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Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.

Research & information: general --- Mathematics & science --- Bregman divergence --- f-divergence --- Jensen–Bregman divergence --- Jensen diversity --- Jensen–Shannon divergence --- capacitory discrimination --- Jensen–Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data–processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson–Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker’s inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin–Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference --- n/a --- Jensen-Bregman divergence --- Jensen-Shannon divergence --- Jensen-Shannon centroid --- conditional Rényi divergence --- Rényi divergence --- Rényi mutual information --- strong data-processing inequalities --- Rényi entropy --- Carlson-Levin inequality --- Pinsker's inequality --- Augustin-Csiszár mutual information

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Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.

Research & information: general --- Mathematics & science --- Bregman divergence --- f-divergence --- Jensen-Bregman divergence --- Jensen diversity --- Jensen-Shannon divergence --- capacitory discrimination --- Jensen-Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data-processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson-Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker's inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin-Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference

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Divergence theorem. --- Functional analysis. --- Anàlisi funcional --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Gauss-Ostrogradsky theorem --- Gauss's theorem --- Vector algebra --- Vector analysis --- Càlcul funcional --- Càlcul de variacions --- Àlgebres de Hilbert --- Àlgebres topològiques --- Anàlisi funcional no lineal --- Anàlisi microlocal --- Espais analítics --- Espais de Hardy --- Espais d'Orlicz --- Espais funcionals --- Espais vectorials normats --- Espais vectorials --- Filtres digitals (Matemàtica) --- Funcionals --- Funcions vectorials --- Multiplicadors (Anàlisi matemàtica) --- Pertorbació (Matemàtica) --- Teoria d'operadors --- Teoria de distribucions (Anàlisi funcional) --- Teoria de functors --- Teoria de l'aproximació --- Teoria del funcional de densitat --- Teoria espectral (Matemàtica) --- Equacions funcionals --- Equacions integrals

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This book focuses on systematics, biogeography, and evolution of arachnids, a group of ancient chelicerate lineages that have taken on terrestrial lifestyles. The book opens with the questions of what arachnology represents, and where the field should go in the future. Twelve original contributions then dissect the current state-of-the-art in arachnological research. These papers provide innovative phylogenomic, evolutionary and biogeographic analyses and interpretations of new data and/or synthesize our knowledge to offer new directions for the future of arachnology.

BioGeoBEARS --- Caatinga --- dispersal --- Galapagos --- Neotropical --- speciation --- spiders --- tropical dry forests --- vicariance --- coin spider --- Nephilidae --- phylogenomics --- biogeography --- dispersal probability --- Arthropoda --- circular reasoning --- investigator bias --- paleontology --- Arachnida --- tissue --- X-rays --- micro-CT --- cerebrum --- nervous system --- neuroanatomy --- imaging --- Araneae --- biodiversity --- community ecology --- elevation --- Pantepui --- species turnover --- Tetragnatha --- dynamic disperser --- intermediate dispersal model of biogeography --- GAARlandia --- Tetragnathidae --- taxonomy --- taxonomic crisis --- species concepts --- data management --- monographic research --- molecular phylogeny --- divergence time --- relict group --- Linyphiidae --- phylogeny --- Caribbean biogeography --- arachnid --- araneae --- Micrathena --- long distance dispersal --- distribution --- diversity --- Salticidae --- target sequencing --- reduced representation sequencing (RRS) --- spider phylogenomics --- deep phylogeny --- molecular dating --- ancestral range analysis --- endemics --- founder-event --- intermediate dispersal model --- n/a --- Research. --- Biology. --- Microbiology.

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This book focuses on systematics, biogeography, and evolution of arachnids, a group of ancient chelicerate lineages that have taken on terrestrial lifestyles. The book opens with the questions of what arachnology represents, and where the field should go in the future. Twelve original contributions then dissect the current state-of-the-art in arachnological research. These papers provide innovative phylogenomic, evolutionary and biogeographic analyses and interpretations of new data and/or synthesize our knowledge to offer new directions for the future of arachnology.

Research. --- Biology. --- Microbiology. --- BioGeoBEARS --- Caatinga --- dispersal --- Galapagos --- Neotropical --- speciation --- spiders --- tropical dry forests --- vicariance --- coin spider --- Nephilidae --- phylogenomics --- biogeography --- dispersal probability --- Arthropoda --- circular reasoning --- investigator bias --- paleontology --- Arachnida --- tissue --- X-rays --- micro-CT --- cerebrum --- nervous system --- neuroanatomy --- imaging --- Araneae --- biodiversity --- community ecology --- elevation --- Pantepui --- species turnover --- Tetragnatha --- dynamic disperser --- intermediate dispersal model of biogeography --- GAARlandia --- Tetragnathidae --- taxonomy --- taxonomic crisis --- species concepts --- data management --- monographic research --- molecular phylogeny --- divergence time --- relict group --- Linyphiidae --- phylogeny --- Caribbean biogeography --- arachnid --- araneae --- Micrathena --- long distance dispersal --- distribution --- diversity --- Salticidae --- target sequencing --- reduced representation sequencing (RRS) --- spider phylogenomics --- deep phylogeny --- molecular dating --- ancestral range analysis --- endemics --- founder-event --- intermediate dispersal model