Separating common from distinctive variation

BACKGROUND: Joint and individual variation explained (JIVE), distinct and common simultaneous component analysis (DISCO) and O2-PLS, a two-block (X-Y) latent variable regression method with an integral OSC filter can all be used for the integrated analysis of multiple data sets and decompose them in three terms: a low(er)-rank approximation capturing common variation across data sets, low(er)-rank approximations for structured variation distinctive for each data set, and residual noise. In this paper these three methods are compared with respect to their mathematical properties and their respective ways of defining common and distinctive variation. RESULTS: The methods are all applied on simulated data and mRNA and miRNA data-sets from GlioBlastoma Multiform (GBM) brain tumors to examine their overlap and differences. When the common variation is abundant, all methods are able to find the correct solution. With real data however, complexities in the data are treated differently by the three methods. CONCLUSIONS: All three methods have their own approach to estimate common and distinctive variation with their specific strength and weaknesses. Due to their orthogonality properties and their used algorithms their view on the data is slightly different. By assuming orthogonality between common and distinctive, true natural or biological phenomena that may not be orthogonal at all might be misinterpreted

Common and Distinct Components in Data Fusion

In many areas of science multiple sets of data are collected pertaining to the same system. Examples are food products which are characterized by different sets of variables, bio-processes which are on-line sampled with different instruments, or biological systems of which different genomics measurements are obtained. Data fusion is concerned with analyzing such sets of data simultaneously to arrive at a global view of the system under study. One of the upcoming areas of data fusion is exploring whether the data sets have something in common or not. This gives insight into common and distinct variation in each data set, thereby facilitating understanding the relationships between the data sets. Unfortunately, research on methods to distinguish common and distinct components is fragmented, both in terminology as well as in methods: there is no common ground which hampers comparing methods and understanding their relative merits. This paper provides a unifying framework for this subfield of data fusion by using rigorous arguments from linear algebra. The most frequently used methods for distinguishing common and distinct components are explained in this framework and some practical examples are given of these methods in the areas of (medical) biology and food science.Comment: 50 pages, 12 figure

Continuum of many-particle states near the metal-insulator transition in the Hubbard model

The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green's function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green's functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtained. The insulating solutions vary in the width of the Mott gap, while the metallic solutions differ in the shape of the spectral function in the vicinity of the Fermi level. Besides, different scenarios of the metal-insulator transition -- with a sudden onset of a band of mobile states near the Fermi level and with gradual closure of the Mott gap -- are observed with a change in temperature. In spite of these dissimilarities, all solutions have a common curve separating metallic and insulating states in the phase diagram. Near this curve metallic and insulating solutions coexist. For moderate Hubbard repulsions metallic solutions are not Fermi liquids.Comment: 10 pages, 9 figure

Systematics of Beringian threespine sticklebacks

Thesis (M.S.) University of Alaska Fairbanks, 2000In Pleistocene Beringia, large-scale glaciations exposed high latitude species to variable environmental conditions that created disjunct populations of terrestrial and marine species. The general nature of the dynamic biogeographic history of Beringia can be assessed by studying genetic patterns across many Beringian organisms. Mitochondrial DNA sequences were used to study the phylogenetic and phylogeographic structure of the threespine stickleback, Gasterosteus aculeatus. A 714 bp fragment of the cytochrome b gene was sequenced from 66 individuals from 17 locations extending from southeast Alaska northwest to coastal Siberia. These data were combined with 36 homologous cyt-b sequences from a previous study to provide a preliminary assessment of patterns of genetic variation in threespine stickleback- with a particular emphasis on Alaskan populations. Cytochrome b data show the existence of two major clades in the Pacific, with an extensive zone of overlap that spans the Bering Straits

