Arbitrary vs. Random

Multiplicative vs. arbitrary gene action in heterosis.

In this article we investigate multiplicative effects between genes in relation to heterosis. The extensive literature on heterosis due to multiplicative effects between characters is reviewed, as is earlier work on the genetic description of heterosis. A two-locus diallelic model of arbitrary gene action is used to derive linear parameters for two multiplicative models. With multiplicative act...

Random Lazy Random Walks on Arbitrary Finite Groups

This paper considers \lazy" random walks supported on a random subset of k elements of a nite group G with order n. If k = dalog 2 ne where a > 1 is constant, then most such walks take no more than a multiple of log 2 n steps to get close to uniformly distributed on G. If k = log 2 n + f (n) where f (n) ! 1 and f (n)= log 2 n ! 0 as n ! 1, then most such walks take no more than a multiple of (l...

Circuits with arbitrary gates for random operators

We consider boolean circuits computing n-operators f : {0, 1} n → {0, 1} n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes a matrix-vector product A x over GF (2). We prove the existence of n-operators requiring about n 2 wires in any circuit, and linear n-operators requiring ...

Random graphs with arbitrary i.i.d. degrees

In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree distribution is regularly varying with exponent 1 − τ . There are three distinct cases: (i) τ > 3, where the degrees have finite variance, (ii) τ ∈ (2, 3), where the d...

Vertex-Reinforced Random Walk on Arbitrary Graphs