Every random number generator has its advantages and deficiencies. There are no `̀ safe'' generators. The practitioner's problem is how to decide which random number generator will suit his needs best. In this paper, we will discuss criteria for good random number generators: theoretical support, empirical evidence and practical aspects. We will study several recent algorithms that perform bette...

Many scientific disciplines use n samples to extrapolate information on the species composition of additional unobservable samples. Given a population with unknown species proportions (pi)i≥1, we consider the problem of estimating: i) the number Uλn,r of unseen species with frequency r ≥ 1 in an additional sample of size λn; ii) the probability Vλn,r of discovering at the (λn + n + 1)-th draw a...

An important utility that digital computer systems should provide is the ability to generate random numbers. Certainly this is true in scientific computing where many years of experience has demonstrated the importance of access to a good random number generator. And in a wider sense, largely due to the encyclopedic efforts of Donald Knuth [18], there is now a realization that random number gen...

The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty gr...

Inferring phylogenetic trees is a fundamental problem in computational biology. We present a new objective criterion, the phylogenetic number, for evaluating evolutionary trees for species deened by biomolecular sequences or other qualitative characters. The phylogenetic number of a tree T is the maximum number of times that any given character state arises in T. By contrast, the classical pars...