We formulate and prove a finite version of Vinogradov’s bilinear sum inequality.We use it together with Ratner’s joinings theorems to prove that the Mobius function is disjoint from discrete horocycle flows on Γ\SL2(R).

This paper presents the results of a project to develop an omni-directional robotic system at NASA Langley’s Robotics and Intelligent Machines Lab. The robot, named Mobius, was created as part of an investigation into omni-directional motion (using four Mecanum wheels) and fuzzy-logic control. The robot uses a highlevel processor running Linux to connect to wireless networks, process user-input...

The unspoken background for this article is a hypothesis for origins (of life, the universe and everything). That hypothesis believes human science is responsible for everything, and neither supernatural nor evolutionary means originate anything. In a biological sense, the Theory of Evolution certainly explains adaptations and modifications. But believing it also explains origins is unwarranted...

Golden Gate Assembly is a powerful synthetic biology tool, which utilizes Type IIS enzymes for unidirectional assembly of multiple DNA fragments. The simplicity of its DNA assembly and the exchangeability of standard parts greatly facilitate the generation of combinatorial assembly libraries. Currently there are two popular Golden Gate Assembly frameworks that allow multigene augmentation (MoCl...

Reverse simulation models of facial expression recognition suggest that we recognize the emotions of others by running implicit motor programmes responsible for the production of that expression. Previous work has tested this theory by examining facial expression recognition in participants with Möbius sequence, a condition characterized by congenital bilateral facial paralysis. However, a mixe...

Moebius syndrome (MS) is a rare disorder mainly characterized by bi- or unilateral palsy of the facial and abducens nerves. Among the various orofacial characteristics related to this syndrome, the following are pointed out, difficulty with sucking, tongue malformation, mandibular hypoplasia, saliva drooling, arched palate and micrognathia. In spite of the diversity of oral features described f...

BACKGROUND Moebius syndrome (MBS) is rare disease characterized by nonprogressive congenital uni- or bi-lateral facial (i. e. VII cranial nerve) and abducens (i. e. VI cranial nerve) palsy. Although the neurological and ophthalmological findings are quite well-known, data concerning the attendant functional difficulties and their changes over time are seldom addressed. In this study we attempt ...

Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this transformation. This class – which has been recently introduced – has interesting properties, in particular if we want to control both the Hamming weight and t...