Results 1  10
of
19,451
A note on Finsler–Minkowski norms
 Houston Journal of Mathematics
"... Abstract. In this paper we prove the result that the metric tensor of a regular Finsler –Minkowski norm is automatically positive definite. 1. ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Abstract. In this paper we prove the result that the metric tensor of a regular Finsler –Minkowski norm is automatically positive definite. 1.
Hilbert metrics and Minkowski norms
 J. Geom
"... It is shown that the Hilbert geometry (D, hD) associated to a bounded convex domain D ⊂ E n is isometric to a normed vector space (V,   · ) if and only if D is an open nsimplex. One further result on the asymptotic geometry of Hilbert’s metric is obtained with corollaries for the behavior of g ..."
Abstract

Cited by 16 (4 self)
 Add to MetaCart
It is shown that the Hilbert geometry (D, hD) associated to a bounded convex domain D ⊂ E n is isometric to a normed vector space (V,   · ) if and only if D is an open nsimplex. One further result on the asymptotic geometry of Hilbert’s metric is obtained with corollaries for the behavior
Á.: On bisectors in Minkowski normed spaces
 Acta Math. Hungar
, 2000
"... In this paper we discuss the concept of the bisector of a segment in a Minkowski normed nspace. We prove that if the unit ball K of the space is strictly convex then all bisectors are topological images of a hyperplane of the embedding Euclidean nspace. The converse statement is not true. We give ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
In this paper we discuss the concept of the bisector of a segment in a Minkowski normed nspace. We prove that if the unit ball K of the space is strictly convex then all bisectors are topological images of a hyperplane of the embedding Euclidean nspace. The converse statement is not true. We give
VisualSEEk: a fully automated contentbased image query system
, 1996
"... 1 We describe a highly functional prototype system for searching by visual features in an image database. The VisualSEEk system is novel in that the user forms the queries by diagramming spatial arrangements of color regions. The system finds the images that contain the most similar arrangements of ..."
Abstract

Cited by 752 (31 self)
 Add to MetaCart
1 We describe a highly functional prototype system for searching by visual features in an image database. The VisualSEEk system is novel in that the user forms the queries by diagramming spatial arrangements of color regions. The system finds the images that contain the most similar arrangements of similar regions. Prior to the queries, the system automatically extracts and indexes salient color regions from the images. By utilizing efficient indexing techniques for color information, region sizes and absolute and relative spatial locations, a wide variety of complex joint color/spatial queries may be computed. KEYWORDS: image databases, contentbased retrieval, image indexing, similarity retrieval, spatial query. 1 INTRODUCTION In this paper we investigate a new contentbased image query system that enables querying by image regions and spatial layout. VisualSEEk is a hybrid system in that it integrates featurebased image indexing with spatial query methods. The integration relie...
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
Abstract

Cited by 5350 (67 self)
 Add to MetaCart
In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Locally weighted learning
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, ass ..."
Abstract

Cited by 594 (53 self)
 Add to MetaCart
This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
Abstract

Cited by 566 (11 self)
 Add to MetaCart
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
Abstract

Cited by 1108 (51 self)
 Add to MetaCart
This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
Abstract

Cited by 800 (26 self)
 Add to MetaCart
The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Results 1  10
of
19,451