For fixed t ≥ 2, we consider the class of representations of 1 as sum of unit fractions whose denominators are powers of t or equivalently the class of canonical compact t-ary Huffman codes or equivalently rooted t-ary plane “canonical” trees. We study the probabilistic behaviour of the height (limit distribution is shown to be normal), the number of distinct summands (normal distribution), the...

We don’t see doughnut shapes when we look up in the sky. But what if the Earth we live on were shaped like a torus instead of a sphere? This remote, but otherwise intriguing possibility, lead me to explore the formation of islands and pools in a toroidal world. In this exposition, I start with a programming perspective on counting islands and pools, and finish by presenting a probabilistic anal...

Useless paths are a chronic problem for marker-passing techniques. We use a prob­ abilistic analysis to justify a method for quickly identifying and rejecting useless paths. Using the same analysis, we identify key conditions and assumptions necessary for marker-passing to perform well.

The recently-introduced OM3 aggregation operators fulfill three appealing properties: they are simultaneously minitive, maxitive, and modular. Among the instances of OM3 operators we find e.g. OWMax and OWMin operators, the famous Hirsch h-index and all its natural generalizations. In this paper the basic axiomatic and probabilistic properties of extended, i.e. in an arity-dependent setting, OM...

This paper is a first attempt to describe the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which provides precise information on the structure of such a word. With each Sturmian word of slope α, we associate particular sequences of factor lengths which have a given “position” with respect to the sequence of continuants of α...

Bayesian probabilistic analysis offers a new approach to characterize semantic representations by inferring the most likely feature structure directly from the patterns of brain activity. In this study, infinite latent feature models [1] are used to recover the semantic features that give rise to the brain activation vectors when people think about properties associated with 60 concrete concept...

This paper describes work carried out to develop a method for considering actual traffic loads during bridge evaluation. This method is based on the use of load correction factors which have been determined using a probabilistic analysis of bridge loads and resistance. Load correction factors are selected as a function of site characteristics and used in order to modify load effects calculated ...

In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable capacities. This model was introduced by Kazemi in 2012. We obtain the mean and variance of the first Zagreb index and introduce a martingale based on this quantity.

Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called “Count”, which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further probabilistic analysis of “Count”. We derive an exact formula for the average number of swaps needed by “Count” as well as an asymptotic formula for the varia...