We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form: Pr{n} = (1− apa) ( an+ 1 n ) (1− pa) pa where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported for the ca...

We present an explicit formula for the mask of odd points n-ary, for any odd n 3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point a-ary schemes introduced by Lian, 2008, and 2m 1 -point a-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point n-ar...

We consider the classic problem of designing heaps. Standard binary heaps run faster in practice than Fibonacci heaps but have worse time guarantees. Here we present a new type of heap that runs faster in practice than both standard binary and Fibonacci heaps, but has asymptotic insert times arbitrarily better than O(logn), namely O((logn)) for arbitrary positive integer m. Our heap is defined ...

We propose in this paper a method to extract instances of n-ary relations in a text guided by an Ontological and Terminological Resource (OTR). An OTR is a resource composed of a conceptual component (the ontology) and a terminological component (the terminology) in which the terms are distinguished from the concepts they denote. The ontology allows n-ary relationships to be described between a...

The notion of n-ary algebras, that is vector spaces with a multiplication concerning n-arguments, n ≥ 3, became fundamental since the works of Nambu. Here we first present general notions concerning n-ary algebras and associative n-ary algebras. Then we will be interested in the notion of n-Lie algebras, initiated by Filippov, and which is attached to the Nambu algebras. We study the particular...

In this paper, we propose a construction of fullrank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of fullrank binary 1-perfect codes (1994). Properties of i-components of q-ary Hamming codes are investigated and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1...

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p-ary low correlation zone (LCZ) sequence set with parameters (p − 1, p − 1, (p − 1)/(p − 1), 1) from a p-ary sequence of the same length with ideal autocorrelation.

For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups. AMS Classification: 17A42, 16N34, 20N15

Asymptotically-Tight Bounds on the Number of Cycles in Generalized de Bruijn-Good Graphs Ueli M. Maurer Institute for Signal and Information Processing Swiss Federal Institute of Technology CH-8092 Z urich, Switzerland Abstract. The number of cycles of length k that can be generated by q-ary n-stage feedback shift-registers is studied. This problem is equivalent to nding the number of cycles o...