Results 1  10
of
2,546,679
Noncomputable Julia sets
 Journ. Amer. Math. Soc
"... Polynomial Julia sets have emerged as the most studied examples of fractal sets generated by a dynamical system. Apart from the beautiful mathematics, one of the reasons for their popularity is the beauty of the computergenerated images of such sets. The algorithms used to draw these pictures vary; ..."
Abstract

Cited by 35 (10 self)
 Add to MetaCart
Polynomial Julia sets have emerged as the most studied examples of fractal sets generated by a dynamical system. Apart from the beautiful mathematics, one of the reasons for their popularity is the beauty of the computergenerated images of such sets. The algorithms used to draw these pictures vary
Constructing NonComputable Julia Sets
 Proc. of STOC 2007
"... While most polynomial Julia sets are computable, it has been recently shown [12] that there exist noncomputable Julia sets. The proof was nonconstructive, and indeed there were doubts as to whether specific examples of parameters with noncomputable Julia sets could be constructed. It was also unk ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
While most polynomial Julia sets are computable, it has been recently shown [12] that there exist noncomputable Julia sets. The proof was nonconstructive, and indeed there were doubts as to whether specific examples of parameters with noncomputable Julia sets could be constructed. It was also
Constructing NonComputable Julia Sets
"... We show how to construct a specific polynomial with a noncomputable Julia set. In fact, in the case of Julia sets of quadratic polynomials we give a precise characterization of Julia sets with computable parameters. Moreover, assuming a widely believed conjecture in Complex Dynamics, we give a poly ..."
Abstract
 Add to MetaCart
We show how to construct a specific polynomial with a noncomputable Julia set. In fact, in the case of Julia sets of quadratic polynomials we give a precise characterization of Julia sets with computable parameters. Moreover, assuming a widely believed conjecture in Complex Dynamics, we give a
CONSTRUCTING LOCALLY CONNECTED NONCOMPUTABLE JULIA SETS
, 2008
"... Abstract. A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia s ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
sets are noncomputable, yet locally connected. 1. Preliminaries In this paper, we will assume that the reader is familiar with the concept of computability of a subset of R n and its applications to Julia sets of rational functions. We refer the reader to our paper [BY08a] and the book [BY08b
ON COMPUTABILITY OF JULIA SETS: ANSWERS TO QUESTIONS OF MILNOR AND SHUB
, 2006
"... Abstract. In this note we give answers to questions posed to us by J. Milnor and M. Shub, which shed further light on the structure of noncomputable Julia sets. 1. ..."
Abstract
 Add to MetaCart
Abstract. In this note we give answers to questions posed to us by J. Milnor and M. Shub, which shed further light on the structure of noncomputable Julia sets. 1.
Functions from a set to a set
 Journal of Formalized Mathematics
, 1989
"... function from a set X into a set Y, denoted by “Function of X,Y ”, the set of all functions from a set X into a set Y, denoted by Funcs(X,Y), and the permutation of a set (mode Permutation of X, where X is a set). Theorems and schemes included in the article are reformulations of the theorems of [1] ..."
Abstract

Cited by 1094 (23 self)
 Add to MetaCart
function from a set X into a set Y, denoted by “Function of X,Y ”, the set of all functions from a set X into a set Y, denoted by Funcs(X,Y), and the permutation of a set (mode Permutation of X, where X is a set). Theorems and schemes included in the article are reformulations of the theorems of [1
Relations defined on sets
 Journal of Formalized Mathematics
, 1989
"... Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse ima ..."
Abstract

Cited by 517 (0 self)
 Add to MetaCart
Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
Abstract

Cited by 526 (72 self)
 Add to MetaCart
This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
The SimpleScalar tool set, version 2.0
 Computer Architecture News
, 1997
"... This report describes release 2.0 of the SimpleScalar tool set, a suite of free, publicly available simulation tools that offer both detailed and highperformance simulation of modern microprocessors. The new release offers more tools and capabilities, precompiled binaries, cleaner interfaces, bette ..."
Abstract

Cited by 1827 (44 self)
 Add to MetaCart
This report describes release 2.0 of the SimpleScalar tool set, a suite of free, publicly available simulation tools that offer both detailed and highperformance simulation of modern microprocessors. The new release offers more tools and capabilities, precompiled binaries, cleaner interfaces
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
for correspondences – generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function which maps unordered feature sets to multiresolution histograms and computes a weighted histogram intersection in this space. This “pyramid match” computation is linear
Results 1  10
of
2,546,679