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BACKGROUND: Gene-expression analysis is increasingly important in biological research, with real-time reverse transcription PCR (RT-PCR) becoming the method of choice for high-throughput and accurate expression profiling...

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...

Abstract For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of si...

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficienc...

A diagram has been devised that can provide a concise statistical summary of how well patterns match each other in terms of their correlation, their root‐mean‐square difference, and the ratio of their variances. Alth...

We present ab initio quantum-mechanical molecular-dynamics simulations of the liquid-metal--amorphous-semiconductor transition in Ge. Our simulations are based on (a) finite-temperature density-functional theory of the o...

Deep convolutional neural networks have performed remarkably well on many Computer Vision tasks. However, these networks are heavily reliant on big data to avoid overfitting. Overfitting refers to the phenomenon when a n...

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessaril...

The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six...

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors ...

Materias / palabras clave: mathematical analysis, geometrical inequalities, metric spaces, measure theory, geometric mapping; Science: Mathematics: Analysis

Materias / palabras clave: mathematical analysis, partial differential equations, geometric analysis; Science: Mathematics: Analysis

Materias / palabras clave: integral and partial differential equations, dynamical systems, calculus of variations, geometric analysis; Science: Mathematics

Materias / palabras clave: geometry, geometric analysis, algebraic geometry, differential geometry, euclidean geometry; Science: Mathematics

Materias / palabras clave: functional analysis and operator theory, partial differential equations, applied mathematics, convex and geometric analysis, control and optimization; Science: Mathematics

Materias / palabras clave: computational geometry, geometric algorithms; Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software; Science: Mathematics: Analysis

Materias / palabras clave: nonlinear mathematical physics, nonlinear continuous and discrete equations of mathematical physics, integrability and non-integrability of continuous and discrete systems, painlevé analysis, geometry of soliton equatio...