Analogies between the crossing number and the tangle crossing number

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tanglegram is the minimum crossing number over all such drawings and is related to biologically relevant quantities, such as the number of times a parasite switched hosts. Our main results for tanglegrams which parallel known theorems for crossing numbers are as follows. The removal of a single matching edge in a tanglegram with $n$ leaves decreases the tangle crossing number by at most $n-3$, and this is sharp. Additionally, if $\gamma(n)$ is the maximum tangle crossing number of a tanglegram with $n$ leaves, we prove $\frac{1}{2}\binom{n}{2}(1-o(1))\le\gamma(n)<\frac{1}{2}\binom{n}{2}$. Further, we provide an algorithm for computing non-trivial lower bounds on the tangle crossing number in $O(n^4)$ time. This lower bound may be tight, even for tanglegrams with tangle crossing number $\Theta(n^2)$.Comment: 13 pages, 6 figure

Linking Hydrogen (δ2H) Isotopes in Feathers and Precipitation: Sources of Variance and Consequences for Assignment to Isoscapes

Background: Tracking small migrant organisms worldwide has been hampered by technological and recovery limitations and sampling bias inherent in exogenous markers. Naturally occurring stable isotopes of H (d 2 H) in feathers provide an alternative intrinsic marker of animal origin due to the predictable spatial linkage to underlying hydrologically driven flow of H isotopes into foodwebs. This approach can assess the likelihood that a migrant animal originated from a given location(s) within a continent but requires a robust algorithm linking H isotopes in tissues of interest to an appropriate hydrological isotopic spatio-temporal pattern, such as weighted-annual rainfall. However, a number of factors contribute to or alter expected isotopic patterns in animals. We present results of an extensive investigation into taxonomic and environmental factors influencing feather d 2 H patterns across North America. Principal Findings: Stable isotope data were measured from 544 feathers from 40 species and 140 known locations. For d 2 H, the most parsimonious model explaining 83 % of the isotopic variance was found with amount-weighted growingseason precipitation d 2 H, foraging substrate and migratory strategy. Conclusions/Significance: This extensive H isotopic analysis of known-origin feathers of songbirds in North America and elsewhere reconfirmed the strong coupling between tissue d 2 H and global hydrologic d 2 H patterns, and accounting for variance associated with foraging substrate and migratory strategy, can be used in conservation and research for th

Hydrodynamical simulations of the Sunyaev–Zel'dovich effect: the kinetic effect

We use hydrodynamical N-body simulations to study the kinetic Sunyaev–Zel'dovich effect. We construct sets of maps, one square degree in size, in three different cosmological models. We confirm earlier calculations that on the scales studied the kinetic effect is much smaller than the thermal (except close to the thermal null point), with an rms dispersion smaller by about a factor of 5 in the Rayleigh–Jeans region. We study the redshift dependence of the rms distortion and the pixel distribution at the present epoch. We compute the angular power spectra of the maps, including their redshift dependence, and compare them with the thermal Sunyaev–Zel'dovich effect and with the expected cosmic microwave background anisotropy spectrum as well as with determinations by other authors. We correlate the kinetic effect with the thermal effect both pixel-by-pixel and for identified thermal sources in the maps to assess the extent to which the kinetic effect is enhanced in locations of strong thermal signal

Catalog Extraction in SZ Cluster Surveys: a matched filter approach

We present a method based on matched multifrequency filters for extracting cluster catalogs from Sunyaev-Zel'dovich (SZ) surveys. We evaluate its performance in terms of completeness, contamination rate and photometric recovery for three representative types of SZ survey: a high resolution single frequency radio survey (AMI), a high resolution ground-based multiband survey (SPT), and the Planck all-sky survey. These surveys are not purely flux limited, and they loose completeness significantly before their point-source detection thresholds. Contamination remains relatively low at <5% (less than 30%) for a detection threshold set at S/N=5 (S/N=3). We identify photometric recovery as an important source of catalog uncertainty: dispersion in recovered flux from multiband surveys is larger than the intrinsic scatter in the Y-M relation predicted from hydrodynamical simulations, while photometry in the single frequency survey is seriously compromised by confusion with primary cosmic microwave background anisotropy. The latter effect implies that follow-up observations in other wavebands (e.g., 90 GHz, X-ray) of single frequency surveys will be required. Cluster morphology can cause a bias in the recovered Y-M relation, but has little effect on the scatter; the bias would be removed during calibration of the relation. Point source confusion only slightly decreases multiband survey completeness; single frequency survey completeness could be significantly reduced by radio point source confusion, but this remains highly uncertain because we do not know the radio counts at the relevant flux levels.Comment: 14 pages, 13 figures, replaced to match version accepted for publication in A&

