12 research outputs found
Characterizing Distances of Networks on the Tensor Manifold
At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, or regime-shift detection. Recently, to explore such functional
properties, a convenient representation has been to model such dynamical
systems as a weighted graph consisting of a finite, but very large number of
interacting agents. This said, there exists very limited relevant statistical
theory that is able cope with real-life data, i.e., how does perform analysis
and/or statistics over a family of networks as opposed to a specific network or
network-to-network variation. Here, we are interested in the analysis of
network families whereby each network represents a point on an underlying
statistical manifold. To do so, we explore the Riemannian structure of the
tensor manifold developed by Pennec previously applied to Diffusion Tensor
Imaging (DTI) towards the problem of network analysis. In particular, while
this note focuses on Pennec definition of geodesics amongst a family of
networks, we show how it lays the foundation for future work for developing
measures of network robustness for regime-shift detection. We conclude with
experiments highlighting the proposed distance on synthetic networks and an
application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex
Networks 201
Statistical approaches to viral phylodynamics
The recent years have witnessed a rapid increase in the quantity and quality of
genomic data collected from human and animal pathogens, viruses in particular.
When coupled with mathematical and statistical models, these data allow us to
combine evolutionary theory and epidemiology to understand pathogen dynamics.
While these developments led to important epidemiological questions being tackled,
it also exposed the need for improved analytical methods. In this thesis I employ
modern statistical techniques to address two pressing issues in phylodynamics: (i)
computational tools for Bayesian phylogenetics and (ii) data integration. I detail
the development and testing of new transition kernels for Markov Chain Monte
Carlo (MCMC) for time-calibrated phylogenetics in Chapter 2 and show that an
adaptive kernel leads to improved MCMC performance in terms of mixing for a
range of data sets, in particular for a challenging Ebola virus phylogeny with 1610
taxa/sequences. As a trade-off, I also found that the new adaptive kernels have
longer warm up times in general, suggesting room for improvement. Chapter 3
shows how to apply state-of-the-art techniques to visualise and analyse phylogenetic
space and MCMC for time-calibrated phylogenies, which are crucial to the viral
phylodynamics analysis pipeline. I describe a pipeline for a typical phylodynamic
analysis which includes convergence diagnostics for continuous parameters and in
phylogenetic space, extending existing methods to deal with large time-calibrated
phylogenies. In addition I investigate different representations of phylogenetic space
through multi-dimensional scaling (MDS) or univariate distributions of distances
to a focal tree and show that even for the simplest toy examples phylogenetic
space remains complex and in particular not all metrics lead to desirable or useful
representations. On the data integration front, Chapters 4 and 5 detail the use data
from the 2013-2016 Ebola virus disease (EVD) epidemic in West Africa to show how
one can combine phylogenetic and epidemiological data to tackle epidemiological
questions. I explore the determinants of the Ebola epidemic in Chapter 4 through a
generalised linear model framework coupled with Bayesian stochastic search variable
selection (BSSVS) to assess the relative importance climatic and socio-economic
variables on EVD number of cases. In Chapter 5 I tackle the question of whether
a particular glycoprotein mutation could lead to increased human mortality from
EVD. I show that a principled analysis of the available data that accounts for several
sources of uncertainty as well as shared ancestry between samples does not allow us
to ascertain the presence of such effect of a viral mutation on mortality. Chapter
6 attempts to bring the findings of the thesis together and discuss how the field of
phylodynamics, in special its methodological aspect, might move forward
The Graph Curvature Calculator and the curvatures of cubic graphs
We classify all cubic graphs with either non-negative Ollivier-Ricci
curvature or non-negative Bakry-\'Emery curvature everywhere. We show in both
curvature notions that the non-negatively curved graphs are the prism graphs
and the M\"obius ladders. We also highlight an online tool for calculating the
curvature of graphs under several variants of these curvature notions that we
use in the classification. As a consequence of the classification result we
show, that non-negatively curved cubic expanders do not exist
Transforming phylogenetic networks: Moving beyond tree space
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent reticulate evolution. Unrooted phylogenetic networks form a special class of such networks, which naturally generalize unrooted phylogenetic trees. In this paper we define two operations on unrooted phylogenetic networks, one of which is a generalization of the well-known nearest-neighbor interchange (NNI) operation on phylogenetic trees. We show that any unrooted phylogenetic network can be transformed into any other such network using only these operations. This generalizes the well-known fact that any phylogenetic tree can be transformed into any other such tree using only NNI operations. It also allows us to define a generalization of tree space and to define some new metrics on unrooted phylogenetic networks. To prove our main results, we employ some fascinating new connections between phylogenetic networks and cubic graphs that we have recently discovered. Our results should be useful in developing new strategies to search for optimal phylogenetic networks, a topic that has recently generated some interest in the literature, as well as for providing new ways to compare networks