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

Intuitive Confidence Reflects Speed of Initial Responses in Point Spread Predictions

Previous research has revealed that intuitive confidence is an important predictor of how people choose between intuitive and non-intuitive alternatives. Two studies were conducted to investigate the determinants of intuitive confidence. Across these studies participants predicted the outcomes of several National Basketball Association games, both with and without reference to a point spread. As predicted, after controlling for the variability associated with point spread magnitude, the faster participants were to predict the outright winner of a game (i.e., generate an intuition), the more likely participants were to predict the favourite against the point spread (i.e., endorse the intuition). Overall, my findings point to the speed of intuition generation as a determinant of intuitive confidence, and thus a predictor of choice in situations featuring intuitive and non-intuitive alternatives

Twentieth Century Geomorphic Changes of the Lower Green River in Canyonlands National Park, Utah: An Investigation of Timing, Magnitude and Process

Since the early 20th century, the Green River, the longest tributary of the Colorado River, has narrowed, decreasing available riparian and aquatic habitat. Initially, the widespread establishment of non-native tamarisk was considered to be the primary driver of channel narrowing. An alternative hypothesis postulated that changes in hydrology drove narrowing. Reductions in total streamflow and changes to flow regime occurred due to wide-spread water development, decreased snowmelt flood magnitude, and the increased cyclicity of wet and dry years. The two hypotheses agree on channel narrowing, but each influences modern river management differently. A tamarisk-driven model of narrowing implies that modern flow management doesn’t substantially affect channel change. Conversely, channel narrowing driven by changes in hydrology implies that present flow management decisions matter and continued adjustments to flow regime may result in future channel change. To understand the roles of decreasing total annual flow, declining annual peak flood magnitude, and changing vegetation communities on 20th century channel narrowing, we investigated channel narrowing along the lower Green River within Canyonlands National Park (CNP). Previous studies agree that the channel has narrowed, however, the rate, timing and magnitude of documented narrowing are only partially understood. Multiple lines of evidence were used to reconstruct the history of channel narrowing in the lower Green River. This study focuses on channel narrowing, but additionally investigated possible changes to channel depth, identified process, timing and magnitude of floodplain formation. Floodplain formation was described in the field using stratigraphy, sedimentology, and dendrogeomorphology exposed in a floodplain trench. Channel and floodplain surveys were conducted to determine possible changes in bed elevation. Additionally, existing aerial imagery, hydrologic data, and sediment transport data were analyzed. These techniques were applied to determine magnitude, timing and processes of channel narrowing at multiple spatial and temporal scales. The floodplain investigation identified a new period of channel narrowing by vertical accretion after high peak flow years of 1983 and 1984. Narrowing was initiated by vertical accretion in the active channel, deposited by moderate floods exceeded more than 50% of the time. Vertical accretion continued in the early 1990s, converting the active channel into a periodically inundated floodplain surface. Suspended-sediment deposition dominated deposits, resulting in the formation of natural levees and floodplain troughs in both inset floodplains. Rates of deposition were highly variable, ranging from 0.03-0.50 m/yr. The lower Green River within Canyonlands National Park has narrowed substantially since the late 1800s, resulting in a narrower channel. Changes to flood magnitude, rate and timing since 1900, driven by increased water storage and diversion in the Green River basin and declines in annual precipitation, were responsible for inset floodplain formation. Floodplains of the contemporary lower Green River in CNP began forming in the late 1930s and continued to form and vertically aggrade in the 20th century by inset floodplain formation. During this time period, peak flow and total runoff declined due to climatic changes and water development. Analysis of aerial imagery covering 61 kilometers (km) of the Green River in CNP shows that changes to the floodplain identified in the trench are representative of the entire study area. The establishment of non-native tamarisk (Tamarix spp.) did not drive channel narrowing, though dense stands stabilized banks and likely promoted sediment deposition. The lower Green River narrowed 12% from 1940-2014, with the majority of narrowing (10% of all narrowing) occurring from the 1980s to the present. Inset floodplain formation reflects changes to flood magnitude and timing resulting from water development and decreases in natural runoff. Findings suggest that long-term management of the riverine corridor within Canyonlands National Park will require a greater focus on upstream flow contributions and how those flows are currently managed. Recovery of endangered endemic native fishes, the Colorado pikeminnow (Ptychocheilus lucius), and the razorback sucker (Xyrauchen texanus), plays a primary role in determining current flow allocations. Collaboration with upstream stakeholders and managers is necessary to maximize elements of the flow regime that preserve channel width and limit channel narrowing

Intestinal barrier tightening by a cell-penetrating antibody to Bin1, a candidate target for immunotherapy of ulcerative colitis.

