Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solid-state quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multiple-world theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.

Stern–Gerlach experiment --- channel entropy --- non-locality --- nonsignaling --- retro-causal channel --- communication complexity --- controlled-NOT --- Bell test --- quantum measurement --- quantum mechanics --- quantum transport --- semiconductor nanodevices --- optimization --- quantum correlation --- PR Box --- non-linear Schrödinger model --- retrocausality --- entanglement --- device-independent --- Einstein–Podolsky–Rosen argument --- quantum nonlocality --- parallel lives --- PR box --- nonlocal correlations --- hypothesis testing --- quantum bounds --- channel capacity --- Wigner-function simulations --- quantum correlations --- quantum --- pre- and post-selected systems --- local hidden variables --- density-matrix formalism --- collapse of the quantum state --- local polytope --- quantum teleportation of unknown qubit --- parity measurements --- uncertainty relations --- nonlocality --- hybrid entanglement --- selectivity filter --- p-value --- steering --- axioms for quantum theory --- no-signalling --- ion channels --- KS Box --- EPR steering --- local realism --- Non-contextuality inequality --- entropic uncertainty relation --- continuous-variable states --- nonlocal dissipation models --- Bell’s theorem --- tsallis entropy --- classical limit --- general entropies --- pigeonhole principle --- biological quantum decoherence --- discrete-variable states

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Mathematical physics. --- Diffusion. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Gases --- Liquids --- Separation (Technology) --- Solution (Chemistry) --- Solutions, Solid --- Matter --- Packed towers --- Semiconductor doping --- Physical mathematics --- Diffusion --- Properties --- Mathematics --- Affine space. --- Algebra. --- Axiom. --- Bell's theorem. --- Brownian motion. --- Central limit theorem. --- Classical mathematics. --- Classical mechanics. --- Clifford algebra. --- Combinatorial proof. --- Commutative property. --- Constructive quantum field theory. --- Continuum hypothesis. --- David Hilbert. --- Dimension (vector space). --- Discrete mathematics. --- Distribution (mathematics). --- Eigenfunction. --- Equation. --- Euclidean space. --- Experimental mathematics. --- Fermi–Dirac statistics. --- Feynman–Kac formula. --- First-order logic. --- Fokker–Planck equation. --- Foundations of mathematics. --- Fractal dimension. --- Gaussian process. --- Girsanov theorem. --- Gödel's incompleteness theorems. --- Hilbert space. --- Hilbert's program. --- Holomorphic function. --- Infinitesimal. --- Integer. --- Internal set theory. --- Interval (mathematics). --- Limit (mathematics). --- Mathematical induction. --- Mathematical optimization. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Measurable function. --- Measure (mathematics). --- Minkowski space. --- Natural number. --- Neo-Riemannian theory. --- Non-standard analysis. --- Number theory. --- Operator algebra. --- Ornstein–Uhlenbeck process. --- Orthonormal basis. --- Perturbation theory (quantum mechanics). --- Philosophy of mathematics. --- Predicate (mathematical logic). --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Projection (linear algebra). --- Pure mathematics. --- Pythagorean theorem. --- Quantum field theory. --- Quantum fluctuation. --- Quantum gravity. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Quantum system. --- Quantum teleportation. --- Random variable. --- Real number. --- Renormalization group. --- Renormalization. --- Riemann mapping theorem. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schrödinger equation. --- Scientific notation. --- Set (mathematics). --- Sign (mathematics). --- Sobolev inequality. --- Special relativity. --- Spectral theorem. --- Spin (physics). --- Statistical mechanics. --- Stochastic calculus. --- Stochastic differential equation. --- Tensor algebra. --- Theorem. --- Theoretical physics. --- Theory. --- Turing machine. --- Variable (mathematics). --- Von Neumann algebra. --- Wiener process. --- Wightman axioms. --- Zermelo–Fraenkel set theory.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

We present three main research fields in which multimedia cartography and the study of the effectiveness of multimedia maps are currently taking place. In each of these fields, we describe how published research is embedded in the broader context of map design and user studies. The research refers to contemporary technological trends such as web HTML5 standards, virtual reality, eye tracking, or 3D printing. Efficiency, performance, and usability studies of multimedia maps were also included. The research published in this issue is interdisciplinary. They combine traditional mapping methods with new technologies. They are searching for new places for cartography in, e.g., the environment of computer games. They combine the design of the map with its perception by users.

Research & information: general --- Geography --- cartographic design --- animated map --- people gathering presentation --- orthophoto --- dot distribution map --- buffer map --- drone image --- expert opinion --- objective effectiveness --- multiperspective cartographic visualization --- usefulness of visualizations --- pedestrian tracks --- complementary visualizations --- time–spatial behavior --- space–time paths --- trajectories --- set of visualizations --- sightseeing spot recommendation system --- social networking service (SNS) --- web-geographic information systems (GIS) --- recommendation system --- visiting frequency --- sightseeing spot information --- multimedia cartography --- web map --- graphical user interface --- eye-tracking --- UI/UX --- freeway junction --- topographic maps from the 19th century --- interactive web map --- Leaflet --- GeoJSON --- dashboard --- spatiotemporal analysis --- usability --- evaluation of cartographic multimedia --- gamer opinion --- immersion way --- graphical enrichment --- medieval stronghold --- virtual reality --- design process --- historico-geographical space --- cultural heritage --- engineering education --- image stitching --- information technology --- multimedia --- panorama --- thematic map --- mapping techniques transformation --- land use --- UAV --- geometric representation --- pedestrian --- chorochromatic maps --- dot map --- heat map --- mini-map --- virtual stronghold --- walking --- teleportation --- medium effectiveness --- Unity --- topographical space --- gamer --- gameplay --- eye tracking --- 3D printing --- topography --- terrain --- elevation --- geoscience education --- web --- Python --- Earth Engine --- open source --- effectiveness --- responsive GUI --- GUI effectiveness index --- road map --- route memorizing --- cartography --- choropleth map animation --- local outliers --- generalization --- animation --- spatial visualization --- multimedia cartographic product --- medium efficiency --- medium attractiveness