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255
On the second eigenvalue and random walks in random dregular graphs
 Combinatorica
, 1991
"... The main goal of this paper is to estimate the magnitude of the second largest eigenvalue in absolute value, λ2, of (the adjacency matrix of) a random dregular graph, G. In order to do so, we study the probability that a random walk on a random graph returns to its originating vertex at the kth st ..."
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Cited by 62 (9 self)
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The main goal of this paper is to estimate the magnitude of the second largest eigenvalue in absolute value, λ2, of (the adjacency matrix of) a random dregular graph, G. In order to do so, we study the probability that a random walk on a random graph returns to its originating vertex at the kth step, for various values of k. Our main theorem about eigenvalues is that E {λ2(G)  m �
Transparent dynamic optimization: The design and implementation of Dynamo
, 1999
"... Dynamic optimization refers to the runtime optimization of a native program binary. This report describes the design and implementation of Dynamo, a prototype dynamic optimizer that is capable of optimizing a native program binary at runtime. Dynamo is a realistic implementation, not a simulation, t ..."
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Cited by 51 (2 self)
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Dynamic optimization refers to the runtime optimization of a native program binary. This report describes the design and implementation of Dynamo, a prototype dynamic optimizer that is capable of optimizing a native program binary at runtime. Dynamo is a realistic implementation, not a simulation, that is written entirely in userlevel software, and runs on a PARISC machine under the HPUX operating system. Dynamo does not depend on any special programming language, compiler, operating system or hardware support. Contrary to
Symphony: An Integrated Multimedia File System
, 1997
"... An integrated multimedia file system supports the storage and retrieval of multiple data types. In this paper, we first discuss various design methodologies for building integrated file systems and examine their tradeoffs. We argue that, to efficiently support the storage and retrieval of heterogene ..."
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Cited by 48 (5 self)
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An integrated multimedia file system supports the storage and retrieval of multiple data types. In this paper, we first discuss various design methodologies for building integrated file systems and examine their tradeoffs. We argue that, to efficiently support the storage and retrieval of heterogeneous data types, an integrated file system should enable the coexistence of multiple data type specific techniques. We then describe the design of Symphonyan integrated file system that achieves this objective. Some of the novel features of Symphony include: a QoSaware disk scheduling algorithm; support for data type specific placement, failure recovery, and caching policies; and support for assigning data type specific structure to files. We discuss the prototype implementation of Symphony, and present results of our preliminary experimental evaluation. Keywords: Multimedia file systems, multimedia operating systems, integrated file systems 1. INTRODUCTION Recent advances in compression...
The curious history of Faà di Bruno’s formula
 Amer. Math. Monthly
, 2002
"... the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t)) ..."
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Cited by 46 (0 self)
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the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t))
Detecting Perfect Powers In Essentially Linear Time
 Math. Comp
, 1998
"... This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n>1, either writes n as a perfect power or proves that n is not a perfect power; (3) proves, using Loxton's theorem on multiple linear forms in logarithms, th ..."
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Cited by 41 (12 self)
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This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n>1, either writes n as a perfect power or proves that n is not a perfect power; (3) proves, using Loxton's theorem on multiple linear forms in logarithms, that this perfectpower decomposition algorithm runs in time (log n) . 1.
Similaritybased approaches to natural language processing
, 1997
"... Statistical methods for automatically extracting information about associations between words or documents from large collections of text have the potential to have considerable impact in a number of areas, such as information retrieval and naturallanguagebased user interfaces. However, even huge ..."
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Cited by 40 (3 self)
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Statistical methods for automatically extracting information about associations between words or documents from large collections of text have the potential to have considerable impact in a number of areas, such as information retrieval and naturallanguagebased user interfaces. However, even huge bodies of text yield highly unreliable estimates of the probability of relatively common events, and, in fact, perfectly reasonable events may not occur in the training data at all. This is known as the sparse data problem. Traditional approaches to the sparse data problem use crude approximations. We propose a different solution: if we are able to organize the data into classes of similar events, then, if information about an event is lacking, we can estimate its behavior from information about similar events. This thesis presents two such similaritybased approaches, where, in general, we measure similarity by the KullbackLeibler divergence, an informationtheoretic quantity. Our first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster centroids are iteratively split to model finer distinctions. Our clustering method, which uses the technique of deterministic annealing,
Combinatorics of geometrically distributed random variables: Lefttoright maxima
 Discrete Mathematics
, 1996
"... Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1. ..."
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Cited by 39 (9 self)
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Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1.
An ObjectOriented Architecture for Text Retrieval
 In Conference Proceedings of RIAO'91, Intelligent Text and Image Handling
, 1991
"... For almost all aspects of information access systems it is still the case that their optimal composition and functionality is hotly debated. Moreover, different application scenarios put different demands on individual components. It is therefore of the essence to be able to quickly build systems th ..."
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Cited by 36 (10 self)
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For almost all aspects of information access systems it is still the case that their optimal composition and functionality is hotly debated. Moreover, different application scenarios put different demands on individual components. It is therefore of the essence to be able to quickly build systems that permit exploration of different designs and implementation strategies. This paper presents a software implementation architecture for text retrieval systems that facilitates (a) functional modularization (b) mixandmatch combination of module implementations and (c) definition of intermodule protocols. We show how an objectoriented approach easily accommodates this type of architecture. The design principles are exemplified by code examples in Common Lisp. Taken together these code examples constitute an operational retrieval system. The design principles and protocols implemented have also been instantiated in a large scale retrieval prototype in our research laboratory. 1 Introductio...