656 research outputs found
Inferring phylogenetic trees under the general Markov model via a minimum spanning tree backbone
Phylogenetic trees are models of the evolutionary relationships among species, with species typically placed at the leaves of trees. We address the following problems regarding the calculation of phylogenetic trees. (1) Leaf-labeled phylogenetic trees may not be appropriate models of evolutionary relationships among rapidly evolving pathogens which may contain ancestor-descendant pairs. (2) The models of gene evolution that are widely used unrealistically assume that the base composition of DNA sequences does not evolve. Regarding problem (1) we present a method for inferring generally labeled phylogenetic trees that allow sampled species to be placed at non-leaf nodes of the tree. Regarding problem (2), we present a structural expectation maximization method (SEM-GM) for inferring leaf-labeled phylogenetic trees under the general Markov model (GM) which is the most complex model of DNA substitution that allows the evolution of base composition. In order to improve the scalability of SEM-GM we present a minimum spanning tree (MST) framework called MST-backbone. MST-backbone scales linearly with the number of leaves. However, the unrealistic location of the root as inferred on empirical data suggests that the GM model may be overtrained. MST-backbone was inspired by the topological relationship between MSTs and phylogenetic trees that was introduced by Choi et al. (2011). We discovered that the topological relationship does not necessarily hold if there is no unique MST. We propose so-called vertex-order based MSTs (VMSTs) that guarantee a topological relationship with phylogenetic trees.Phylogenetische BĂ€ume modellieren evolutionĂ€re Beziehungen zwischen Spezies, wobei die Spezies typischerweise an den BlĂ€ttern der BĂ€ume sitzen. Wir befassen uns mit den folgenden Problemen bei der Berechnung von phylogenetischen BĂ€umen. (1) Blattmarkierte phylogenetische BĂ€ume sind möglicherweise keine geeigneten Modelle der evolutionĂ€ren Beziehungen zwischen sich schnell entwickelnden Krankheitserregern, die Vorfahren-Nachfahren-Paare enthalten können. (2) Die weit verbreiteten Modelle der Genevolution gehen unrealistischerweise davon aus, dass sich die Basenzusammensetzung von DNA-Sequenzen nicht Ă€ndert. BezĂŒglich Problem (1) stellen wir eine Methode zur Ableitung von allgemein markierten phylogenetischen BĂ€umen vor, die es erlaubt, Spezies, fĂŒr die Proben vorliegen, an inneren des Baumes zu platzieren. BezĂŒglich Problem (2) stellen wir eine strukturelle Expectation-Maximization-Methode (SEM-GM) zur Ableitung von blattmarkierten phylogenetischen BĂ€umen unter dem allgemeinen Markov-Modell (GM) vor, das das komplexeste Modell von DNA-Substitution ist und das die Evolution von Basenzusammensetzung erlaubt. Um die Skalierbarkeit von SEM-GM zu verbessern, stellen wir ein Minimale Spannbaum (MST)-Methode vor, die als MST-Backbone bezeichnet wird. MST-Backbone skaliert linear mit der Anzahl der BlĂ€tter. Die Tatsache, dass die Lage der Wurzel aus empirischen Daten nicht immer realistisch abgeleitet warden kann, legt jedoch nahe, dass das GM-Modell möglicherweise ĂŒbertrainiert ist. MST-backbone wurde von einer topologischen Beziehung zwischen minimalen SpannbĂ€umen und phylogenetischen BĂ€umen inspiriert, die von Choi et al. 2011 eingefĂŒhrt wurde. Wir entdeckten, dass die topologische Beziehung nicht unbedingt Bestand hat, wenn es keinen eindeutigen minimalen Spannbaum gibt. Wir schlagen so genannte vertex-order-based MSTs (VMSTs) vor, die eine topologische Beziehung zu phylogenetischen BĂ€umen garantieren
Investigating the effect of in-plane spin directions for Precessing BBH systems
Morphology of coalescing BBH waveforms are affected by its spins. Waveform
models built for inference of source parameters have several in-built
approximations. In current precessing IMRPhenom and SEOBNR waveform models,
systems with the same spin magnitude but varying orientation of spins projected
on the orbital plane are effectively mapped to the same system (bar an overall
phase change) and the asymmetry due to precession between the and
modes is not modelled. In this study, we investigate the validity of these
approximations by generating numerical relativity (NR) simulations of
single-spin NR systems with varying in-plane spin directions (including several
superkick configurations) and provide an estimate of the SNR at which the
effect of varying in-plane spin directions would be measurable. This is done
computing the match between these waveforms and using these match values to
estimate the distinguishability SNR. We also use NR waveforms with different
spin magnitudes to compare the measurability of spin magnitude vs. in-plane
spin direction. We find that the in-plane spin direction could be measurable at
SNRs accessible by current generation detectors, with the distinguishability
SNR of varying in-plane spins comparable to or lower than varying the in-plane
spin magnitude. We then remove the mode-asymmetry content from the waveforms
and find that, i) removing mode-asymmetry increases the SNR at which in-plane
spin direction can be measured and ii) not modelling mode-asymmetry will lead
to measurement biases. The SNRs that we see at which the in-plane spins would
be measurable and at which mode-asymmetric content impacts the measurements are
the SNRs at which precession would be measurable, and we therefore conclude
that modelling in-plane spin direction and mode-asymmetry effects is necessary
for unbiassed measurements of precession.Comment: 13 pages, 8 figure
Selecting Optimal Minimum Spanning Trees that Share a Topological Correspondence with Phylogenetic Trees
