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Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. UMAP has a rigorous math...

Materias / palabras clave: hermitian geometry, kähler and hyperkähler geometry, calabi-yau metrics, holomorphic dynamics, almost complex geometry; Science: Mathematics

Materias / palabras clave: Mathematics; Algorithm; Noise (video); Constraint (computer-aided design); Image (mathematics); Curvature; Projection (relational algebra); Manifold (fluid mechanics); Partial differential equation; Nonlinear system; Set...

Materias / palabras clave: Basic reproduction number; Ordinary differential equation; Stability (learning theory); Applied mathematics; Stability theory; Transmission (telecommunications); Manifold (fluid mechanics); Mathematics; Simple (philosoph...

We show how to use "complementary priors" to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast...

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningfu...

Recently, it has been proposed by Maldacena that large N limits of certain conformal field theories in d dimensions can be described in terms of supergravity (and string theory) on the product of d 4-1dimensional AdS spa...

1 Engine Types and Their Operations 2 Engine Design and Operating Parameters 3 Thermochemistry of Fuel-Air Mixtures 4 Properties of Working Fluids 5 Ideal Models of Engine Cycles 6 Gas Exchange Processes 7 SI Engine Fuel...

Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact repr...

Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture de...

We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compa...

Materias / palabras clave: topology, geometry, manifolds, fuzzy sets, differential topology, algebraic topology; Science: Mathematics

Materias / palabras clave: differential geometry, geometry, spaces of affine and projective connections, methods of studying immersed manifolds, elementary geometry, manifolds with a complex or almost complex structure; Science: Mathematics