We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...
The standard framework to study vision is typically hierarchical and feedforward, which facilitates deconstructing complex mechanisms into smaller, more tractable problems. However, this framework can fail when elements are presented in context, as they ar ...
Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...
Today, many control applications in cyberphysical systems are implemented on shared platforms. Such resource sharing may lead to complex timing behaviors and, in turn, instability of control applications. This paper highlights a number of anomalies demonst ...
We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...
We discover a novel mechanism allowing for successive reduction of the number of dissipative Kerr solitons in optical microresonators. It is demonstrated that multiple and single soliton state can be deterministically accessed. ...
