Beyond Flatland : exploring graphs in many dimensions

Societies, technologies, economies, ecosystems, organisms, . . . Our world is composed of complex networks—systems with many elements that interact in nontrivial ways. Graphs are natural models of these systems, and scientists have made tremendous progress in developing tools for their analysis. However, research has long focused on relatively simple graph representations and problem specifications, often discarding valuable real-world information in the process. In recent years, the limitations of this approach have become increasingly apparent, but we are just starting to comprehend how more intricate data representations and problem formulations might benefit our understanding of relational phenomena. Against this background, our thesis sets out to explore graphs in five dimensions: descriptivity, multiplicity, complexity, expressivity, and responsibility. Leveraging tools from graph theory, information theory, probability theory, geometry, and topology, we develop methods to (1) descriptively compare individual graphs, (2) characterize similarities and differences between groups of multiple graphs, (3) critically assess the complexity of relational data representations and their associated scientific culture, (4) extract expressive features from and for hypergraphs, and (5) responsibly mitigate the risks induced by graph-structured content recommendations. Thus, our thesis is naturally situated at the intersection of graph mining, graph learning, and network analysis.Gesellschaften, Technologien, Volkswirtschaften, Ökosysteme, Organismen, . . . Unsere Welt besteht aus komplexen Netzwerken—Systemen mit vielen Elementen, die auf nichttriviale Weise interagieren. Graphen sind natürliche Modelle dieser Systeme, und die Wissenschaft hat bei der Entwicklung von Methoden zu ihrer Analyse große Fortschritte gemacht. Allerdings hat sich die Forschung lange auf relativ einfache Graphrepräsentationen und Problemspezifikationen beschränkt, oft unter Vernachlässigung wertvoller Informationen aus der realen Welt. In den vergangenen Jahren sind die Grenzen dieser Herangehensweise zunehmend deutlich geworden, aber wir beginnen gerade erst zu erfassen, wie unser Verständnis relationaler Phänomene von intrikateren Datenrepräsentationen und Problemstellungen profitieren kann. Vor diesem Hintergrund erkundet unsere Dissertation Graphen in fünf Dimensionen: Deskriptivität, Multiplizität, Komplexität, Expressivität, und Verantwortung. Mithilfe von Graphentheorie, Informationstheorie, Wahrscheinlichkeitstheorie, Geometrie und Topologie entwickeln wir Methoden, welche (1) einzelne Graphen deskriptiv vergleichen, (2) Gemeinsamkeiten und Unterschiede zwischen Gruppen multipler Graphen charakterisieren, (3) die Komplexität relationaler Datenrepräsentationen und der mit ihnen verbundenen Wissenschaftskultur kritisch beleuchten, (4) expressive Merkmale von und für Hypergraphen extrahieren, und (5) verantwortungsvoll den Risiken begegnen, welche die Graphstruktur von Inhaltsempfehlungen mit sich bringt. Damit liegt unsere Dissertation naturgemäß an der Schnittstelle zwischen Graph Mining, Graph Learning und Netzwerkanalyse

Computational approaches to discovering differentiation genes in the peripheral nervous system of drosophila melanogaster

In the common fruit fly, Drosophila melanogaster, neural cell fate specification is triggered by a group of conserved transcriptional regulators known as proneural factors. Proneural factors induce neural fate in uncommitted neuroectodermal progenitor cells, in a process that culminates in sensory neuron differentiation. While the role of proneural factors in early fate specification has been described, less is known about the transition between neural specification and neural differentiation. The aim of this thesis is to use computational methods to improve the understanding of terminal neural differentiation in the Peripheral Nervous System (PNS) of Drosophila. To provide an insight into how proneural factors coordinate the developmental programme leading to neural differentiation, expression profiling covering the first 3 hours of PNS development in Drosophila embryos had been previously carried out by Cachero et al. [2011]. The study revealed a time-course of gene expression changes from specification to differentiation and suggested a cascade model, whereby proneural factors regulate a group of intermediate transcriptional regulators which are in turn responsible for the activation of specific differentiation target genes. In this thesis, I propose to select potentially important differentiation genes from the transcriptional data in Cachero et al. [2011] using a novel approach centred on protein interaction network-driven prioritisation. This is based on the insight that biological hypotheses supported by diverse data sources can represent stronger candidates for follow-up studies. Specifically, I propose the usage of protein interaction network data because of documented transcriptome-interactome correlations, which suggest that differentially expressed genes encode products that tend to belong to functionally related protein interaction clusters. Experimental protein interaction data is, however, remarkably sparse. To increase the informative power of protein-level analyses, I develop a novel approach to augment publicly available protein interaction datasets using functional conservation between orthologous proteins across different genomes, to predict interologs (interacting orthologs). I implement this interolog retrieval methodology in a collection of open-source software modules called Bio:: Homology::InterologWalk, the first generalised framework using web-services for “on-the- fly” interolog projection. Bio::Homology::InterologWalk works with homology data for any of the hundreds of genomes in Ensembl and Ensembgenomes Metazoa, and with experimental protein interaction data curated by EBI Intact. It generates putative protein interactions and optionally collates meta-data into a prioritisation index that can be used to help select interologs with high experimental support. The methodology proposed represents a significant advance over existing interolog data sources, which are restricted to specific biological domains with fixed underlying data sources often only accessible through basic web-interfaces. Using Bio::Homology::InterologWalk, I build interolog models in Drosophila sensory neurons and, guided by the transcriptome data, find evidence implicating a small set of genes in a conserved sensory neuronal specialisation dynamic, the assembly of the ciliary dendrite in mechanosensory neurons. Using network community-finding algorithms I obtain functionally enriched communities, which I analyse using an array of novel computational techniques. The ensuing datasets lead to the elucidation of a cluster of interacting proteins encoded by the target genes of one of the intermediate transcriptional regulators of neurogenesis and ciliogenesis, fd3F. These targets are validated in vivo and result in improved knowledge of the important target genes activated by the transcriptional cascade, suggesting a scenario for the mechanisms orchestrating the ordered assembly of the cilium during differentiation

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282