Higher-Dimensional Algebra VII: Groupoidification

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of "degroupoidification": a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present three applications of groupoidification. The first is to Feynman diagrams. The Hilbert space for the quantum harmonic oscillator arises naturally from degroupoidifying the groupoid of finite sets and bijections. This allows for a purely combinatorial interpretation of creation and annihilation operators, their commutation relations, field operators, their normal-ordered powers, and finally Feynman diagrams. The second application is to Hecke algebras. We explain how to groupoidify the Hecke algebra associated to a Dynkin diagram whenever the deformation parameter q is a prime power. We illustrate this with the simplest nontrivial example, coming from the A2 Dynkin diagram. In this example we show that the solution of the Yang-Baxter equation built into the A2 Hecke algebra arises naturally from the axioms of projective geometry applied to the projective plane over the finite field with q elements. The third application is to Hall algebras. We explain how the standard construction of the Hall algebra from the category of representations of a simply-laced quiver can be seen as an example of degroupoidification. This in turn provides a new way to categorify - or more precisely, groupoidify - the positive part of the quantum group associated to the quiver.Comment: 67 pages, 14 eps figures; uses undertilde.sty. This is an expanded version of arXiv:0812.486

Automated CNC Micromachining for Integrated THz Waveguide Circuits

Computer Numerically Controlled (CNC) machining of splitblock waveguide circuits has become the primary method of constructing terahertz waveguide circuits. The majority of these circuits have been made on traditional CNC machining centers or on custom-made laboratory machining systems. At both the University of Arizona and Arizona State University, we have developed techniques for machining splitblock waveguide circuits using purpose-built ultra high precision CNC machining centers designed for micromachining. These systems combine the automation of a traditional CNC machining center, including a high capacity toolchanger, workpiece and tool metrology systems and a large work volume, with the precision of custom laboratory systems. The systems at UofA and ASU are built by Kern Micro and deliver typical measured dimensional accuracies of 2-3 microns. Waveguide surface finish has been measured with a Veeco white light interferometric microscope to be Ra~75 nm. Tools of sizes between 25 microns and 10mm are available, with toolchanger capacities of 24-32 tools

Smallholder Participation in Agricultural Value Chains: Comparative Evidence from Three Continents

Supermarkets, specialized wholesalers, and processors and agro-exporters’ agricultural value chains have begun to transform the marketing channels into which smallholder farmers sell produce in low-income economies. We develop a conceptual framework through which to study contracting between smallholders and a commodity-processing firm. We then conduct an empirical meta-analysis of agricultural value chains in five countries across three continents (Ghana, India, Madagascar, Mozambique, and Nicaragua). We document patterns of participation, the welfare gains associated with participation, reasons for non-participation, the significant extent of contract non-compliance, and the considerable dynamism of these value chains, as farmers and firms enter and exit frequently.

Millimeter and Submillimeter Survey of the R Corona Australis Region

Using a combination of data from the Antarctic Submillimeter Telescope and Remote Observatory (AST/RO), the Arizona Radio Observatory Kitt Peak 12m telescope and the Arizona Radio Observatory 10m Heinrich Hertz Telescope, we have studied the most active part of the R CrA molecular cloud in multiple transitions of Carbon Monoxide, HCO$^+$ and 870\micron continuum emission. Since R CrA is nearby (130 pc), we are able to obtain physical spatial resolution as high as 0.01pc over an area of 0.16 pc$^2$, with velocity resolution finer than 1 km/s. Mass estimates of the protostar driving the mm-wave emission derived from HCO$^+$, dust continuum emission and kinematic techniques point to a young, deeply embedded protostar of $\sim$0.5-0.75 M$_\odot$, with a gaseous envelope of similar mass. A molecular outflow is driven by this source that also contains at least 0.8 M$_\odot$ of molecular gas with $\sim$0.5 L$_\odot$ of mechanical luminosity. HCO$^+$ lines show the kinematic signature of infall motions as well as bulk rotation. The source is most likely a Class 0 protostellar object not yet visible at near-IR wavelengths. With the combination of spatial and spectral resolution in our data set, we are able to disentangle the effects of infall, rotation and outflow towards this young object.Comment: 29 pages, 9 figures. Accepted for publication in the Astrophysical Journa

Warm-Dense Molecular Gas in the ISM of Starbursts, LIRGs and ULIRGs

The role of star formation in luminous and ultraluminous infrared galaxies is a hotly debated issue: while it is clear that starbursts play a large role in powering the IR luminosity in these galaxies, the relative importance of possible enshrouded AGNs is unknown. It is therefore important to better understand the role of star forming gas in contributing to the infrared luminosity in IR-bright galaxies. The J=3 level of 12CO lies 33K above ground and has a critical density of ~1.5 X 10^4 cm^-3. The 12CO(J=3-2) line serves as an effective tracer for warm-dense molecular gas heated by active star formation. Here we report on 12CO (J=3-2) observations of 17 starburst spirals, LIRGs and ULIRGs which we obtained with the Heinrich Hertz Submillimeter Telescope on Mt. Graham, Arizona. Our main results are the following: 1. We find a nearly linear relation between the infrared luminosity and warm-dense molecular gas such that the infrared luminosity increases as the warm-dense molecular gas to the power 0.92; We interpret this to be roughly consistent with the recent results of Gao & Solomon (2004a,b). 2. We find L_IR/M_H2 ratios ranging from ~10 to ~128 L_sun/M_sun using a standard CO-H2 conversion factor of 3 X 10^20 cm^-2 (K km s^-1)^-1. If this conversion factor is ~an order of magnitude less, as suggested in a recent statistical survey (Yao et al. 2003), then 2-3 of our objects may have significant contributions to the L_IR by dust-enshrouded AGNs.Comment: 15 Pages, 2 figures, Accepted for Publication in Ap

