were colonized, with advocates supporting either a pre-[2] or post-[1], [3], [4], [5], [6] last glacial maximum (LGM) colonization, via either a land bridge across Beringia [3], [4], [5], a sea-faring Pacific Rim coastal route [1], [3], a trans-Arctic route [4], or a trans-Atlantic oceanic route [5]. Here we analyze a large sample of radiocarbon dates from the northeast Eurasian Upper Paleolithic to identify the origin of this expansion, and estimate the velocity of colonization wave as it moved across northern Eurasia and into the Americas. Methodology/Principal Findings We use diffusion models [6], [7] to quantify these dynamics. Our results show the expansion originated in the Altai region of southern Siberia ~46kBP , and from there expanded across northern Eurasia at an average velocity of 0.16 km per year. However, the movement of the colonizing wave was not continuous but underwent three distinct phases: 1) an initial expansion from 47-32k calBP; 2) a hiatus from ~32-16k calBP, and 3) a second expansion after the LGM ~16k calBP. These results provide archaeological support for the recently proposed three-stage model of the colonization of the Americas [8], [9]. Our results falsify the hypothesis of a pre-LGM terrestrial colonization of the Americas and we discuss the importance of these empirical results in the light of alternative models. Conclusions/Significance Our results demonstrate that the radiocarbon record of Upper Paleolithic northeastern Eurasia supports a post-LGM terrestrial colonization of the Americas falsifying the proposed pre-LGM terrestrial colonization of the Americas. We show that this expansion was not a simple process, but proceeded in three phases, consistent with genetic data, largely in response to the variable climatic conditions of late Pleistocene northeast Eurasia. Further, the constraints imposed by the spatiotemporal gradient in the empirical radiocarbon record across this entire region suggests that North America cannot have been colonized much before the existing Clovis radiocarbon record suggests

Haplotype differences for copy number variants in the 22q11.23 region among human populations: a pigmentation-based model for selective pressure.

Two gene clusters are tightly linked in a narrow region of chromosome 22q11.23: the macrophage migration inhibitory factor (MIF) gene family and the glutathione S-transferase theta class. Within 120 kb in this region, two 30-kb deletions reach high frequencies in human populations. This gives rise to four haplotypic arrangements, which modulate the number of genes in both families. The variable patterns of linkage disequilibrium (LD) between these copy number variants (CNVs) in diverse human populations remain poorly understood. We analyzed 2469 individuals belonging to 27 human populations with different ethnic origins. Then we correlated the genetic variability of 22q11.23 CNVs with environmental variables. We confirmed an increasing strength of LD from Africa to Asia and to Europe. Further, we highlighted strongly significant correlations between the frequency of one of the haplotypes and pigmentation-related variables: skin color (R2=0.675, P<0.001), distance from the equator (R2=0.454, P<0.001), UVA radiation (R2=0.439, P<0.001), and UVB radiation (R2=0.313, P=0.002). The fact that all MIF-related genes are retained on this haplotype and the evidences gleaned from experimental systems seem to agree with the role of MIF-related genes in melanogenesis. As such, we propose a model that explains the geographic and ethnic distribution of 22q11.23 CNVs among human populations, assuming that MIF-related gene dosage could be associated with adaptation to low UV radiatio

The development and validation of the Addiction-like Eating Behaviour Scale

Background: Overeating and obesity are frequently attributed to an addiction to food. However, there is currently a lack of evidence to support the idea that certain foods contain any specific addictive substance. An alternative approach is to focus on dimensions of observable behaviour, which may underpin a behavioural addiction to eating. To facilitate this, it is necessary to develop a tool to quantify addiction-like eating behaviour, which is not based on the clinical criteria for substance dependence. The current study provides initial validation of the Addiction-like Eating Behaviour Scale (AEBS). Methods: English speaking male and female participants (N=511) from a community sample completed the AEBS, alongside a range of other health- and eating-related questionnaires including the Yale Food Addiction Scale (YFAS) and Binge Eating Scale (BES). Participants also provided their height and weight to enable calculation of body mass index (BMI). Finally, to assess test–retest reliability, an additional 70 participants completed the AEBS twice, 2 weeks apart. Results: Principle components analysis revealed that a two-factor structure best accounted for the data. Factor 1 consisted of items that referred to appetitive drive, whereas factor two consisted of items that referred to dietary control practices. Both subscales demonstrated good internal reliability and test–retest reliability, and a confirmatory factor analysis confirmed the two-factor scale structure. AEBS scores correlated positively with body mass index (BMI) (P<0.001) and other self-report measures of overeating. Importantly, the AEBS significantly predicted variance in BMI above that accounted for by both the YFAS and BES (P=0.027). Conclusions: The AEBS provides a valid and reliable tool to quantify the behavioural features of a potential ‘eating addiction’. In doing so, the AEBS overcomes many limitations associated with applying substance-dependence criteria to eating

Utrophin Up-Regulation by an Artificial Transcription Factor in Transgenic Mice

Duchenne Muscular Dystrophy (DMD) is a severe muscle degenerative disease, due to absence of dystrophin. There is currently no effective treatment for DMD. Our aim is to up-regulate the expression level of the dystrophin related gene utrophin in DMD, complementing in this way the lack of dystrophin functions. To this end we designed and engineered several synthetic zinc finger based transcription factors. In particular, we have previously shown that the artificial three zinc finger protein named Jazz, fused with the appropriate effector domain, is able to drive the transcription of a test gene from the utrophin promoter “A”. Here we report on the characterization of Vp16-Jazz-transgenic mice that specifically over-express the utrophin gene at the muscular level. A Chromatin Immunoprecipitation assay (ChIP) demonstrated the effective access/binding of the Jazz protein to active chromatin in mouse muscle and Vp16-Jazz was shown to be able to up-regulate endogenous utrophin gene expression by immunohistochemistry, western blot analyses and real-time PCR. To our knowledge, this is the first example of a transgenic mouse expressing an artificial gene coding for a zinc finger based transcription factor. The achievement of Vp16-Jazz transgenic mice validates the strategy of transcriptional targeting of endogenous genes and could represent an exclusive animal model for use in drug discovery and therapeutics