The Effect of Physiography on the Trade Routes of East Tennessee

Preface: The parallelism of the topographic forms of East Tennessee is classic in the world. The influence of topography on the trade routes of the region is evident from a map of roads or railroads. This paper is an attempt to show the adjustment of trade routes to physiographic forms in East Tennessee

Gravitational Microlensing by Neutron Stars and Radio Pulsars: Event Rates, Timescale Distributions, and Mass Measurements

We investigate properties of Galactic microlensing events in which a stellar object is lensed by a neutron star. For an all-sky photometric microlensing survey, we determine the number of lensing events caused by $\sim10^{5}$ potentially-observable radio pulsars to be $\sim0.2\ \rm{yr^{-1}}$ for $10^{10}$ background stellar sources. We expect a few detectable events per year for the same number of background sources from an astrometric microlensing survey. We show that such a study could lead to precise measurements of radio pulsar masses. For instance, if a pulsar distance could be constrained through radio observations, then its mass would be determined with a precision of $\sim10\%$. We also investigate the time-scale distributions for neutron star events, finding that they are much shorter than had been previously thought. For photometric events towards the Galactic centre that last $\sim15$ days, around $7\%$ will have a neutron star lens. This fraction drops rapidly for longer time-scales. Away from the bulge region we find that neutron stars will contribute $\sim40\%$ of the events that last less than $\sim10$ days. These results are in contrast to earlier work which found that the maximum fraction of neutron star events would occur on time-scales of hundreds of days.Comment: 10 pages, accepted for publication in ApJ. v2 updated to reflect change of title in proof stag

Common Learning with Intertemporal Dependence

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps, Ely, Mailath, and Samuelson, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.Common learning, common belief, private signals, private beliefs

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, common belief, private signals, private beliefs

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, Common belief, Private signals, Private beliefs

Relativistic Precessing Jets and Cosmological Gamma Ray Bursts

We discuss the possibility that gamma-ray bursts may result from cosmological relativistic blob emitting neutron star jets that precess past the line of sight. Beaming reduces the energy requirements, so that the jet emission can last longer than the observed burst duration. One precession mode maintains a short duration time scale, while a second keeps the beam from returning to the line of sight, consistent with the paucity of repeaters. The long life of these objects reduces the number required for production as compared to short lived jets. Blobs can account for the time structure of the bursts. Here we focus largely on kinematic and time scale considerations of beaming, precession, and blobs--issues which are reasonably independent of the acceleration and jet collimation mechanisms. We do suggest that large amplitude electro-magnetic waves could be a source of blob acceleration.Comment: 15 pages, plain TeX, accepted to ApJ