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Embedding theorems. --- CR submanifolds. --- Manifolds (Mathematics) --- Embeddings (Mathematics) --- Kernel functions. --- Asymptotic expansions. --- CR-sous-variétés --- Théorèmes de plongement --- Variétés (Mathématiques) --- Plongements (Mathématiques) --- Noyaux (Mathématiques) --- Développements asymptotiques

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The purpose of this Special Issue is to create an an academic platform whereby high-quality research papers are published on the applications of innovative AI algorithms to transportation planning and operation. The authors present their original research articles related to the applications of AI or machine-learning techniques to transportation planning and operation. The topics of the articles encompass traffic surveillance, traffic safety, vehicle emission reduction, congestion management, traffic speed forecasting, and ride sharing strategy.

History of engineering & technology --- autoencoder --- deep learning --- traffic volume --- vehicle counting --- CycleGAN --- bottleneck and gridlock identification --- gridlock prediction --- urban road network --- long short-term memory --- link embedding --- traffic speed prediction --- traffic flow centrality --- reachability analysis --- spatio-temporal data --- artificial neural network --- context-awareness --- dynamic pricing --- reinforcement learning --- ridesharing --- supply improvement --- taxi --- preventive automated driving system --- automated vehicle --- traffic accidents --- deep neural networks --- vehicle GPS data --- driving cycle --- micro-level vehicle emission estimation --- link emission factors --- MOVES --- black ice --- CNN --- prevention

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This Special Issue is a book composed by collecting documents published through peer review on the research of various advanced technologies related to applications and theories of signal processing for multimedia systems using ML or advanced methods. Multimedia signals include image, video, audio, character recognition and optimization of communication channels for networks. The specific contents included in this book are data hiding, encryption, object detection, image classification, and character recognition. Academics and colleagues who are interested in these topics will find it interesting to read.

Technology: general issues --- History of engineering & technology --- data hiding --- AMBTC --- BTC --- Hamming code --- LSB --- predicate encryption --- inner product encryption --- constant-size private key --- efficient decryption --- constant pairing computations --- watermarking --- self-embedding --- digital signature --- fragile watermarking --- constrained backtracking matching pursuit --- sparse reconstruction --- compressed sensing --- greedy pursuit algorithm --- image processing --- visual surveillance --- deep learning --- object detection --- latency optimization --- mobile edge cloud --- connected autonomous cars --- smart city --- video surveillance --- physical layer security --- secure transmission --- secrecy capacity --- secrecy capacity optimization artificial noise --- power allocation --- channel estimation error --- neural network --- transfer learning --- scalograms --- MFCC --- Log-mel --- pre-trained models --- seismic patch classification --- CNN-features --- data complexity --- handwritten text recognition --- Residual Network --- Transformer model --- named entity recognition --- n/a

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The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Cartes harmoniques --- Harmonic maps --- Harmonische kaarten --- Immersies (Wiskunde) --- Immersions (Mathematics) --- Immersions (Mathématiques) --- Harmonic maps. --- Differential equations, Elliptic --- Applications harmoniques --- Immersions (Mathematiques) --- Équations différentielles elliptiques --- Numerical solutions. --- Solutions numériques --- Équations différentielles elliptiques --- Solutions numériques --- Differential equations [Elliptic] --- Numerical solutions --- Embeddings (Mathematics) --- Manifolds (Mathematics) --- Mappings (Mathematics) --- Maps, Harmonic --- Arc length. --- Catenary. --- Clifford algebra. --- Codimension. --- Coefficient. --- Compact space. --- Complex projective space. --- Connected sum. --- Constant curvature. --- Corollary. --- Covariant derivative. --- Curvature. --- Cylinder (geometry). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Differential geometry. --- Elliptic partial differential equation. --- Embedding. --- Energy functional. --- Equation. --- Existence theorem. --- Existential quantification. --- Fiber bundle. --- Gauss map. --- Geometry and topology. --- Geometry. --- Gravitational field. --- Harmonic map. --- Hyperbola. --- Hyperplane. --- Hypersphere. --- Hypersurface. --- Integer. --- Iterative method. --- Levi-Civita connection. --- Lie group. --- Mathematics. --- Maximum principle. --- Mean curvature. --- Normal (geometry). --- Numerical analysis. --- Open set. --- Ordinary differential equation. --- Parabola. --- Quadratic form. --- Sign (mathematics). --- Special case. --- Stiefel manifold. --- Submanifold. --- Suggestion. --- Surface of revolution. --- Symmetry. --- Tangent bundle. --- Theorem. --- Vector bundle. --- Vector space. --- Vertical tangent. --- Winding number. --- Differential equations, Elliptic - Numerical solutions

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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

coarse structure --- descriptive set theory --- group representation --- thick set --- free topological group --- character --- selectively sequentially pseudocompact --- separable topological group --- quotient group --- Chabauty topology --- pseudo-?-bounded --- topological group --- free precompact Boolean group --- right-angled Artin groups --- Neretin’s group --- coarse space --- ultrafilter space --- endomorphism --- separable --- absolutely closed topological group --- tree --- strongly pseudocompact --- Gromov’s compactification --- dynamical system --- semigroup compactification --- tame function --- compact topological semigroup --- vast set --- space of closed subgroups --- reflexive group --- Lie group --- matrix coefficient --- maximal ideal --- topological semigroup --- ballean --- continuous inverse algebra --- extension --- subgroup --- Thompson’s group --- scale --- isomorphic embedding --- arrow ultrafilter --- H-space --- paratopological group --- pseudocompact --- Ramsey ultrafilter --- fibre bundle --- locally compact group --- product --- large set in a group --- Vietoris topology --- topological group of compact exponent --- Bourbaki uniformity --- p-compact --- mapping cylinder --- syndetic set --- p-adic Lie group --- Boolean topological group --- non-trivial convergent sequence --- fixed point algebra --- polish group topologies --- varieties of coarse spaces --- piecewise syndetic set --- maximal space