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Linear Maps
"... 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 ..."
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Cited by 7 (3 self)
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. 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
The GoGo Interaction Technique: Nonlinear Mapping for Direct Manipulation in VR
, 1996
"... The GoGo immersive interaction technique uses the metaphor of interactively growing the user's arm and nonlinear 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. ..."
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Cited by 235 (9 self)
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The GoGo immersive interaction technique uses the metaphor of interactively growing the user's arm and nonlinear 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
, 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 ..."
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Cited by 526 (20 self)
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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
"... 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 wellknown 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 wellknown theorems on compact linear mappings: T is compact if and only if T * is compact
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime 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 ..."
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Cited by 860 (3 self)
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We present a new polynomialtime 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
SupportVector Networks
 Machine Learning
, 1995
"... The supportvector network is a new learning machine for twogroup classification problems. The machine conceptually implements the following idea: input vectors are nonlinearly mapped to a very highdimension feature space. In this feature space a linear decision surface is constructed. Special pr ..."
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Cited by 3703 (35 self)
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The supportvector network is a new learning machine for twogroup classification problems. The machine conceptually implements the following idea: input vectors are nonlinearly mapped to a very highdimension feature space. In this feature space a linear decision surface is constructed. Special
ON THE MATRICES OF CENTRAL LINEAR MAPPINGS
"... Summary. We show that a central linear mapping of a projectively embedded Euclidean nspace onto a projectively embedded Euclidean mspace 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 nspace onto a projectively embedded Euclidean mspace 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
, 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 . . .
"... This paper presents a complete analytical characterization of a large class of central and noncentral 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 noncentral 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
Results 1  10
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