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On Radix Representation of Rings
 IEEE Transactions on Computers
, 1997
"... This paper presents a thorough analysis of radix representations of elements from general rings, in particular we study the questions of redundancy, completeness and mappings into such representations. After a brief description of the more usual representations of integers, a more detailed analysis ..."
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Cited by 9 (2 self)
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This paper presents a thorough analysis of radix representations of elements from general rings, in particular we study the questions of redundancy, completeness and mappings into such representations. After a brief description of the more usual representations of integers, a more detailed analysis
Nonnegative Radix Representations for the Orthant ...
, 1996
"... Let A be a nonnegative real matrix which is expanding, i.e. all eigenvalues jj ? 1. Suppose that j det(A)j is an integer and let D consists of exactly j det(A)j nonnegative vectors in R n . We classify all pairs (A; D) such that all x in the orthant R n + have at least one radix expansion using ..."
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Cited by 1 (0 self)
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Let A be a nonnegative real matrix which is expanding, i.e. all eigenvalues jj ? 1. Suppose that j det(A)j is an integer and let D consists of exactly j det(A)j nonnegative vectors in R n . We classify all pairs (A; D) such that all x in the orthant R n + have at least one radix expansion using
Radix representations, selfaffine tiles, and multivariable wavelets
 Proc. Amer. Math. Soc
"... Abstract. We investigate the connection between radix representations for Z n and selfaffine tilings of R n. We apply our results to show that Haarlike multivariable wavelets exist for all dilation matrices that are sufficiently large. 1. ..."
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Cited by 5 (0 self)
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Abstract. We investigate the connection between radix representations for Z n and selfaffine tilings of R n. We apply our results to show that Haarlike multivariable wavelets exist for all dilation matrices that are sufficiently large. 1.
Thuswaldner, Generalized radix representations and dynamical systems
 II, Acta Arith
"... Abstract. For r = (r1,..., rd) ∈ R d the map τr: Z d → Z d given by τr(a1,..., ad) = (a2,..., ad, −⌊r1a1 + · · · + rdad⌋) is called a shift radix system if for each a ∈ Zd there exists an integer k> 0 with τk r (a) = 0. As shown in the first two parts of this series of papers shift radix sys ..."
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Cited by 47 (17 self)
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Abstract. For r = (r1,..., rd) ∈ R d the map τr: Z d → Z d given by τr(a1,..., ad) = (a2,..., ad, −⌊r1a1 + · · · + rdad⌋) is called a shift radix system if for each a ∈ Zd there exists an integer k> 0 with τk r (a) = 0. As shown in the first two parts of this series of papers shift radix
On a generalization of the radix representation  a survey
 IN ”HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS”, FIELDS INSTITUTE COMMUCATIONS
, 2004
"... ..."
FFTW: An Adaptive Software Architecture For The FFT
, 1998
"... FFT literature has been mostly concerned with minimizing the number of floatingpoint operations performed by an algorithm. Unfortunately, on presentday microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have ..."
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Cited by 605 (4 self)
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FFT literature has been mostly concerned with minimizing the number of floatingpoint operations performed by an algorithm. Unfortunately, on presentday microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have a larger impact on performance. Consequently, one must know the details of a computer architecture in order to design a fast algorithm. In this paper, we propose an adaptive FFT program that tunes the computation automatically for any particular hardware. We compared our program, called FFTW, with over 40 implementations of the FFT on 7 machines. Our tests show that FFTW's selfoptimizing approach usually yields significantly better performance than all other publicly available software. FFTW also compares favorably with machinespecific, vendoroptimized libraries. 1. INTRODUCTION The discrete Fourier transform (DFT) is an important tool in many branches of science and engineering [1] and...
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 ..."
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Cited by 546 (29 self)
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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 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 in the number of features, and it implicitly finds correspondences based on the finest resolution histogram cell where a matched pair first appears. Since the kernel does not penalize the presence of extra features, it is robust to clutter. We show the kernel function is positivedefinite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels. We demonstrate our algorithm on object recognition tasks and show it to be accurate and dramatically faster than current approaches.
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping generalpurpose computation to graphics hardware. We begin with the technical motivations that underlie generalpurpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping generalpurpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in generalpurpose application development on graphics hardware.
Tapestry: A Resilient Globalscale Overlay for Service Deployment
 IEEE Journal on Selected Areas in Communications
, 2004
"... We present Tapestry, a peertopeer overlay routing infrastructure offering efficient, scalable, locationindependent routing of messages directly to nearby copies of an object or service using only localized resources. Tapestry supports a generic Decentralized Object Location and Routing (DOLR) API ..."
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Cited by 593 (14 self)
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We present Tapestry, a peertopeer overlay routing infrastructure offering efficient, scalable, locationindependent routing of messages directly to nearby copies of an object or service using only localized resources. Tapestry supports a generic Decentralized Object Location and Routing (DOLR) API using a selfrepairing, softstate based routing layer. This paper presents the Tapestry architecture, algorithms, and implementation. It explores the behavior of a Tapestry deployment on PlanetLab, a global testbed of approximately 100 machines. Experimental results show that Tapestry exhibits stable behavior and performance as an overlay, despite the instability of the underlying network layers. Several widelydistributed applications have been implemented on Tapestry, illustrating its utility as a deployment infrastructure.
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