As the World Wide Web (Web) is increasingly adopted as the infrastructure for large-scale distributed information systems, issues of performance modeling become ever more critical. In particular, locality of reference is an important property in the performance modeling of distributed information systems. In the case of the Web, understanding the nature of reference locality will help improve the design of middleware, such as caching, prefetching, and document dissemination systems. For example, good measurements of reference locality would allow us to generate synthetic reference streams with accurate performance characteristics, would allow us to compare empirically measured streams to explain differences, and would allow us to predict expected performance for system design and capacity planning. In this paper we propose models for both temporal and spatial locality of reference in streams of requests arriving at Web servers. We show that simple models based only on document popularity (likelihood of reference) are insufficient for capturing either temporal or spatial locality. Instead, we rely on an equivalent, but numerical, representation of a reference stream: a stack distance trace. We show that temporal locality can be characterized by

Abstract. For an operator, A, with cyclic vector ϕ, we study A + λP where P is the rank one projection onto multiples of ϕ. If [α, β] ⊂ spec(A) andA has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s. The subject of rank one perturbations of self-adjoint operators and the closely related issue of the boundary condition dependence of Sturm-Liouville operators on [0, ∞) has a long history. We’re interested here in the connection with Borel-Stieltjes transforms of measures (Im z>0):

We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical systems. Lutz (2000) has recently proven a simple characterization of Hausdorff dimension in terms of gales, which are betting strategies that generalize martingales. Imposing various computability and complexity constraints on these gales produces a spectrum of effective versions of Hausdorff dimension, including constructive, computable, polynomial-space, polynomial-time, and finite-state dimensions. Work by several investigators has already used these effective dimensions to shed significant new light on a variety of topics in theoretical computer science. In this paper we show that packing dimension can also be characterized in terms of gales. Moreover, even though the usual definition of packing dimension is considerably more complex than that of Hausdorff dimension, our gale characterization of packing dimension is an exact dual

. We study relations between quantum dynamics and spectral properties, concentrating on spectral decompositions which arise from decomposing measures with respect to dimensional Hausdorff measures. 1. Introduction Let H be a separable Hilbert space, H : H ! H a self adjoint operator, and / 2 H (with k/k = 1). The spectral measure ¯/ of / (and H ) is uniquely defined by [24]: h/ ; f(H)/i = Z oe(H) f(x) d¯/ (x) ; (1:1) for any measurable (Borel) function f . The time evolution of the state / , in the Schrodinger picture of quantum mechanics, is given by /(t) = e \GammaiHt / : (1:2) The relations between various properties of the spectral measure ¯/ (with an emphasis on "fractal" properties) and the nature of the time evolution have been the subject of several recent papers [7,13,15--18,20,22,33,36,39]. Our purpose in this paper is twofold: First, we use a theory, due to Rogers and Taylor [28,29], of decomposing singular continuous measures with respect to Hausdorff measures to i...

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For describing the local structure of a random self-similar measure we use the multifractal decomposition of its support into sets of points of different local dimension. Under the strong open set condition we compute the Hausdorff dimensions of these sets and the generalized dimensions of the random self-similar measure. Furthermore, the tangential distribution of the random self--similar measure is investigated.

We generalize the definition of the fractional Brownian motion of exponent H to the case where H is no longer a constant, but a function of the time index of the process. This allows us to model non stationary continuous processes, and we show that H(t) and 2 \Gamma H(t) are indeed respectively the local Holder exponent and the local box and Hausdorff dimension at point t. Finally, we propose a simulation method and an estimation procedure for H(t) for our model.

We propose a natural and simple model for the joint throughput evolution of a set of TCP sessions sharing a common tail drop bottleneck router, via products of random matrices. This model allows one to predict the fluctuations of the throughput of each session, as a function of the synchronization rate in the bottleneck router; several other and more refined properties of the protocol are analyzed such as the instantaneous imbalance between sessions, the autocorrelation function or the performance degradation due to synchronization of losses. When aggregating traffic obtained from this model, one obtains, for certain ranges of the parameters, short time scale statistical properties that are consistent with a fractal scaling similar to what was identified on real traces using wavelets.

We introduce the notion of weakly hyperbolic iterated function system (IFS) on a compact metric space, which generalises that of hyperbolic IFS. Based on a domain-theoretic model, which uses the Plotkin power domain and the probabilistic power domain respectively, we prove the existence and uniqueness of the attractor of a weakly hyperbolic IFS and the invariant measure of a weakly hyperbolic IFS with probabilities, extending the classic results of Hutchinson for hyperbolic IFSs in this more general setting. We also present finite algorithms to obtain discrete and digitised approximations to the attractor and the invariant measure, extending the corresponding algorithms for hyperbolic IFSs. We then prove the existence and uniqueness of the invariant distribution of a weakly hyperbolic recurrent IFS and obtain an algorithm to generate the invariant distribution on the digitised screen. The generalised Riemann integral is used to provide a formula for the expected value of almost everywh...