The Chimpanzee Model of Viral Hepatitis: Advances in Understanding the Immune Response and Treatment of Viral Hepatitis

Chimpanzees (Pan troglodytes) have contributed to diverse fields of biomedical research due to their close genetic relationship to humans and in many instances due to the lack of any other animal model. This review focuses on the contributions of the chimpanzee model to research on hepatitis viruses where chimpanzees represented the only animal model (hepatitis B and C) or the most appropriate animal model (hepatitis A). Research with chimpanzees led to the development of vaccines for HAV and HBV that are used worldwide to protect hundreds of millions from these diseases and, where fully implemented, have provided immunity for entire generations. More recently, chimpanzee research was instrumental in the development of curative therapies for hepatitis C virus infections. Over a span of 40 years, this research would identify the causative agent of NonA,NonB hepatitis, validate the molecular tools for drug discovery, and provide safety and efficacy data on the therapies that now provide a rapid and complete cure of HCV chronic infections. Several cocktails of antivirals are FDA approved that eliminate the virus following 12 weeks of once-per-day oral therapy. This represents the first cure of a chronic viral disease and, once broadly implemented, will dramatically reduce the occurrence of cirrhosis and liver cancer. The recent contributions of chimpanzees to our current understanding of T cell immunity for HCV, development of novel therapeutics for HBV, and the biology of HAV are reviewed. Finally, a perspective is provided on the events leading to the cessation of the use of chimpanzees in research and the future of the chimpanzees previously used to bring about these amazing breakthroughs in human healthcare

Smallholder Participation in Agricultural Value Chains: Comparative Evidence from Three Continents

Supermarkets, specialized wholesalers, and processors and agro-exporters’ agricultural value chains have begun to transform the marketing channels into which smallholder farmers sell produce in low-income economies. We develop a conceptual framework through which to study contracting between smallholders and a commodity-processing firm. We then conduct an empirical meta-analysis of agricultural value chains in five countries across three continents (Ghana, India, Madagascar, Mozambique, and Nicaragua). We document patterns of participation, the welfare gains associated with participation, reasons for non-participation, the significant extent of contract non-compliance, and the considerable dynamism of these value chains, as farmers and firms enter and exit frequently.Agricultural Value Chains, Contract Farming, Africa, Asia, Latin America

Star Formation in the Northern Cloud Complex of NGC 2264

We have made continuum and spectral line observations of several outflow sources in the Mon OB1 dark cloud (NGC 2264) using the Heinrich Hertz Telescope (HHT) and ARO 12m millimeter-wave telescope. This study explores the kinematics and outflow energetics of the young stellar systems observed and assesses the impact star formation is having on the surrounding cloud environment. Our data set incorporates 12CO(3-2), 13CO(3-2), and 12CO(1-0) observations of outflows associated with the sources IRAS 06382+1017 and IRAS 06381+1039, known as IRAS 25 and 27, respectively, in the northern cloud complex. Complementary 870 micron continuum maps were made with the HHT 19 channel bolometer array. Our results indicate that there is a weak (approximately less than 0.5%) coupling between outflow kinetic energy and turbulent energy of the cloud. An analysis of the energy balance in the IRAS 25 and 27 cores suggests they are maintaining their dynamical integrity except where outflowing material directly interacts with the core, such as along the outflow axes.Comment: 28 pages including 6 figures, to be published in ApJ 01 July 2006, v645, 1 issu

Plans for a 10-m Submillimeter-wave Telescope at the South Pole

A 10 meter diameter submillimeter-wave telescope has been proposed for the NSF Amundsen-Scott South Pole Station. Current evidence indicates that the South Pole is the best submillimeter-wave telescope site among all existing or proposed ground-based observatories. Proposed scientific programs place stringent requirements on the optical quality of the telescope design. In particular, reduction of the thermal background and offsets requires an off-axis, unblocked aperture, and the large field of view needed for survey observations requires shaped optics. This mix of design elements is well-suited for large scale (square degree) mapping of line and continuum radiation from submillimeter-wave sources at moderate spatial resolutions (4 to 60 arcsecond beam size) and high sensitivity (milliJansky flux density levels). the telescope will make arcminute angular scale, high frequency Cosmic Microwave Background measurements from the best possible ground-based site, using an aperture which is larger than is currently possible on orbital or airborne platforms. Effective use of this telescope will require development of large (1000 element) arrays of submillimeter detectors which are background-limited when illuminated by antenna temperatures near 50 K.Comment: 12 pages, 3 figure