We present a phylogeographic study of at least six reproductively isolated lineages of new world harvester ants within the Pogonomyrmex barbatus and P. rugosus species group. The genetic and geographic relationships within this clade are complex: Four of the identified lineages show genetic caste determination (GCD) and are divided into two pairs. Each pair has evolved under a mutualistic syste...

Purpose To examine the preoperative conjunctival dendritic cell density (DCD), goblet cell density (GCD), and stromal meshwork reflectivity (SMR) in glaucomatous patients undergoing filtration surgery, using in vivo confocal microscopy (IVCM). Methods Sixty-six patients were enrolled. At baseline, IVCM was performed at the site planned for surgery, and was repeated after 12 months at bleb sit...

Granule cell dispersion (GCD) represents a pathological widening of the granule cell layer in the dentate gyrus and it is frequently observed in patients with mesial temporal lobe epilepsy (MTLE). Recent studies in human MTLE specimens and in animal epilepsy models have shown that a decreased expression and functional inactivation of the extracellular matrix protein Reelin correlates with GCD f...

The gcd-sum is an arithmetic function defined as the sum of the gcd’s of the first n integers with n : g(n) = ∑n i=1(i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of par...

A probabilistic algorithm is exhibited that calculates the gcd of many integers using gcds of pairs of integers; the expected number of pairwise gcds required is less than two.

Let f (m, n) denote the number of relatively prime subsets of {m+ 1, m + 2,. .. , n}, and let Φ(m, n) denote the number of subsets A of {m + 1, m + 2,. .. , n} such that gcd(A) is relatively prime to n. Let f k (m, n) and Φ k (m, n) be the analogous counting functions restricted to sets of cardinality k. Simple explicit formulas and asymptotic estimates are obtained for these four functions. A ...

The GCN4 gene encodes a transcriptional activator in yeast whose expression is regulated at the translational level in response to amino acid availability. gcn3 mutations block derepression of GCN4 expression in starvation conditions. gcd1 and gcd12 mutations restore derepression of GCN4 expression in gcn3 deletion mutants, suggesting that GCN3 positively regulates GCN4 indirectly by antagonism...

We consider the problem of computing the monic gcd of two polynomials over a number field L = Q(α1, . . . , αn). Langemyr and McCallum have already shown how Brown’s modular GCD algorithm for polynomials over Q can be modified to work for Q(α) and subsequently, Langemyr extended the algorithm to L[x]. Encarnacion also showed how to use rational number to make the algorithm for Q(α) output sensi...