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Linear Maps

by Shuvendu K. Lahiri, Shaz Qadeer, David Walker
"... Verification of large programs is impossible without proof techniques that allow local reasoning and information hiding. In this paper, we resurrect, extend and modernize an old approach to this problem first considered in the context of the programming language Euclid, developed in the 70s. The cen ..."
Abstract - Cited by 7 (3 self) - Add to MetaCart
. The central idea is that rather than modeling the heap as a single total function from addresses (integers) to integers, we model the heap as a collection of partial functions with disjoint domains. We call each such partial function a linear map. Programmers may select objects from linear maps, update linear

LINEAR MAPS

by unknown authors
"... ar ..."
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Abstract not found

The Go-Go Interaction Technique: Non-linear Mapping for Direct Manipulation in VR

by Ivan Poupyrev , Mark Billinghurst, Suzanne Weghorst, Tadao Ichikawa , 1996
"... The Go-Go immersive interaction technique uses the metaphor of interactively growing the user's arm and non-linear mapping for reaching and manipulating distant objects. Unlike others, our technique allows for seamless direct manipulation of both nearby objects and those at a distance. ..."
Abstract - Cited by 235 (9 self) - Add to MetaCart
The Go-Go immersive interaction technique uses the metaphor of interactively growing the user's arm and non-linear mapping for reaching and manipulating distant objects. Unlike others, our technique allows for seamless direct manipulation of both nearby objects and those at a distance.

Lambertian Reflectance and Linear Subspaces

by Ronen Basri, David Jacobs , 2000
"... We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wi ..."
Abstract - Cited by 526 (20 self) - Add to MetaCart
We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a

CONSTRUCTIVE COMPACT LINEAR MAPPINGS

by Hajime Ishihara
"... In this paper, we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics. We prove the constructive substitutes for the classically well-known theorems on compact linear mappings: T is compact if and only if T * is compact; if S is ..."
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In this paper, we deal with compact linear mappings of a normed linear space, within the framework of Bishop's constructive mathematics. We prove the constructive substitutes for the classically well-known theorems on compact linear mappings: T is compact if and only if T * is compact

A NEW POLYNOMIAL-TIME ALGORITHM FOR LINEAR PROGRAMMING

by N. Karmarkar - COMBINATORICA , 1984
"... We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
Abstract - Cited by 860 (3 self) - Add to MetaCart
We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than

Support-Vector Networks

by Corinna Cortes, Vladimir Vapnik - Machine Learning , 1995
"... The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special pr ..."
Abstract - Cited by 3703 (35 self) - Add to MetaCart
The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special

ON THE MATRICES OF CENTRAL LINEAR MAPPINGS

by Hans Havlicek Wien
"... Summary. We show that a central linear mapping of a projectively embedded Euclidean n-space onto a projectively embedded Euclidean m-space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity ≥ 2m − n + 1. T ..."
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Summary. We show that a central linear mapping of a projectively embedded Euclidean n-space onto a projectively embedded Euclidean m-space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity ≥ 2m − n + 1

Tropical linear mappings on the plane

by M. J. De La Puente , 2009
"... In this paper we fully describe all tropical linear mappings in the tropical projective plane TP 2, that is, maps from the tropical plane to itself given by tropical multiplication by a 3 × 3 matrix A with entries in T. First we will allow only real entries in the matrix A and, only at the end of th ..."
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In this paper we fully describe all tropical linear mappings in the tropical projective plane TP 2, that is, maps from the tropical plane to itself given by tropical multiplication by a 3 × 3 matrix A with entries in T. First we will allow only real entries in the matrix A and, only at the end

Admissible linear map . . .

by Guillaume Batog, Xavier Goaoc, Jean Ponce
"... This paper presents a complete analytical characterization of a large class of central and non-central imaging devices dubbed linear cameras by Ponce [9]. Pajdla [7] has shown that a subset of these, the oblique cameras, can be modelled by a certain type of linear map. We give here a full tabulation ..."
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This paper presents a complete analytical characterization of a large class of central and non-central imaging devices dubbed linear cameras by Ponce [9]. Pajdla [7] has shown that a subset of these, the oblique cameras, can be modelled by a certain type of linear map. We give here a full
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