A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract Any binary image can be represented by a quadtree. Therefore random quadtrees correspond to bounded random sets in the plane. We discuss various possibilities for randomizing the quadtree. The most natural randomization yields Mandelbrot percolation.

Using Monte-Carlo simulations, we estimate numerically disconnection exponents for planar Brownian motions. These simulations tend to confirm conjectures by Duplantier and Mandelbrot.

We exploit the Feller-Pareto characterization of the classical Pareto distribution to derive a law relating the probability of a given term frequency in a document and its the length. A similar law was derived by Mandelbrot. We exploit the paretian distribution to obtain a term frequency normalization to substitute for the actual term frequency in the probabilistic models of Information Retriev...

This work extends a model proposed by Voldman, Mandelbrot, et al. on the fractal nature of the gaps separating cache misses, and shows how the fractal dimension of the gap distribution can be used to predict the miss ratio experienced by the program that has generated the series of cache misses. This result supports the thesis that the fractal dimension of the distribution of the intermiss gaps...

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we ...

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J....

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical dat...

Combinatorial search methods often exhibit a large variability in performance. We study the cost pro les of combinatorial search procedures. Our study reveals some intriguing properties of such cost pro les. The distributions are often characterized by very long tails or \heavy tails". We will show that these distributions are best characterized by a general class of distributions that have no ...

Sufficient conditions are derived for solutions of a general autonomous system of quad-ratic ordinary vector differential equations to exhibit finite escape times. These results are extended to a matrix Riccati-type differential equation using Kronecker matrix products and a "stacking operator". Finally, these results are applied to a class of models used extensively in population dynamics.

Mining massive daily news media data to infer patterns of cultural trends, including political conflicts and instabilities, is an important goal of computational social science and the new interdisciplinary field called “culturnomics.” While the sheer size of media data makes this task challenging, a greater hurdle is the nonstationarity of data, manifested in several ways, which invalidates su...