Results 1  10
of
133,678
The ordinal numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. We present the choice function rule in the beginning of the article. In the main part of the article we formalize the base of cardinal theory. In the first section we introduce the concept of cardinal numbers and order relations between them. We present here CantorBernstein theorem and oth ..."
Abstract

Cited by 722 (70 self)
 Add to MetaCart
Summary. We present the choice function rule in the beginning of the article. In the main part of the article we formalize the base of cardinal theory. In the first section we introduce the concept of cardinal numbers and order relations between them. We present here CantorBernstein theorem
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
Abstract

Cited by 778 (5 self)
 Add to MetaCart
Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
The pyramid match kernel: Discriminative classification with sets of image features
 IN ICCV
, 2005
"... Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondenc ..."
Abstract

Cited by 546 (29 self)
 Add to MetaCart
Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernelbased classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve
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
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.
A Behavioral Notion of Subtyping
 ACM Transactions on Programming Languages and Systems
, 1994
"... The use of hierarchy is an important component of objectoriented design. Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding of ..."
Abstract

Cited by 514 (18 self)
 Add to MetaCart
The use of hierarchy is an important component of objectoriented design. Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding
A Theory of Diagnosis from First Principles
 ARTIFICIAL INTELLIGENCE
, 1987
"... Suppose one is given a description of a system, together with an observation of the system's behaviour which conflicts with the way the system is meant to behave. The diagnostic problem is to determine those components of the system which, when assumed to be functioning abnormally, will explain ..."
Abstract

Cited by 1117 (5 self)
 Add to MetaCart
Suppose one is given a description of a system, together with an observation of the system's behaviour which conflicts with the way the system is meant to behave. The diagnostic problem is to determine those components of the system which, when assumed to be functioning abnormally
The Anatomy of a ContextAware Application
 WIRELESS NETWORKS, VOL
, 1999
"... We describe a platform for contextaware computing which enables applications to follow mobile users as they move around a building. The platform is particularly suitable for richly equipped, networked environments. The only item a user is required to carry is a small sensor tag, which identifies th ..."
Abstract

Cited by 532 (3 self)
 Add to MetaCart
We describe a platform for contextaware computing which enables applications to follow mobile users as they move around a building. The platform is particularly suitable for richly equipped, networked environments. The only item a user is required to carry is a small sensor tag, which identifies
Experiments with a New Boosting Algorithm
, 1996
"... In an earlier paper, we introduced a new “boosting” algorithm called AdaBoost which, theoretically, can be used to significantly reduce the error of any learning algorithm that consistently generates classifiers whose performance is a little better than random guessing. We also introduced the relate ..."
Abstract

Cited by 2176 (21 self)
 Add to MetaCart
In an earlier paper, we introduced a new “boosting” algorithm called AdaBoost which, theoretically, can be used to significantly reduce the error of any learning algorithm that consistently generates classifiers whose performance is a little better than random guessing. We also introduced
A translation approach to portable ontology specifications
 KNOWLEDGE ACQUISITION
, 1993
"... To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse — definitions of classes, relations, functions ..."
Abstract

Cited by 3282 (9 self)
 Add to MetaCart
To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse — definitions of classes, relations
Results 1  10
of
133,678