An introduction to geometric and topological methods to analyze large scale biological data; includes statistics and genomic applications.

Network science has accelerated a deep and successful trend in research that influences a range of disciplines like mathematics, graph theory, physics, statistics, data science and computer science (just to name a few) and adapts the relevant techniques and insights to address relevant but disparate social, biological, technological questions. We are now in an era of 'big biological data' supported by cost-effective high-throughput genomic, transcriptomic, proteomic, metabolomic data collection techniques that allow one to take snapshots of the cells' molecular profiles in a systematic fashion. Moreover recently, also phenotypic data, data on diseases, symptoms, patients, etc. are being collected at nation-wide level thus giving us another source of highly related (causal) 'big data'. This wealth of data is usually modeled as networks (aka binary relations, graphs or webs) of interactions, (including protein-protein, metabolic, signaling and transcription-regulatory interactions). The network model is a key view point leading to the uncovering of mesoscale phenomena, thus providing an essential bridge between the observable phenotypes and 'omics' underlying mechanisms. Moreover, network analysis is a powerful 'hypothesis generation' tool guiding the scientific cycle of 'data gathering', 'data interpretation, 'hypothesis generation' and 'hypothesis testing'. A major challenge in contemporary research is the synthesis of deep insights coming from network science with the wealth of data (often noisy, contradictory, incomplete and difficult to replicate) so to answer meaningful biological questions, in a quantifiable way using static and dynamic properties of biological networks.

The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.

Written for non-experts, this volume introduces the mechanisms that underlie reticulate evolution. Chapters are either accompanied with glossaries that explain new terminology or timelines that position pioneering scholars and their major discoveries in their historical contexts. The contributing authors outline the history and original context of discovery of symbiosis, symbiogenesis, lateral gene transfer, hybridization or divergence with gene flow and infectious heredity. By applying key insights from the areas of molecular (phylo)genetics, microbiology, virology, ecology, systematics, immunology, epidemiology and computational science, they demonstrate how reticulate evolution impacts successful survival, fitness and speciation. Reticulate evolution brings forth a challenge to the standard Neo-Darwinian framework, which defines life as the outcome of bifurcation and ramification patterns brought forth by the vertical mechanism of natural selection. Reticulate evolution puts forward a pattern in the tree of life that is characterized by horizontal mergings and lineage crossings induced by symbiosis, symbiogenesis, lateral gene transfer, hybridization or divergence with gene flow and infective heredity, making the “tree of life” look more like a “web of life.” On an epistemological level, the various means by which hereditary material can be transferred horizontally challenges our classic notions of units and levels of evolution, fitness, modes of transmission, linearity, communities and biological individuality. The case studies presented examine topics including the origin of the eukaryotic cell and its organelles through symbiogenesis; the origin of algae through primary and secondary symbiosis and dinoflagellates through tertiary symbiosis; the superorganism and holobiont as units of evolution; how endosymbiosis induces speciation in multicellular life forms; transferrable and non-transferrable plasmids and how they symbiotically interact with their host; the means by which pro- and eukaryotic organisms transfer genes laterally (bacterial transformation, transduction and conjugation as well as transposons and other mobile genetic elements); hybridization and divergence with gene flow in sexually-reproducing individuals; current (human) microbiome and viriome studies that impact our knowledge concerning the evolution of organismal health and acquired immunity; and how symbiosis and symbiogenesis can be modelled in computational evolution.

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.