Patients afflicted with ulcerative colitis (UC) are at increased risk of colorectal cancer. While its causes are not fully understood, UC is associated with defects in colonic epithelial barriers that sustain inflammation of the colon mucosa caused by recruitment of lymphocytes and neutrophils into the lamina propria. Based on genetic evidence that attenuation of the bridging integrator 1 (Bin1) gene can limit UC pathogenicity in animals, we have explored Bin1 targeting as a therapeutic option. Early feasibility studies in the dextran sodium sulfate mouse model of experimental colitis showed that administration of a cell-penetrating Bin1 monoclonal antibody (Bin1 mAb 99D) could prevent lesion formation in the colon mucosa in part by preventing rupture of lymphoid follicles. In vivo administration of Bin1 mAb altered tight junction protein expression and cecal barrier function. Strikingly, electrophysiology studies in organ cultures showed that Bin1 mAb could elevate resistance and lowe

Cultures of psychiatry and the professional socialization process: the case of containment methods for disturbed patients

Acute mental disorder necessitating admission to hospital is often accompanied by disturbed behaviour that threatens the health of the person concerned or that of those around them. A range of containment methods are used by psychiatric professionals to keep patients and staff safe. These strategies are strongly emotive and attract strong moral valuations, yet differ sharply between countries. This paper reports a study to investigate the relationship between attitudes to these containment methods, and exposure to psychiatric education and practice. It was hypothesized that the culture of psychiatry in the study country would socialise students' views towards the locally dominant pattern of relative evaluations. Nine cohorts of student psychiatric nurses at different stages of their training at one UK University were asked to complete ratings on 11 containment methods. Containment methods fell into five groups, with mechanical restraint and net beds attracting the most severe disapproval. Neither the relative evaluation of methods, nor the intensity of those evaluations, changed systematically with duration of training. The findings support the interpretation that the relative evaluations of psychiatric containment methods are a property of wider national cultures, rather than an isolated tradition of professional psychiatric practice

Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet NaYbO2_2

We present the structural characterization and low-temperature magnetism of the triangular-lattice delafossite NaYbO$_2$. Synchrotron x-ray diffraction and neutron scattering exclude both structural disorder and crystal-electric-field randomness, whereas heat-capacity measurements and muon spectroscopy reveal the absence of magnetic order and persistent spin dynamics down to at least 70\,mK. Continuous magnetic excitations with the low-energy spectral weight accumulating at the $K$-point of the Brillouin zone indicate the formation of a novel spin-liquid phase in a triangular antiferromagnet. This phase is gapless and shows a non-trivial evolution of the low-temperature specific heat. Our work demonstrates that NaYbO$_2$ practically gives the most direct experimental access to the spin-liquid physics of triangular antiferromagnets.Comment: 6 pages, 4figure

Multilevel modelling of the incidence of visceral leishmaniasis in Teresina, Brazil

Epidemics of visceral leishmaniasis (VL) in major Brazilian cities are new phenomena since 1980. As determinants of transmission in urban settings probably operate at different geographic scales, and information is not available for each scale, a multilevel approach was used to examine the effect of canine infection and environmental and socio-economic factors on the spatial variability of incidence rates of VL in the city of Teresina. Details on an outbreak of greater than 1200 cases of VL in Teresina during 1993-1996 were available at two hierarchical levels: census tracts (socio-economic characteristics, incidence rates of human VL) and districts, which encompass census tracts (prevalence of canine infection). Remotely sensed data obtained by satellite generated environmental information at both levels. Data from census tracts and districts were analysed simultaneously by multilevel modelling. Poor socio-economic conditions and increased vegetation were associated with a high incidence of human VL. Increasing prevalence of canine infection also predicted a high incidence of human VL, as did high prevalence of canine infection before and during the epidemic. Poor socio-economic conditions had an amplifying effect on the association between canine infection and the incidence of human VL. Focusing interventions on areas with characteristics identified by multilevel analysis could be a cost-effective strategy for controlling VL. Because risk factors for infectious diseases operate simultaneously at several levels and ecological data usually are available at different geographical scales, multilevel modelling is a valuable tool for epidemiological investigation of disease transmission