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MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
The vast amount of knowledge in Cell Signaling gathered through reductionist efforts and omics technology is poised to approach a Systems Biology understanding of precise representations of cell structure and function and predictions at multi-scale levels despite the complexity. Super-resolution microscopy and single cell analysis are also providing opportunities to explore both spatial and temporal landscapes. Notably, many basic biological processes have been studied capturing mechanistic detail with the goal to understand cellular proliferation and differentiation, gene regulation, morphogenesis, metabolism, and cell-cell communication. Similarly, at the intracellular level, addressing functions such as self-assembly, phase separation, and transport is leading to insights not readily understood as linear pathways. Therefore, network-based mathematical modeling, delineating dynamic biochemical reactions through ordinary and partial differential equations, promises to discover emergent biological properties not heretofore expected.
The book integrates approaches from mathematics, physics and computer sciences to analyse the organisation of complex networks. Every organisational principle of networks is defined, quantified and then analysed for its influences on the properties and functions of molecular, biological, ecological and social networks.
This book focuses on the discoveries in M. truncatula genomic research which has been undertaken in the last two decades. Legumes are important for their economic values as food, feed, and fodder and also serve as the pillar of sustainable agriculture because of its biological nitrogen fixation capacity. Medicago truncatula was established as a model legume in the 1990s and has been well adopted as a model internationally since then. M. truncatula is an autogamous, diploid (2n = 16) species with a short generation time, and relatively small genome size (~375 Mbp). The M. truncatula genome was initially sequenced by the International Medicago Genome Annotation Group (IMGAG) in 2011 and has been well-annotated. M. truncatula research benefits from the availability of several genetic and genomic tools, such as gene expression atlas (MtGEA), insertion and neutron bombardment mutant populations, and a HapMap panel containing 384 sequenced inbred lines for genome-wide association studies. This book covers the current status and latest advancements of the M. truncatula genomics and transcriptomics resources along with a glimpse of newly developed tools that makes M. truncatula a front runner model in functional genomic studies.