Inequalities and Positive-Definite Functions Arising From a Problem in Multidimensional Scaling

We solve the following variational problem: Find the maximum of E ∥ X−Y ∥ subject to E ∥ X ∥2 ≤ 1, where X and Y are i.i.d. random n-vectors, and ∥⋅∥ is the usual Euclidean norm on Rn. This problem arose from an investigation into multidimensional scaling, a data analytic method for visualizing proximity data. We show that the optimal X is unique and is (1) uniform on the surface of the unit sphere, for dimensions n ≥ 3, (2) circularly symmetric with a scaled version of the radial density ρ/(1−ρ2)1/2, 0 ≤ ρ ≤1, for n=2, and (3) uniform on an interval centered at the origin, for n=1 (Plackett\u27s theorem). By proving spherical symmetry of the solution, a reduction to a radial problem is achieved. The solution is then found using the Wiener-Hopf technique for (real) n \u3c 3. The results are reminiscent of classical potential theory, but they cannot be reduced to it. Along the way, we obtain results of independent interest: for any i.i.d. random n-vectors X and Y,E ∥ X−Y ∥ ≤ E ∥ X+Y ∥. Further, the kernel Kp, β(x,y) = ∥ x+y ∥βp− ∥x−y∥βp, x, y∈Rn and ∥ x ∥ p=(∑|xi|p)1/p, is positive-definite, that is, it is the covariance of a random field, Kp,β(x,y) = E [ Z(x)Z(y) ] for some real-valued random process Z(x), for 1 ≤ p ≤ 2 and 0 \u3c β ≤ p ≤ 2 (but not for β \u3ep or p\u3e2 in general). Although this is an easy consequence of known results, it appears to be new in a strict sense. In the radial problem, the average distance D(r1,r2) between two spheres of radii r1 and r2 is used as a kernel. We derive properties of D(r1,r2), including nonnegative definiteness on signed measures of zero integral

On OMEGA (Online Multivariate Exploratory Graphical Analysis): Routine Searching for Structure: Comment

Abstract included in text

On OMEGA (Online Multivariate Exploratory Graphical Analysis): Routine Searching for Structure: Comment

Abstract included in text

Hypertrophic cardiomyopathy: two-dimensional echocardiographic score versus clinical and electrocardiographic findings.

The severity and site of hypertrophy is important in determining the clinical picture and the natural history of hypertrophic cardiomyopathy (HCM). We evaluated left ventricular hypertrophy by means of two-dimensional echocardiographic score and score index, and correlated these findings with symptoms, electrovector-cardiographic data, and ventricular arrhythmias. A total of 42 patients with HCM were studied by clinical examination, ECG, VCG, M-mode and 2D echocardiography, and 24-h Holter monitoring. The extent and severity of the hypertrophic process were calculated by a score system. The left ventricle was divided into 11 segments and a hypertrophic score (HS) was given to each segment. A hypertrophy score index (HSI) was also calculated by dividing the number of hypertrophied segments by 13. No correlation was found between symptoms and HS and HSI, nor ECG-VCG abnormalities and HS and HSI. A statistically significant relationship between the severity of ventricular arrhythmias and HS and HSI was found (p less than 0.01). The mechanism responsible for ventricular tachyarrhythmias in severe and diffuse hypertrophy might reside in the high intraventricular pressures which produce or worsen areas of myocardial ischemia

Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.Comment: 20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figure

Measuring shared variants in cohorts of discordant siblings with applications to autism

We develop a method of analysis [affected to discordant sibling pairs (A2DS)] that tests if shared variants contribute to a disorder. Using a standard measure of genetic relation, test individuals are compared with a cohort of discordant sibling pairs (CDS) to derive a comparative similarity score. We ask if a test individual is more similar to an unrelated affected than to the unrelated unaffected sibling from the CDS and then, sum over such individuals and pairs. Statistical significance is judged by randomly permuting the affected status in the CDS. In the analysis of published genotype data from the Simons Simplex Collection (SSC) and the Autism Genetic Resource Exchange (AGRE) cohorts of children with autism spectrum disorder (ASD), we find strong statistical significance that the affected are more similar to the affected than to the unaffected of the CDS (P value approximately 0.00001). Fathers in multiplex families have marginally greater similarity (P value = 0.02) to unrelated affected individuals. These results do not depend on ethnic matching or gender

