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Several characteristic parameters of randomly grown quadtrees of any dimension are analyzed. Additive parameters have expectations whose generating functions are express-ible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit… (More)

It is shown that the depth of the last node inserted in a random quad tree constructed from independent uniform [Q, 11 d random vectors is in probability asymptotic to (2/d) log n, where log denotes the natural logarithm. In addition, for d =2, exact values are obtained for all the moments of the depth of the last node .

Oto is a customizable and <i>extensible</i> marking tool which aims at providing <i>timely</i> feedback to students. Based on simple test cases description formats, Oto also includes operations that help students easily test-even "mark"-their own programs.

- Gilbert Labelle, Louise Laforest, Xavier Provençal
- 2006

We analyse the distribution of the root pattern of randomly grown multidimensional point quadtrees. In particular, exact, recursive and asymptotic formulas are given for the expected arity of the root.

Curious parallels between the processes of species and language evolution have been observed by many researchers. Retracing the evolution of Indo-European (IE) languages remains one of the most intriguing intellectual challenges in historical linguistics. Most of the IE language studies use the traditional phylogenetic tree model to represent the evolution… (More)

- Louise Laforest, Uqam
- 2007

- Philippe Flajolet, Gilbert Labelle, Louise Laforest, Bruno Salvy, Philippe Fla, Bruno Salvy Rocquencourt +1 other
- 1994

Several characteristic parameters of randomly grown quadtrees of any dimension are analysed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit… (More)

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