Choi et. al (2011) introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. In this work we remove this indeterminacy by introducing so-called vertex-ranked MSTs. We note that the effectiveness of CLGrouping is inversely related to the number of leaves in the MST. This motivates the problem of finding a vertex-ranked MST with the minimum number of leaves (MLVRMST). We provide a polynomial time algorithm for the MLVRMST problem, and prove its correctness for graphs whose edges are weighted with tree-additive distances
Parameter Estimation with a spinning multi-mode waveform model: IMRPhenomHM
Gravitational waves from compact binary coalescence sources can be decomposed
into spherical-harmonic multipoles, the dominant being the quadrupole () modes. The contribution of sub-dominant modes towards total signal
power increases with increasing binary mass ratio and source inclination to the
detector. It is well-known that in these cases neglecting higher modes could
lead to measurement biases, but these have not yet been quantified with a
higher-mode model that includes spin effects. In this study, we use the
multi-mode aligned-spin phenomenological waveform model IMRPhenomHM to
investigate the effects of including multi-mode content in estimating source
parameters and contrast the results with using a quadrupole-only model
(IMRPhenomD). We use as sources IMRPhenomHM and hybrid EOB-NR waveforms over a
range of mass-ratio and inclination combinations, and recover the parameters
with IMRPhenomHM and IMRPhenomD. These allow us to quantify the accuracy of
parameter measurements using a multi-mode model, the biases incurred when using
a quadrupole-only model to recover full (multi-mode) signals, and the
systematic errors in the IMRPhenomHM model. We see that the parameters
recovered by multi-mode templates are more precise for all non-zero
inclinations as compared to quadrupole templates. For multi-mode injections,
IMRPhenomD recovers biased parameters for non-zero inclinations with lower
likelihood while IMRPhenomHM recovered parameters are accurate for most cases,
and if a bias exists, it can be explained as a combined effect of observational
priors and (in the case of hybrid-NR signals) waveform inaccuracies. For cases
where IMRPhenomHM recovers biased parameters, the bias is always smaller than
the corresponding IMRPhenomD recovery, and we conclude that IMRPhenomHM will be
sufficiently accurate to allow unbiased measurements for most GW observations.Comment: 14 pages, 7 figure
First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries
Gravitational-wave observations of binary black holes currently rely on
theoretical models that predict the dominant multipoles (l,m) of the radiation
during inspiral, merger and ringdown. We introduce a simple method to include
the subdominant multipoles to binary black hole gravitational waveforms, given
a frequency-domain model for the dominant multipoles. The amplitude and phase
of the original model are appropriately stretched and rescaled using
post-Newtonian results (for the inspiral), perturbation theory (for the
ringdown), and a smooth transition between the two. No additional tuning to
numerical-relativity simulations is required. We apply a variant of this method
to the non-precessing PhenomD model. The result, PhenomHM, constitutes the
first higher-multipole model of spinning black-hole binaries, and currently
includes the (l,m) = (2,2), (3,3), (4,4), (2,1), (3,2), (4,3) radiative
moments. Comparisons with numerical-relativity waveforms demonstrate that
PhenomHM is more accurate than dominant-multipole-only models for all binary
configurations, and typically improves the measurement of binary properties.Comment: 4 pages, 4 figure
Modelling and studying gravitational waves from black-hole-binary mergers
The source parameters of the first direct detection (GW150914 [3]) of gravitational waves
(GW) from a binary black hole (BBH) system were determined by using approximate models
of the BBH coalescence, the errors on which could be driven by the noise (statistical
errors) or the approximate nature of the model (systematic errors). To determine the systematic
errors, a set of numerical relativity (NR) waveforms with similar parameters as of
GW150914 were injected over a range of inclination and polarisation values and recovered
with IMRPhenomPv2. The main result of this study was that the systematic errors induced
due to waveform model inaccuracies were much smaller than corresponding statistical errors,
and hence, the statistical errors dominate the systematic for the inferred parameters of
GW150914.
For current precessing waveform models, the six dimensional spin space is mapped to a
two dimensional space of effective spin parameters. We investigate the effects of changing
the in-plane spin direction on the GW signal and determine whether these effects are strong
enough to be measured by current ground based GW detectors. We also study the effect
of disregarding the mode-asymmetry content present in the signals and attempt to answer
whether mode-asymmetries need to be included in future waveform models.
GW signals, when decomposed in the spin weighted spherical harmonic basis, are made
of its different modes (hlms), with the quadrupole mode being dominant. The waveform
model IMRPhenomHM models a few of the sub-dominant modes with the quadrupole mode for
aligned-spin binaries. We wanted to investigate the effects of using a multimode (IMRPhenomHM)
and quadrupole only (IMRPhenomD) waveform model to recover source parameters from
multimode signals (IMRPhenomHM signals) and real physical signals (NR waveform signals)
across a range of physical parameters and inclination values
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