For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

We examined the distribution and ancestral relationships of genetic caste determination (GCD) in 46 populations of the seed-harvester ants Pogonomyrmex barbatus and P. rugosus across the east-to-west range of their distributions. Using a mtDNA sequence and two nuclear markers diagnostic for GCD, we distinguished three classes of population phenotypes: those with GCD, no evidence of GCD, and mix...

In this paper we focus on connected directed/undirected circulant graphs Cn(a, b). We investigate some topological characteristics, and define a simple combinatorial model, which is new for the topic. Building on such a model, we derive a necessary and sufficient condition to test whether two circulant graphs Cn(a, b) and Cn(a , b) are isomorphic or not. The method is entirely elementary and co...

Mesio-temporal lobe epilepsy (MTLE) is often accompanied by granule cell dispersion (GCD), a widening of the granule cell layer. The molecular determinants of GCD are poorly understood. Here, we used an animal model to study whether GCD results from an increased dentate neurogenesis associated with an abnormal migration of the newly generated granule cells. Adult mice were given intrahippocampa...

An embedding (called a GCD theory) of partly ordered abelian group G into abelian l-group Γ is investigated such that any element of Γ is an infimum of a subset (possible non-finite) from G. It is proved that a GCD theory need not be unique. A complete GCD theory is introduced and it is proved that G admits a complete GCD theory if and only if it admits a GCD theory G Γ such that Γ is an Archim...

We undertake a thorough complexity study of the following fundamental optimization problem, known as the `p-norm shortest extended GCD multiplier problem: given a1, . . . , an ∈ Z, find an `p-norm shortest gcd multiplier for a1, . . . , an, i.e., a vector x ∈ Z with minimum ( ∑n i=1 |xi|) satisfying ∑n i=1 xiai = gcd(a1, . . . , an). First, we prove that the shortest GCD multiplier problem (in ...

The computation of the Greatest Common Divisor (GCD) of many polynomials is a nongeneric problem. Techniques defining “approximate GCD” solutions have been defined, but the proper definition of the “approximate” GCD, and the way we can measure the strength of the approximation has remained open. This paper uses recent results on the representation of the GCD of many polynomials, in terms of fac...