Finite unions of balls in C^n are rationally convex

It is shown that the rational convexity of any finite union of disjoint closed balls in C^n follows easily from the results of Duval and Sibony.Comment: V.2 - minor edits, 2 page

J Public Health Manag Pract

Since 2003, the National Association of County and City Health Officials (NACCHO) has administered the Model Practice Award Program to commemorate the outstanding work of local health departments that have demonstrated creative and dynamic action in addressing identified public health needs. This nationally recognized award has been bestowed to over 3,000 local health departments since its inception and provides local health departments with a shared database of hundreds of health departments and over 850 best practices that are immediately replicable in their communities without having to \u201creinvent the wheel.\u201d In 2022, five outstanding local health department programs were recognized as Model Practices and sixteen programs were recognized as Promising Practices. The following article highlights on of those Model Practices, which was submitted by the Florida Department of Health in Duval County and highlights what they were able to achieve within their community when it comes to overdose intervention. For additional information about the Model Practices Program or to search Model Practices Database, visit https://www.naccho.org/membership/awards/model-practices.NU17CE925022/ImCDC/Intramural CDC HHSUnited States

On the Status of the Geodesic Principle in Newtonian and Relativistic Physics

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides a sense in which the geodesic principle has the status of a theorem in General Relativity (GR). I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation (Newton-Cartan theory) [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52(3), (2011)]. Here I compare the interpretations of these two theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case.Comment: 16 page

Galilean Isometries

We introduce three nested Lie algebras of infinitesimal `isometries' of a Galilei space-time structure which play the r\^ole of the algebra of Killing vector fields of a relativistic Lorentz space-time. Non trivial extensions of these Lie algebras arise naturally from the consideration of Newton-Cartan-Bargmann automorphisms.Comment: Plain TeX, 8 page

A recollection of Souriau's derivation of the Weyl equation via geometric quantization

These notes merely intend to memorialize Souriau's overlooked achievements regarding geo\-metric quantization of Poincar\'e-elementary symplectic systems. Restricting attention to his model of massless, spin-\half, particles, we faithfully rephrase and expound here Sections (18.82)--(18.96) & (19.122)--(19.134) of his book \cite{SSD} edited in 1969. Missing details about the use of a preferred Poincar\'e-invariant polarizer are provided for completeness

New solutions to the Hurwitz problem on square identities

The Hurwitz problem of composition of quadratic forms, or of "sum of squares identity" is tackled with the help of a particular class of $(\mathbb{Z}_2)^n$-graded non-associative algebras generalizing the octonions. This method provides an explicit formula for the classical Hurwitz-Radon identity and leads to new solutions in a neighborhood of the Hurwitz-Radon identity.Comment: 13 pages, 2 figures, final version to appear in J. Pure Appl. Al

Bigraphical Arrangements

We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.Comment: Added Remark 19 addressing arbitrary G-parking functions; minor revision

Space-Time Noncommutativity from Particle Mechanics

We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard `commuting' gauge. Therefore the Poisson algebra, and the resulting quantum theory, are identical in the two gauges. The only difference is in the interpretation of space-time coordinates. The procedure is repeated for the case of a coupling with a constant electromagnetic field, where the reparametrization symmetry is preserved. For more arbitrary interactions, we show that standard dynamical system can be rendered noncommutative in space and time by a simple change of variables.Comment: 13 p

Early Pleistocene hominins in europe: the sites of Barranco León and Fuente Nueva-3 (Orce, Spain)

The Early Pleistocene (Late Villafranchian) sites of Orce, placed in the northeastern sector of the Guadix-Baza Basin (Granada, southeastern Spain), are key to the study of the first human settlements in the European subcontinent. Evidence of human presence and anthropic activity has been found at two sites, Barranco Leon and Fuente Nueva-3. In this sedimentary basin, the hominins inhabited a mild environment rich in vegetation, which provided all resources necessary for their living, including the presence of a lake with a permanent water sheet fed by thermal springs and abundant ungulate carcasses. However, these animal resources were also focus of attention for scavenging carnivores. In Barranco León, with a chronology of 1.4 Ma, and slightly older than Fuente Nueva-3, 1.3 Ma, a deciduous tooth of Homo sp. has been unearthed in 2002 [1] and a huge assemblage of Oldowan (i. e. Mode 1) tools, made in flint and limestones, have been recovered in both localities. In addition, evidences of human modification are frequents on the bone surfaces, as cut-marks, resulting from disarticulation, defleshing and evisceration activities, and percussion marks that evidence bone fracturing for accessing marrow contents. Cut marks are mostly present on large ungulates limb bones, although a number of axial elements, as rib and vertebrae fragments, show cut marked surfaces. Percussion evidences are located almost exclusively in appendicular elements. Carnivores activities are present too, and are focused, as cut marks, on limb bones. These modifications were mostly originated by the giant, short-faced hyena of African origin Pachycrocuta brevirostris, althought the study of the fossil bones from the last four dig seasons evidence the presence of tooth marks from other carnivores of smaller body size. In any case, anthropic activity predominates in both, Barranco León and Fuente Nueva-3, which suggest a secondary access of carnivores to these areas. However, the upper archaeological level of Fuente Nueva-3, which has provided 150 coprolites and several tooth remains of P. brevirostris, is an exception to the pattern of competitive exclusion depicted above for hominins and scavenging carnivores. Taphonomic analysis of ungulate postcranial remains preserved in this level has shown increased carnivoran activity, thus evidencing a possible competition for ungulate carcasses between Homo and Pachycrocuta This work has been done in the framework of the contract Exp. B090678SV18BC funded and authorized by Consejería de Cultura de la Junta de Andalucía, and the project P11-HUM-7248 by Junta deAndalucía References:[1] Toro-Moyano, I, Martínez-Navarro, B., Agustí, J., Souday, C., Bermúdez De Castro, J.M., Martinón-Torres, M., Fajardo, B., Duval, M., Falguères, C., Oms, O., Parés, J.M., Anadón, P., Julià, R., García-Aguilar, J.M., Moigne, A.-M., Espigares, M.P., Ros-Montoya, S., Palmqvist, P., 2013. The oldest human fossil in Europe, from Orce (Spain). Journal of Human Evolution, 65, 1-9.[2] Espigares, M.P., Martínez-Navarro, B., Palmqvist, P., Ros-Montoya, S., Toro, I., Agustí, J. Sala, R., 2013. Homo vs. Pachycrocuta: Earliest evidence of competition for an elephant carcass between scavengers at Fuente Nueva-3 (Orce, Spain). Quaternary International. 295, 113 -125.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech