Fast robust correlation for high-dimensional data

The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the corresponding Pearson correlation are very susceptible to outliers (anomalies) in the data. Several robust measures of covariance have been developed, but few are suitable for the ultrahigh dimensional data that are becoming more prevalent nowadays. For that one needs methods whose computation scales well with the dimension, are guaranteed to yield a positive semidefinite covariance matrix, and are sufficiently robust to outliers as well as sufficiently accurate in the statistical sense of low variability. We construct such methods using data transformations. The resulting approach is simple, fast and widely applicable. We study its robustness by deriving influence functions and breakdown values, and computing the mean squared error on contaminated data. Using these results we select a method that performs well overall. This also allows us to construct a faster version of the DetectDeviatingCells method (Rousseeuw and Van den Bossche, 2018) to detect cellwise outliers, that can deal with much higher dimensions. The approach is illustrated on genomic data with 12,000 variables and color video data with 920,000 dimensions

Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons

We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution of molecular vibrational states

Muller's ratchet with overlapping generations

Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly due to a stochastic fluctuation. In spite of the simplicity of the model, a quantitative understanding of the process remains an open challenge. In contrast to previous works, we here study a Moran model of the ratchet with overlapping generations. Employing an approximation which describes the fittest individuals as one class and the rest as a second class, we obtain closed analytical expressions of the ratchet rate in the rare clicking regime. As a click in this regime is caused by a rare large fluctuation from a metastable state, we do not resort to a diffusion approximation but apply an approximation scheme which is especially well suited to describe extinction events from metastable states. This method also allows for a derivation of expressions for the quasi-stationary distribution of the fittest class. Additionally, we confirm numerically that the formulation with overlapping generations leads to the same results as the diffusion approximation and the corresponding Wright-Fisher model with non-overlapping generations

The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,…

Discussion of "The power of monitoring"

This is an invited comment on the discussion paper "The power of monitoring: how to make the most of a contaminated multivariate sample" by A. Cerioli, M. Riani, A. Atkinson and A. Corbellini that will appear in the journal Statistical Methods & Applications

Performance and parasitosis in heifers grazing mixed with sows

The aim of the study was to investigate the effect of mixed grazing with first season heifers and pregnant sows on animal performance, gastro-intestinal helminths, pasture quality and sward structure during three grazing seasons. This presentation will focus on results from 1999, primarily regarding performance and parasitosis in heifers. There have been no earlier reports on such mixed grazing systems. Three grazing systems were studied in replicate: 1) Heifers grazing alone; 2) sows grazing alone; 3) heifers grazing together with sows. The heifers were inoculated with low doses of infective O.ostertagi larvae at turn-out. Continuous grazing was practised in paddocks regulated in size according to herbage allowance. Individual weight gain, faecal egg output and serum pepsinogen concentrations - as indicator of O.ostertagi infection - were measured fortnightly. The sward structure and quality were greatly influenced by the applied grazing system. The average daily gain of the heifers was significantly higher (P=0.0006) when grazing together with sows (1,121±45 g/day, n=16) than when grazing alone (869±48 g/day, n=14). The mean pepsinogen concentrations were elevated in the heifers grazing alone. It is concluded, that weight gains were significantly better and infection levels with O.ostertagi were significantly reduced in heifers grazing together with sows