The emerging spectrum of cardiopulmonary pathology of the Coronavirus disease 2019 (COVID-19): Report of three autopsies from Houston, Texas and review of autopsy findings from other United States cities

This paper collates the pathological findings from initial published autopsy reports on 23 patients with coronavirus disease 2019 (COVID-19) from 5 centers in the United States of America, including 3 cases from Houston, Texas. Findings confirm that COVID-19 is a systemic disease with major involvement of the lungs and heart. Acute COVID-19 pneumonia has features of a distinctive acute interstitial pneumonia with a diffuse alveolar damage component, coupled with microvascular involvement with intra- and extravascular fibrin deposition and intravascular trapping of neutrophils, and, frequently, with formation of microthombi in arterioles. Major pulmonary thromboemboli with pulmonary infarcts and/or hemorrhage occurred in 5 of the 23 patients. Two of the Houston cases had interstitial pneumonia with diffuse alveolar damage pattern. One of the Houston cases had multiple bilateral segmental pulmonary thromboemboli with infarcts and hemorrhages coupled with, in nonhemorrhagic areas, a distinctive interstitial lymphocytic pneumonitis with intra-alveolar fibrin deposits and no hyaline membranes, possibly representing a transition form to acute fibrinous and organizing pneumonia. Multifocal acute injury of cardiac myocytes was frequently observed. Lymphocytic myocarditis was reported in 1 case. In addition to major pulmonary pathology, the 3 Houston cases had evidence of lymphocytic pericarditis, multifocal acute injury of cardiomyocytes without inflammatory cellular infiltrates, depletion of splenic white pulp, focal hepatocellular degeneration and rare glomerular capillary thrombosis. Each had evidence of chronic cardiac disease: hypertensive left ventricular hypertrophy (420 g heart), dilated cardiomyopathy (1070 g heart), and hypertrophic cardiomyopathy (670 g heart). All 3 subjects were obese (BMIs of 33.8, 51.65, and 35.2 Kg/m2). Overall, the autopsy findings support the concept that the pathogenesis of severe COVID-19 disease involves direct viral-induced injury of multiple organs, including heart and lungs, coupled with the consequences of a procoagulant state with coagulopathy

Right pulmonary artery occlusion by an acute dissecting aneurysm of the ascending aorta

We describe the case of a 76-year old female who presented with a Type A aortic dissection requiring repair with an interposition graft and aortic valve replacement. Post-operatively she had clinical features and computerised tomographic images suggestive of a pulmonary embolus and died 24 hours later. The extremely rare finding of intramural thrombus occluding the right pulmonary artery was seen at post mortem

Genome-wide DNA methylation analysis for diabetic nephropathy in type 1 diabetes mellitus

BACKGROUND: Diabetic nephropathy is a serious complication of diabetes mellitus and is associated with considerable morbidity and high mortality. There is increasing evidence to suggest that dysregulation of the epigenome is involved in diabetic nephropathy. We assessed whether epigenetic modification of DNA methylation is associated with diabetic nephropathy in a case-control study of 192 Irish patients with type 1 diabetes mellitus (T1D). Cases had T1D and nephropathy whereas controls had T1D but no evidence of renal disease. METHODS: We performed DNA methylation profiling in bisulphite converted DNA from cases and controls using the recently developed Illumina Infinium(R) HumanMethylation27 BeadChip, that enables the direct investigation of 27,578 individual cytosines at CpG loci throughout the genome, which are focused on the promoter regions of 14,495 genes. RESULTS: Singular Value Decomposition (SVD) analysis indicated that significant components of DNA methylation variation correlated with patient age, time to onset of diabetic nephropathy, and sex. Adjusting for confounding factors using multivariate Cox-regression analyses, and with a false discovery rate (FDR) of 0.05, we observed 19 CpG sites that demonstrated correlations with time to development of diabetic nephropathy. Of note, this included one CpG site located 18 bp upstream of the transcription start site of UNC13B, a gene in which the first intronic SNP rs13293564 has recently been reported to be associated with diabetic nephropathy. CONCLUSION: This high throughput platform was able to successfully interrogate the methylation state of individual cytosines and identified 19 prospective CpG sites associated with risk of diabetic nephropathy. These differences in DNA methylation are worthy of further follow-up in replication studies using larger cohorts of diabetic patients with and without nephropathy