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This monograph, co-authored by three longtime collaborators, aims to promote the interdisciplinary field of mathematical biology by providing accessible new approaches to study natural systems. As there is currently scarce literature on the applications of mathematical modelling for biology research, this book presents a new way of studying interactions at the level of populations, societies, ecosystems, and biomes through open-sourced modeling platforms. It offers an interdisciplinary approach to analyzing natural phenomena—for example, by showing how master equations developed to describe electrical circuits can also describe biological systems mathematically. Ultimately it promotes a method of study based on modelling and mathematical principles, facilitating collaboration between mathematicians, biologists, engineers, and other researchers to enrich knowledge of the world’s ecosystems.

Mathematics. --- Biomathematics. --- Mathematics of Planet Earth. --- Mathematical and Computational Biology. --- Biology --- Mathematics --- Math --- Science

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This monograph summarizes several decades of collaborations between ecologists and mathematicians, presenting novel applications in biological modeling. The authors are among the first researchers to pioneer the use of dynamical systems models to successfully describe and predict animal behavior in relation to environmental changes. The text highlights the biological and mathematical techniques used in the research, including three main components: 1) large data sets on natural populations in the field; 2) mathematical models rigorously tied to data, which describe, explain, and predict behavioral dynamics in relation to environmental variables; and 3) simplified, proof-of-concept models to probe dynamic mechanisms, suggest testable hypotheses, and allow study of the consequences of environmental change and evolving traits. It is a suitable text for field ecologists interested in the modeling procedures and conclusions addressed therein, as well as mathematicians interested in applications to population, ecological, and evolutionary dynamics.

Biomathematics. --- Geography --- Mathematical and Computational Biology. --- Mathematics of Planet Earth. --- Mathematics. --- Animal behavior. --- Animal populations. --- Poblacions animals --- Etologia --- Models matemàtics

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This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Geography --- Stochastic analysis. --- Stochastic models. --- Differential equations. --- Dynamics. --- Nonlinear theories. --- Mathematics of Planet Earth. --- Stochastic Analysis. --- Stochastic Modelling. --- Differential Equations. --- Applied Dynamical Systems. --- Mathematics.

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In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.

Mathematics. --- Probabilities. --- Climate. --- Mathematics of Planet Earth. --- Probability Theory and Stochastic Processes. --- Climate, general. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Climatology.

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The recent explosion of global and regional seismicity data in the world requires new methods of investigation of microseismicity and development of their modelling to understand the nature of whole earth mechanics. In this book, the author proposes a powerful tool to reveal the characteristic features of global and regional microseismicity big data accumulated in the databases of the world. The method proposed in this monograph is based on (1) transformation of stored big data to seismicity density data archives, (2) linear transformation of microseismicity density data matrixes to correlated seismicity matrixes by means of the singular value decomposition method, (3) time series analyses of globally and regionally correlated seismicity rates, and (4) the minimal non-linear equations approximation of their correlated seismicity rate dynamics. Minimal non-linear modelling is the manifestation for strongly correlated seismicity time series controlled by Langevin-type stochastic dynamic equations involving deterministic terms and random Gaussian noises. A deterministic term is composed minimally with correlated seismicity rate vectors of a linear term and of a term with a third exponent. Thus, the dynamics of correlated seismicity in the world contains linearly changing stable nodes and rapid transitions between them with transient states. This book contains discussions of future possibilities of stochastic extrapolations of global and regional seismicity in order to reduce earthquake disasters worldwide. The dataset files are available online and can be downloaded at springer.com.

Geophysics. --- Mathematics. --- Natural disasters. --- Big data. --- Geophysics/Geodesy. --- Mathematics of Planet Earth. --- Natural Hazards. --- Big Data. --- Data sets, Large --- Large data sets --- Data sets --- Natural calamities --- Disasters --- Math --- Science --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Seismology --- Data processing.