A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling

Given a set of objects and a symmetric matrix of dissimilarities between them, Unidimensional Scaling is the problem of finding a representation by locating points on a continuum. Approximating dissimilarities by the absolute value of the difference between coordinates on a line constitutes a serious computational problem. This paper presents an algorithm that implements Simulated Annealing in a new way, via a strategy based on a weighted alternating process that uses permutations and point-wise translations to locate the optimal configuration. Explicit implementation details are given for least squares loss functions and for least absolute deviations. The weighted, alternating process is shown to outperform earlier implementations of Simulated Annealing and other optimization strategies for Unidimensional Scaling in run time efficiency, in solution quality, or in both.     

Investigation of the obscuring circumnuclear torus in the active galaxy Mrk231

Active galaxies are characterized by prominent emission from their nuclei. In the 'unified' view of active galaxies, the accretion of material onto a massive compact object--now generally believed to be a black hole--provides the fundamental power source. Obscuring material along the line of sight can account for the observed differences in the nuclear emission, which determine the classification of AGN (for example, as Seyfert 1 or Seyfert 2 galaxies). Although the physical processes of accretion have been confirmed observationally, the structure and extent of the obscuring material have not been determined. Here we report observations of powerful hydroxyl (OH) line emissions that trace this obscuring material within the circumnuclear environment of the galaxy Markarian 231. The hydroxyl (mega)-maser emission shows the characteristics of a rotating, dusty, molecular torus (or thick disk) located between 30 and 100 pc from the central engine. We now have a clear view of the physical conditions, the kinematics and the spatial structure of this material on intermediate size scales, confirming the main tenets of unification models.     

Enterotypes of the human gut microbiome

Our knowledge of species and functional composition of the human gut microbiome is rapidly increasing, but it is still based on very few cohorts and little is known about variation across the world. By combining 22 newly sequenced faecal metagenomes of individuals from four countries with previously published data sets, here we identify three robust clusters (referred to as enterotypes hereafter) that are not nation or continent specific. We also confirmed the enterotypes in two published, larger cohorts, indicating that intestinal microbiota variation is generally stratified, not continuous. This indicates further the existence of a limited number of well-balanced host-microbial symbiotic states that might respond differently to diet and drug intake. The enterotypes are mostly driven by species composition, but abundant molecular functions are not necessarily provided by abundant species, highlighting the importance of a functional analysis to understand microbial communities. Although individual host properties such as body mass index, age, or gender cannot explain the observed enterotypes, data-driven marker genes or functional modules can be identified for each of these host properties. For example, twelve genes significantly correlate with age and three functional modules with the body mass index, hinting at a diagnostic potential of microbial markers.