The Rise and Fall of Water Net (Hydrodictyon reticulatum) in New Zealand

During the late 1980s to early 1990s a range of aquatic habitats in the central North Island of New Zealand were invaded by the filamentous green alga, water net Hydrodictyon reticulatum (Linn. Lagerheim). The alga caused significant economic and recreational impacts at major sites of infestation, but it was also associated with enhanced invertebrate numbers and was the likely cause of an improvement in the trout fishery. The causes of prolific growth of water net and the range of control options pursued are reviewed. The possible causes of its sudden decline in 1995 are considered, including physical factors, increase in grazer pressure, disease, and loss of genetic vigour

The distribution of pond snail communities across a landscape: separating out the influence of spatial position from local habitat quality for ponds in south-east Northumberland, UK

Ponds support a rich biodiversity because the heterogeneity of individual ponds creates, at the landscape scale, a diversity of habitats for wildlife. The distribution of pond animals and plants will be influenced by both the local conditions within a pond and the spatial distribution of ponds across the landscape. Separating out the local from the spatial is difficult because the two are often linked. Pond snails are likely to be affected by both local conditions, e.g. water hardness, and spatial patterns, e.g. distance between ponds, but studies of snail communities struggle distinguishing between the two. In this study, communities of snails were recorded from 52 ponds in a biogeographically coherent landscape in north-east England. The distribution of snail communities was compared to local environments characterised by the macrophyte communities within each pond and to the spatial pattern of ponds throughout the landscape. Mantel tests were used to partial out the local versus the landscape respective influences. Snail communities became more similar in ponds that were closer together and in ponds with similar macrophyte communities as both the local and the landscape scale were important for this group of animals. Data were collected from several types of ponds, including those created on nature reserves specifically for wildlife, old field ponds (at least 150 years old) primarily created for watering livestock and subsidence ponds outside protected areas or amongst coastal dunes. No one pond type supported all the species. Larger, deeper ponds on nature reserves had the highest numbers of species within individual ponds but shallow, temporary sites on farm land supported a distinct temporary water fauna. The conservation of pond snails in this region requires a diversity of pond types rather than one idealised type and ponds scattered throughout the area at a variety of sites, not just concentrated on nature reserves

A Tonal Analysis of Gurung, with Separate Systems for Register and Contour Pitch Features

An earlier analysis of Gurung, by Burton-Page in BSOAS, 17/1, 1955, put forward a single system, of two terms, for the word unit in the dialect spoken in Ghandrung: tones 1 and 2; the present analysis of the Gurung of a speaker from the centre of the Gurung area differs from Burton-Page's in that it distinguishes two tone systems: a two-term system (tones 1 and 2) for a difference in pitch register and a further two-term system (tones A and B) for a difference in pitch contour. Support for separating register-pitch and contour-pitch differences comes from three associated features, aspiration, phonation and voice: they apply to the register distinction but not to the contour distinction. Further support comes from comparing this tonal analysis with an identical analysis of a closely related language, Tamang, and also with the two-term system put forward for the word in Tibetan

Crawling Water Beetles of Wisconsin (Coleoptera: Haliplidae)

(excerpt) Haliplidae are smail water beetles, less than 5 mm long, that frequently occur in abundance in ponds, marshes, sloughs, and swamps and also along the margins of slow streams or lakes where there is not severe wave action. Adults are readily recognized by their yelloa- to orange ground color with black maculations on the elytra and sometimes on the head and pronotum (Figs. 1,3,4). They have a distinctive shape, being broadest at the basss of the elytra and tapered toward the posterior end. The metacoxae are covered by dis~ctive plates that are unique among water beetles (Fig. 2). The tarsi and tibiae of the adults are modified for swimming, and the beetles can swim quite well, although they mostly crawl among the vegetation. Adults and larvae are found among vegetation upon which they feed, filamentous algae being the primary source of food for most species, but detrims and animal material may form a portion of the diet in some species. In Wisconsin most species probably have a one-year life cycle and overwinter as adults. Eggs are laid during spring and early summer, usually in or upon algae. There are three larval instars, and pupation takes place in moist soil above the water line. Larvae have been derrihd for only a few species, so identification is based upon adult characteristics