Diffusion Of Distances
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Encyclopedia of Distances
This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.
An Introduction to Laplacian Spectral Distances and Kernels
In geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances, such as commute time, biharmonic, diffusion, and wave distances. Within this context, this book is intended to provide a common background on the definition and computation of the Laplacian spectral kernels and distances for geometry processing and shape analysis. To this end, we define a unified representation of the isotropic and anisotropic discrete Laplacian operator on surfaces and volumes; then, we introduce the associated differential equations, i.e., the harmonic equation, the Laplacian eigenproblem, and the heat equation. Filtering the Laplacian spectrum, we introduce the Laplacian spectral distances, which generalize the commute-time, biharmonic, diffusion, and wave distances, and their discretization in terms of the Laplacian spectrum. As main applications, we discuss the design of smooth functions and the Laplacian smoothing of noisy scalar functions. All the reviewed numerical schemes are discussed and compared in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate with respect to shape representation, computational resources, and target application.
Frontiers in Invertebrate Physiology: A Collection of Reviews
This new 3-volume set provides informative reviews on the physiology of sponges, cnidarians, round and flat worms, annelids, echinoderms, and crustaceans, advancing our knowledge of the physiology of these major invertebrate groups (Phyla). Invertebrates exhibit the largest number of species and occupy virtually every conceivable ecological niche. They are economically important in food chains, they recycle organic waste, and they are crucial pollinators of plants and sources of food. They are also medically relevant as parasites that cause major diseases of both humans and livestock. Chapters on crustacean physiology are grouped in this volume and cover diverse physiological topics ranging from moulting, respiration, water balance, biomineralization, bioreceptors, and temperature regulation to the land adaptation of terrestrial crustaceans. The chapters are comprehensive and add new knowledge to crustacean biology. Volume 1 looks at non-bilaterians (sponges, cnidarians, placozoans) while echinoderms and annelids are covered in Volume 3.