Lattice Universes in 2+1-dimensional gravity

Lattice universes are spatially closed space-times of spherical topology in the large, containing masses or black holes arranged in the symmetry of a regular polygon or polytope. Exact solutions for such spacetimes are found in 2+1 dimensions for Einstein gravity with a non-positive cosmological constant. By means of a mapping that preserves the essential nature of geodesics we establish analogies between the flat and the negative curvature cases. This map also allows treatment of point particles and black holes on a similar footing.Comment: 14 pages 7 figures, to appear in Festschrift for Vince Moncrief (CQG

Collapse of Kaluza-Klein Bubbles

Kaluza-Klein theory admits ``bubble" configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of time-symmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) ``Witten bubble" solution. Some of these data have negative total energy. We show here that all the negative energy bubble solutions start out expanding away from the moment of time symmetry, while the positive energy bubbles can start out either expanding or contracting. Thus it is unlikely that the negative energy bubbles would collapse and produce a naked singularity.Comment: 6 pages, plain LaTeX, UMDGR-94-08

Reversibility Checking for Markov Chains

In this paper, we present reversibility preserving operations on Markov chain transition matrices. Simple row and column operations allow us to create new reversible transition matrices and yield an easy method for checking a Markov chain for reversibility

Integrability of the N-body problem in (2+1)-AdS gravity

We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial motion, in such a way that the point sources move as time-like geodesics (in the case of particles) or as space-like geodesics (in the case of BTZ black holes) of a three-dimensional hypersurface immersed in a four-dimensional Minkowskian space-time, and that the two-body dynamics is solved by two invariant masses, whose difference is simply related to the total angular momentum of the system.Comment: 15 pages, LaTeX, no figure

Siri, Alexa, and Other Digital Assistants: A Study of Customer Satisfaction With Artificial Intelligence Applications

Siri, Alexa, and other digital assistants are rapidly becoming embraced by consumers and the adoption is projected to grow from 390 million to 1.8 billion for the period of 2015 to 2021. Digital assistants are offering benefits to consumers while also proving to be a disruptive technology for businesses. Coupling digital assistants with other artificial intelligence technologies offers the potential to transform companies by creating more efficient business processes, automating complex tasks, and improving the customer service experience. Businesses have begun integrating this technology into their operations with the expectation of achieving significant productivity gains. Customer satisfaction has been discussed extensively throughout marketing literature. Yet, there is little empirical evidence of customer satisfaction with digital assistants. This study used PLS-SEM to analyze 244 survey responses obtained from a cross-section of consumers. Using the Expectations Confirmation Theory as its foundation, the study identified that expectations and confirmation of expectations substantially explained customer satisfaction with digital assistants. For practice, the study provides guidance which allows firms to prioritize marketing and managerial activities. Firms should focus priorities on assisting digital assistant users to become aware of new skill capabilities while also providing relevant examples of how these skills can be used to meet user needs. In addition, priorities should be focused on assisting users with understanding how the average person can use digital assistants to perform more than just mundane tasks with relative ease. These priorities were identified as areas of high importance for customer satisfaction and require performance improvements

Perturbative Analysis of the Two-body Problem in (2+1)-AdS gravity

We derive a perturbative scheme to treat the interaction between point sources and AdS-gravity. The interaction problem is equivalent to the search of a polydromic mapping $X^A= X^A(x^\mu)$, endowed with 0(2,2) monodromies, between the physical coordinate system and a Minkowskian 4-dimensional coordinate system, which is however constrained to live on a hypersurface. The physical motion of point sources is therefore mapped to a geodesic motion on this hypersuface. We impose an instantaneous gauge which induces a set of equations defining such a polydromic mapping. Their consistency leads naturally to the Einstein equations in the same gauge. We explore the restriction of the monodromy group to O(2,1), and we obtain the solution of the fields perturbatively in the cosmological constant.Comment: 19 pages, no figures, LaTeX fil

Uniqueness of the asymptotic AdS3 geometry

We explicitly show that in (2+1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neigbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant. Gra