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WideArea Traffic: The Failure of Poisson Modeling
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1995
"... Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 widearea traces, investigating a number of widearea TCP arrival processes (session and con ..."
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Cited by 1405 (21 self)
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Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 widearea traces, investigating a number of widearea TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that userinitiated TCP session arrivals, such as remotelogin and filetransfer, are wellmodeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible selfsimilarity of widearea traffic.
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 704 (4 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
Bayesian Density Estimation and Inference Using Mixtures
 Journal of the American Statistical Association
, 1994
"... We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation, and are exemplified by special cases where data are modelled as a sample from mixtures of normal distributions. Efficien ..."
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Cited by 398 (17 self)
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We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation, and are exemplified by special cases where data are modelled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates, assessment of modality, and the inference on the numbers of components. Also, convergence results are established for a general class of normal mixture models. Keywords: Kernel estimation; Mixtures of Dirichlet processes; Multimodality; Normal mixtures; Posterior sampling; Smoothing parameter estimation * Michael D. Escobar is Assistant Professor, Department of Statistics and Department of Preventive Medicine and Biostatistics, University ...
Tandem repeats finder: a program to analyze DNA sequences
, 1999
"... A tandem repeat in DNA is two or more contiguous, approximate copies of a pattern of nucleotides. Tandem repeats have been shown to cause human disease, may play a variety of regulatory and evolutionary roles and are important laboratory and analytic tools. Extensive knowledge about pattern size, co ..."
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Cited by 372 (6 self)
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A tandem repeat in DNA is two or more contiguous, approximate copies of a pattern of nucleotides. Tandem repeats have been shown to cause human disease, may play a variety of regulatory and evolutionary roles and are important laboratory and analytic tools. Extensive knowledge about pattern size, copy number, mutational history, etc. for tandem repeats has been limited by the inability to easily detect them in genomic sequence data. In this paper, we present a new algorithm for finding tandem repeats which works without the need to specify either the pattern or pattern size. We model tandem repeats by percent identity and frequency of indels between adjacent pattern copies and use statistically based recognition criteria. We demonstrate the algorithm's speed and its ability to detect tandem repeats that have undergone extensive mutational change by analyzing four sequences: the human frataxin gene, the human b T cell receptor locus sequence and two yeast chromosomes. These sequences range in size from 3 kb up to 700 kb. A World Wide Web server interface at c3.biomath.mssm.edu/trf.html has been established for automated use of the program.
The synchronization of periodic routing messages
 IEEE/ACM Transactions on Networking
, 1994
"... Abstract — The paper considers a network with many apparentlyindependent periodic processes and discusses one method by which these processes can inadvertent Iy become synchronized. In particular, we study the synchronization of periodic routing messages, and offer guidelines on how to avoid inadve ..."
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Cited by 264 (10 self)
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Abstract — The paper considers a network with many apparentlyindependent periodic processes and discusses one method by which these processes can inadvertent Iy become synchronized. In particular, we study the synchronization of periodic routing messages, and offer guidelines on how to avoid inadvertent synchronization. Using simulations and analysis, we study the process of synchronization and show that the transition from unsynchronized to synchronized traffic is not one of gradual degradation but is instead a very abrupt ‘phase transition’: in general, the addition of a single router will convert a completely unsynchronized traffic stream into a completely synchronized one. We show that synchronization can be avoided by the addition of randomization to the tra~c sources and quantify how much randomization is necessary. In addition, we argue that the inadvertent synchronization of periodic processes is likely to become an increasing problem in computer networks.
Random sampling with a reservoir
 ACM Transactions on Mathematical Software
, 1985
"... We introduce fast algorithms for selecting a random sample of n records without replacement from a pool of N records, where the value of N is unknown beforehand. The main result of the paper is the design and analysis of Algorithm Z; it does the sampling in one pass using constant space and in O(n(1 ..."
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Cited by 258 (3 self)
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We introduce fast algorithms for selecting a random sample of n records without replacement from a pool of N records, where the value of N is unknown beforehand. The main result of the paper is the design and analysis of Algorithm Z; it does the sampling in one pass using constant space and in O(n(1 + log(N/n))) expected time, which is optimum, up to a constant factor. Several optimizations are studied that collectively improve the speed of the naive version of the algorithm by an order of magnitude. We give an efficient Pascallike implementation that incorporates these modifications and that is suitable for general use. Theoretical and empirical results indicate that Algorithm Z outperforms current methods by a significant margin.
On the Length of Programs for Computing Finite Binary Sequences
 Journal of the ACM
, 1966
"... The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of instructions in programs. A modified form of Turing machine is studied from the same ..."
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Cited by 226 (7 self)
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The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of instructions in programs. A modified form of Turing machine is studied from the same point of view. An application to the problem of defining a patternless sequence is proposed in terms of the concepts here 2 G. J. Chaitin developed. Introduction In this paper the Turing machine is regarded as a general purpose computer and some practical questions are asked about programming it. Given an arbitrary finite binary sequence, what is the length of the shortest program for calculating it? What are the properties of those binary sequences of a given length which require the longest programs? Do most of the binary sequences of a given length require programs of about the same length? The questions posed above are answered in Part 1. In the course of answering them, the logical ...
A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation
 IEEE Transactions on Automatic Control
, 1992
"... Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This p ..."
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Cited by 213 (14 self)
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Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This paper presents an SA algorithm that is based on a "simultaneous perturbation" gradient approximation instead of the standard finite difference approximation of KieferWolfowitz type procedures. Theory and numerical experience indicate that the algorithm presented here can be significanfiy more efficient than the standard finite differencebased algorithms in largedimensional problems.
Evolutionary Programming Made Faster
 IEEE Transactions on Evolutionary Computation
, 1999
"... Evolutionary programming (EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper, a "fast EP" (FEP) is proposed which uses a Cauchy instead of Ga ..."
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Cited by 206 (36 self)
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Evolutionary programming (EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper, a "fast EP" (FEP) is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator. The relationship between FEP and classical EP (CEP) is similar to that between fast simulated annealing and the classical version. Both analytical and empirical studies have been carried out to evaluate the performance of FEP and CEP for different function optimization problems. This paper shows that FEP is very good at search in a large neighborhood while CEP is better at search in a small local neighborhood. For a suite of 23 benchmark problems, FEP performs much better than CEP for multimodal functions with many local minima while being comparable to CEP in performance for unimodal and multimodal functions with only a few local minima. This paper also shows the relationship between the search step size and the probability of finding a global optimum and thus explains why FEP performs better than CEP on some functions but not on others. In addition, the importance of the neighborhood size and its relationship to the probability of finding a nearoptimum is investigated. Based on these analyses, an improved FEP (IFEP) is proposed and tested empirically. This technique mixes different search operators (mutations). The experimental results show that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.