Hydrodynamical simulations of the Sunyaev--Zel'dovich effect

We use a hydrodynamical N-body code to generate simulated maps, of size one square degree, of the thermal SZ effect. We study three different cosmologies; the currently-favoured low-density model with a cosmological constant, a critical-density model and a low-density open model. We stack simulation boxes corresponding to different redshifts in order to include contributions to the Compton y-parameter out to the highest necessary redshifts. Our main results are: 1. The mean y-distortion is around $4 \times 10^{-6}$ for low-density cosmologies, and $1 \times 10^{-6}$ for critical density. These are below current limits, but not by a wide margin in the former case. 2. In low-density cosmologies, the mean y-distortion comes from a broad range of redshifts, the bulk coming from $z < 2$ and a tail out to $z \sim 5$. For critical-density models, most of the contribution comes from $z < 1$. 3. The number of SZ sources above a given $y$ depends strongly on instrument resolution. For a one arcminute beam, there is around 0.1 sources per square degree with $y > 10^{-5}$ in a critical-density Universe, and around 8 such sources per square degree in low-density models. Low-density models with and without a cosmological constant give very similar results. 4. We estimate that the {\sc Planck} satellite will be able to see of order 25000 SZ sources if the Universe has a low density, or around 10000 if it has critical density.Comment: 9 pages LaTeX file with eleven figures (including four in colour) incorporated (uses mn.sty and epsf). Further colour images and animations at http://star-www.cpes.susx.ac.uk/~andrewl/sz/sz.html Updated to match published versio

One More Awareness Gap? The Behaviour–Impact Gap Problem

Preceding research has made hardly any attempt to measure the ecological impacts of pro-environmental behaviour in an objective way. Those impacts were rather supposed or calculated. The research described herein scrutinized the ecological impact reductions achieved through pro-environmental behaviour and raised the question how much of a reduction in carbon footprint can be achieved through voluntary action without actually affecting the socio-economic determinants of life. A survey was carried out in order to measure the difference between the ecological footprint of “green” and “brown” consumers. No significant difference was found between the ecological footprints of the two groups—suggesting that individual pro-environmental attitudes and behaviour do not always reduce the environmental impacts of consumption. This finding resulted in the formulation of a new proposition called the BIG (behaviour–impact gap) problem, which is an interesting addition to research in the field of environmental awareness gaps

A comparison of the galaxy peculiar velocity field with the PSCz gravity field-- A Bayesian hyper-parameter method

We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the \textit{IRAS}-PSC$z$ redshift survey and peculiar velocities measured using different distance indicators. In our analysis we find that the model--data comparison becomes unreliable beyond 70 \hmpc because of the inadequate sampling by \textit{IRAS} survey of prominent, distant superclusters, like the Shapley Concentration. On the other hand, the analysis of the velocity residuals show that the PSC$z$ gravity field provides an adequate model to the local, \le 70 \hmpc, peculiar velocity field. The hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the Bayesian framework constrains the amplitude of the linear flow to be $\beta=0.53 \pm 0.014$. For an rms density fluctuations in the PSC$z$ galaxy number density $\sigma_8^{\rm gal}=0.42\pm0.03$, we obtain an estimate of the growth rate of density fluctuations $f\sigma_{8}(z\sim0) = 0.42 \pm 0.033$, which is in excellent agreement with independent estimates based on different techniques.Comment: 14 pages, 32 figures, MNRAS in press, matched the MNRAS published versio

Detecting Sunyaev-Zel'dovich clusters with PLANCK: I. Construction of all-sky thermal and kinetic SZ-maps

All-sky thermal and kinetic Sunyaev-Zel'dovich (SZ) maps are presented for assessing how well the PLANCK-mission can find and characterise clusters of galaxies, especially in the presence of primary anisotropies of the cosmic microwave background (CMB) and various galactic and ecliptic foregrounds. The maps have been constructed from numerical simulations of structure formation in a standard LCDM cosmology and contain all clusters out to redshifts of z = 1.46 with masses exceeding 5e13 M_solar/h. By construction, the maps properly account for the evolution of cosmic structure, the halo-halo correlation function, the evolving mass function, halo substructure and adiabatic gas physics. The velocities in the kinetic map correspond to the actual density environment at the cluster positions. We characterise the SZ-cluster sample by measuring the distribution of angular sizes, the integrated thermal and kinetic Comptonisations, the source counts in the three relevant PLANCK-channels, and give the angular power-spectra of the SZ-sky. While our results are broadly consistent with simple estimates based on scaling relations and spherically symmetric cluster models, some significant differences are seen which may affect the number of cluster detectable by PLANCK.Comment: 14 pages, 16 figures, 3 tables, submitted to MNRAS, 05.Jul.200

Detection of structural mosaicism from targeted and whole-genome sequencing data.

Structural mosaic abnormalities are large post-zygotic mutations present in a subset of cells and have been implicated in developmental disorders and cancer. Such mutations have been conventionally assessed in clinical diagnostics using cytogenetic or microarray testing. Modern disease studies rely heavily on exome sequencing, yet an adequate method for the detection of structural mosaicism using targeted sequencing data is lacking. Here, we present a method, called MrMosaic, to detect structural mosaic abnormalities using deviations in allele fraction and read coverage from next-generation sequencing data. Whole-exome sequencing (WES) and whole-genome sequencing (WGS) simulations were used to calculate detection performance across a range of mosaic event sizes, types, clonalities, and sequencing depths. The tool was applied to 4911 patients with undiagnosed developmental disorders, and 11 events among nine patients were detected. For eight of these 11 events, mosaicism was observed in saliva but not blood, suggesting that assaying blood alone would miss a large fraction, possibly >50%, of mosaic diagnostic chromosomal rearrangements