The spatial structure of networks

We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from non-geographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.Comment: 5 pages, 3 figure

Optimal design of spatial distribution networks

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.Comment: 6 pages, 5 figure

Just Pictures: Recent Trends in Research and Sentencing in Child Pornography Cases

Introduction and Article from the Honorable James J. Gilvary Symposium on Law, Religion, and Social Justic

Variability in spawning frequency and reproductive development of the narrow-barred Spanish mackerel (Scomberomorus commerson) along the west coast of Australia

The narrow-barred Spanish mackerel (Scomberomorus commerson) is widespread throughout the Indo-West Pacific region. This study describes the reproductive biology of S. commerson along the west coast of Australia, where it is targeted for food consumption and sports fishing. Development of testes occurred at a smaller body size than for ovaries, and more than 90% of males were sexually mature by the minimum legal length of 900 mm TL compared to 50% of females. Females dominated overall catches although sex ratios within daily catches vary considerably and females were rarely caught when spaw n ing. Scomberomorus commerson are seasonally abundant in coastal waters and most of the commercial catch is taken prior to the reproductive season. Spawning occurs between about August and November in the Kimberley region and between October and January in the Pilbara region. No spawning activity was recorded in the more southerly West Coast region, and only in the north Kimberley region were large numbers of fish with spawning gonads collected. Catches dropped to a minimum when spawning began in the Pilbara region, when fish became less abundant in inshore waters and inclement weather conditions limited fishing on still productive offshore reefs. Final maturation and ovulation of oocytes took place within a 24-hour period, and females spawned in the afternoon-evening every three days. A third of these spawning females released batches of eggs on consecutive days. Relationships between length, weight, and batch fecundity are presented

The physical limits of communication

It has been well-known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. In this letter we demonstrate an equivalent result about electromagnetic transmissions. We show that when electromagnetic radiation is used as the transmission medium, the most information-efficient format for a given message is indistinguishable from black-body radiation to a receiver who is unfamiliar with that format. The characteristic temperature of the radiation is set by the amount of energy used to make the transmission. If information is not encoded in the direction of the radiation, but only its timing, energy or polarization, then the most efficient format has the form of a one-dimensional black-body spectrum which is easily distinguished from the three-dimensional case.Comment: 9 pages, 1 postscript figure, typeset in LaTeX using the RevTeX macro packag

On the quantum chromatic number of a graph

We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the graph. After discussing this notion from first principles, we go on to establish relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs. Finally, we show that there can be no separation between classical and quantum chromatic number if the latter is 2, nor if it is 3 in a restricted quantum model; on the other hand, we exhibit a graph on 18 vertices and 44 edges with chromatic number 5 and quantum chromatic number 4.Comment: 7 pages, 1 eps figure; revtex4. v2 has some new references; v3 furthe small improvement

Extended Photometry for the DEEP2 Galaxy Redshift Survey: A Testbed for Photometric Redshift Experiments

This paper describes a new catalog that supplements the existing DEEP2 Galaxy Redshift Survey photometric and spectroscopic catalogs with ugriz photometry from two other surveys; the Canada-France-Hawaii Legacy Survey (CFHTLS) and the Sloan Digital Sky Survey (SDSS). Each catalog is cross-matched by position on the sky in order to assign ugriz photometry to objects in the DEEP2 catalogs. We have recalibrated the CFHTLS photometry where it overlaps DEEP2 in order to provide a more uniform dataset. We have also used this improved photometry to predict DEEP2 BRI photometry in regions where only poorer measurements were available previously. In addition, we have included improved astrometry tied to SDSS rather than USNO-A2.0 for all DEEP2 objects. In total this catalog contains ~27,000 objects with full ugriz photometry as well as robust spectroscopic redshift measurements, 64% of which have r > 23. By combining the secure and accurate redshifts of the DEEP2 Galaxy Redshift Survey with ugriz photometry, we have created a catalog that can be used as an excellent testbed for future photo-z studies, including tests of algorithms for surveys such as LSST and DES.Comment: 12 pages, 6 figures and 5 tables. Accepted to The Astrophysical Journal Supplement. Catalogs are publicly available at http://deep.ps.uci.edu/DR4/photo.extended.htm