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An Invitation to Statistics in Wasserstein Space

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Book Series: SpringerBriefs in Probability and Mathematical Statistics ISBN: 9783030384388 Year: Pages: 147 DOI: 10.1007/978-3-030-38438-8 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-05-14 09:30:34
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This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph. ; Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature. Presents an up to date overview of the state of the art, including some original results, and discusses open problems. Suitable for self-study or to be used as a graduate level course text. Open access.

Biological Communities Respond to Multiple Human-Induced Aquatic Environment Change

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ISBN: 9783039285440 / 9783039285457 Year: Pages: 170 DOI: 10.3390/books978-3-03928-545-7 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Environmental Sciences
Added to DOAB on : 2020-06-09 16:38:57
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Perturbations linked to the direct and indirect impacts of human activities during the Anthropocene affect the structure and functioning of aquatic ecosystems to varying degrees. Some perturbations involve stress to aquatic life, including soil and water acidification, soil erosion, loss of base cations, release of trace metals/organic compounds, and application of essential nutrients capable of stimulating primary productivity. Superimposed onto these changes, climate warming impacts aquatic environments via altering species’ metabolic processes and by modifying food web interactions. The interaction stressors is difficult to predict because of the differential response of species and taxonomic groups, interacting additively, synergistically, or antagonistically. Whenever different trophic levels respond differently to climate warming, food webs are restructured; yet, the consequences of warming-induced changes for the food web structure and long-term population dynamics of different trophic levels remain poorly understood. Such changes are crucial in lakes, where food web production is mainly due to ectotherms, which are highly sensitive to changes in their surrounding environment. Due to its remarkable physical inertia, including thermal stability, global warming also has a profound effect on groundwater ecosystems. Combining contemporary and palaeo data is essential to understand the degree to which mechanisms of stressors impact on lake biological communities and lake ecosystem functioning. The degree to which alterations can affect aquatic ecosystem structure and functioning also requires functional diversity to be addressed at the molecular level, to reconstruct the role different species play in the transfer of material and energy through the food web. In this issue, we present examples of the impact of different stressors and their interaction on aquatic ecosystems, providing long-term, metabolic, molecular, and paleolimnological analyses.

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