Fix an elliptic curve E/Q, and assume the generalized Riemann hypothesis for the L-function L(E D , s) for every quadratic twist E D of E by D ∈ Z. We combine Weil's explicit formula with techniques of Heath-Brown to derive an asymptotic upper bound for the weighted moments of the analytic rank of E D. It follows from this that, for any unbounded increasing function f on R, the analytic rank an...

We show that any lattice of finite length is isomorphic to the lattice of fully dependent flats of a rank-finite independence space, which is finite if the given lattice is finite. If a suitable submodular function is given on the lattice, the independence space may be so chosen that this submodular function corresponds to the rank function of the independence space under the constructed isomor...

This paper presents empirical evidence supporting Goldfeld’s conjecture on the average analytic rank of a family of quadratic twists of a fixed elliptic curve in the function field setting. In particular, we consider representatives of the four classes of non-isogenous elliptic curves over Fq(t) with (q, 6) = 1 possessing two places of multiplicative reduction and one place of additive reductio...

Functional links between bone remodeling and the immune system in chronic inflammatory arthritis are mediated, in part, by the ligand of receptor activator of nuclear factor-kappa-B (RANK-L). Because neutrophils play a crucial role in chronic inflammation, the goal of this study was to determine whether proteins of the RANK/RANK-L pathway are expressed by synovial fluid (SF) neutrophils from pa...

In this article we present a fuzzy logic based method for the construction of thoughts of artificial animals (animats). Due to the substantial increase of the processing power of personal computers in the last decade there was a notable progress in the field of animat construction and simulation. Regardless of the achieved results, the coding of the animat’s behaviour is very inaccurate and can...

We present an observation of D. Ramakrishnan concerning the Tate Conjecture for varieties over a global function field (i.e., the function field of a smooth projecture curve over a finite field), which was pointed out during a lecture given at the AIM’s workshop on the Tate Conjecture in July 2007. The result is perhaps “known to the experts,” but we record it here, as it does not appear to be ...