Stein factors for negative binomial approximation in Wasserstein distance

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The geometry of the Barbour-Bertotti theories I. The reduction process

The dynamics of $N\geq 3$ interacting particles is investigated in the non-relativistic context of the Barbour-Bertotti theories. The reduction process on this constrained system yields a Lagrangian in the form of a Riemannian line element. The involved metric, degenerate in the flat configuration space, is the first fundamental form of the space of orbits of translations and rotations (the Leibniz group). The Riemann tensor and the scalar curvature are computed by a generalized Gauss formula in terms of the vorticity tensors of generators of the rotations. The curvature scalar is further given in terms of the principal moments of inertia of the system. Line configurations are singular for $N\neq 3$. A comparison with similar methods in molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit

Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections

A PRELIMINARY REPORT ON THE NEBRASKA STATE MUSEUM

The Nebraska State Museum has been established a sufficient number of years to make it widely known throughout the state, both by reputation and by personal visits. Incident to a growing clientele and an expanding correspondence, it is expedient that a concise circular letter be issued in bulletin form. Such a pamphlet can be promptly forwarded to inquirers and will offer obvious advantages over individual replies

Nebraska Green Quartzite - An Important Future Industry

ln southern Harlan and Franklin counties, there occur many acres of green quartzite which must be of commercial consequence when made available. It is a neglected resource upon which important industries are sure to be based. With the development of this bed in view, the Nebraska Geological Survey has examined this area. and through this leaflet wishes to place the results before possible investors

TORYNOBELODON LOOMISI, gen et. sp. nov.

The group of proboscideans which we have called the shovel-tuskers or Amebelodonts, was announced in June, 1927,1 following the discovery of Amebelodon fricki. In the field season of 1928, two additional species were found which are represented by mandibular tusks. One of these is a tip of a large and unique tusk, numbered 2-3-9-28, S. and L., the collectors being Bertrand Schultz and John LeMar, both of the class of 1931, the University of Nebraska. It was found within 200 to 300 yards of the spot on his farm where Mr. A. S. Keith, Freedom, Frontier County, Nebraska, found Amebelodon fricki in the spring of 1927, the formation being Late Pliocene to Early Pleistocene. Influenced by the coarse ladle-shaped mandible, we have named this new form Torynobelodon loomisi, in recognition of Dr. Fred A. Loomis, who has spent many field seasons in exploring the Tertiary series of Nebraska

NEBRASKA ROCKS WHICH EXCITE COMMON INQUIRY

This leaflet it intended to serve as an answer to correspondents who make inquiry about the rocks of Nebraska1. Unfortunately for those interested in such matters, the rocks of the State are few in number, and are deeply buried from view by sand and soil, so there are thousands of square miles in which even a pebble is a rarity. That our rocks are level and undisturbed is practically true. Still there are some surprisingly interesting folds and faults

THE MANDIBLE OF AMEBELODON FRICKI

The type specimen of the genus Amebelodon is installed in the Nebraska State Museum, the University of Nebraska, Lincoln. It consists of a mandible with tusks and teeth, all of which are dense and perfect, barring minor cracks and breaks. One toe bone and part of a rib found associated with this mandible may belong to this animal. It was discovered by Mr. A. S. Keith on his farm near Freedom, Frontier County, Nebraska; was secured for the palaeontological collections of Hon. Charles H. Morrill by Mr. Phillip Orr, April 4, 1927; was briefly described and figured in a Museum bulletin June, 1927.1 After a long but unavoidable delay, this mandible has just been mounted and the first photographs with correct measurements are now possible and are presented herewith. Preliminary drawings and measurements were made while the specimen was still in its plaster cinches. This unique specimen, representing a new group of longirostral mastodonts, has been named Amebelodon fricki, and the group designated the Amebelodonts, or shovel-tuskers. Amebelodonts are such distinctive elephants that they plainly belong in a group by themselves, namely the sub-family Amebelodontinae. In them is realized the culmination, in the late Pliocene or early Pleistocene, of the flattened tusks and lengthened mandible of Phiomia osborni of the Egyptian Oligocene