Quasi-isometry classification of RAAGs that split over cyclic subgroups

For a one-ended right-angled Artin group, we give an explicit description of its JSJ tree of cylinders over infinite cyclic subgroups in terms of its defining graph. This is then used to classify certain right-angled Artin groups up to quasi-isometry. In particular, we show that if two right-angled Artin groups are quasi-isometric, then their JSJ trees of cylinders are weakly equivalent. Although the converse to this is not generally true, we define quasi-isometry invariants known as stretch factors that can distinguish quasi-isometry classes of RAAGs with weakly equivalence JSJ trees of cylinders. We then show that for many right-angled Artin groups, being weakly equivalent and having matching stretch factors is a complete quasi-isometry invariant.Comment: 49 pages, 12 figures. The class of dovetail RAAGs is introduced and the main theorem is reformulated in terms of such RAAGs. Accepted by Groups, Geometry, and Dynamic

The Small Number System

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system

The Role of Promotion in the Book Publishing Process

published or submitted for publicatio

Coherently pulsed laser source

An electronically controllable apparatus is described which modulates a continuous wave laser beam so as to produce an output beam consisting of coherent pulses that are electronically controllable as to both pulse repetition rate and pulse width. The apparatus includes two acoustic devices positioned so that the laser beam passes through them in sequence, and apparatus for passing sound waves through the devices to frequency shift the laser radiation as well as to diffract it. Each acoustic device generates sound waves containing a group of frequencies which result in spaced pulses. The first acoustic device is countered by the second acoustic device to produce a collimated, coherently pulsed, laser beam

Book Review: "The Natural Survival of Work: Job Creation and Job Destruction in a Growing Economy". By Pierre Cahuc and André Zylberberg.

Book review of "The Natural Survival of Work: Job Creation and Job Destruction in a Growing Economy". By Pierre Cahuc and André Zylberberg.Job displacement, worker turnover, active labor market policy, unemployment