Topology of Exceptional Orbit Hypersurfaces of Prehomogeneous Spaces

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups with open orbits. These hypersurface singularities include both determinantal hypersurfaces and linear free (and free*) divisors. Although these hypersurfaces have highly nonisolated singularities, we determine the topology of their Milnor fibers, complements and links. We do so by using the action of linear algebraic groups beginning with the complement, instead of using Morse type arguments on the Milnor fibers. This includes replacing the local Milnor fiber by a global Milnor fiber which has a complex geometry resulting from a transitive action of an appropriate algebraic group, yielding a compact model submanifold for the homotopy type of the Milnor fiber. The topology includes the (co)homology (in characteristic 0, and 2 torsion in one family) and homotopy groups, and we deduce the triviality of the monodromy transformations on rational (or complex) cohomology. The cohomology of the Milnor fibers and complements are isomorphic as algebras to exterior algebras or for one family, modules over exterior algebras; and cohomology of the link is, as a vector space, a truncated and shifted exterior algebra, for which the cohomology product structure is essentially trivial. We also deduce from Bott's periodicity theorem, the homotopy groups of the Milnor fibers for determinantal hypersurfaces in the stable range as the stable homotopy groups of the associated infinite dimensional symmetric spaces. Applying a Theorem of Oka we obtain a class of formal linear combinations of exceptional orbit hypersurfaces which have Milnor fibers which are homotopy equivalent to joins of the compact model submanifolds.Comment: to appear in the Journal of Topolog

Solvable Groups, Free Divisors and Nonisolated Matrix Singularities II: Vanishing Topology

In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singular matrices in a geometric configuration of free divisors which are the "exceptional orbit varieties" for repesentations of solvable groups. Because there are towers of representations for towers of solvable groups, the free divisors actually form a tower of free divisors $E_n$, and we give an inductive procedure for computing the vanishing topology of the matrix singularities. The inductive procedure we use is an extension of that introduced by L\^{e}-Greuel for computing the Milnor number of an ICIS. Instead of linear subspaces, we use free divisors arising from the geometric configuration and which correspond to subgroups of the solvable groups. Here the vanishing topology involves a singular version of the Milnor fiber; however, it still has the good connectivity properties and is homotopy equivalent to a bouquet of spheres, whose number is called the singular Milnor number. We give formulas for this singular Milnor number in terms of singular Milnor numbers of various free divisors on smooth subspaces, which can be computed as lengths of determinantal modules. In addition to being applied to symmetric, general and skew-symmetric matrix singularities, the results are also applied to Cohen--Macaulay singularities defined as 2 x 3 matrix singularities. We compute the Milnor number of isolated Cohen--Macaulay surface singularities of this type in $\mathbb{C}^4$ and the difference of Betti numbers of Milnor fibers for isolated Cohen--Macaulay 3--fold singularities of this type in $\mathbb{C}^5$.Comment: 53 pages. To appear in Geometry & Topology. Changes in response to helpful referee: replace the erroneous Corollary 6.2 with a new version, specify that we consider 2x3 Cohen-Macaulay singularities, calculate more entries of Table 5, improve wording, format for publicatio

Legitimation, professionalisation and accountability in higher education studies:an intergenerational story

The core themes of research into higher education studies (HES) have previously been identified through quantitative approaches focused on publication patterns, but there is a lack of fine-grained, qualitative analysis about the development of the field. This paper provides an intergenerational analysis of the emergence of HES in the UK since the 1960s drawing on autobiographical accounts. It reveals that many who conduct HES research retain a strong sense of disciplinary affiliation and regard its continuing epistemological health as closely linked to maintaining open borders with other disciplines. The professionalisation of the field is regarded as a mixed blessing bringing with it challenges with respect to maintaining an accessible approach to scholarship and communication with public and policy audiences. HES provides a case example of how a new academic subfield has undergone generational challenges in, respectively, seeking legitimacy, being professionalised and most recently responding to greater demands for accountability

The Wigner caustic on shell and singularities of odd functions

We study the Wigner caustic on shell of a Lagrangian submanifold L of affine symplectic space. We present the physical motivation for studying singularities of the Wigner caustic on shell and present its mathematical definition in terms of a generating family. Because such a generating family is an odd deformation of an odd function, we study simple singularities in the category of odd functions and their odd versal deformations, applying these results to classify the singularities of the Wigner caustic on shell, interpreting these singularities in terms of the local geometry of L.Comment: 24 page

Farm Operator Satisfaction with Retail Pesticide Suppliers in the Arkansas Delta

Two hundred ninety farm operators in the three easternmost crop reporting districts in Arkansas responded to a mail survey in November 1996 about their preferences and satisfaction with retail pesticide suppliers.Results show most farmers are quite satisfied with their main retail pesticide supplier, although 55.5% of the farm operators used more than one retail pesticide supplier in 1996. Users of multiple suppliers were less satisfied with their suppliers than those using only one supplier. Availability of certain pesticides was the most frequently mentioned reason for using multiple suppliers. Several attributes were important in selecting the main supplier with reputation being the most important, followed by delivery services, long-term relationship with salesperson, and price. Although not rated highly by the farm operators, location was also an important consideration in choosing a main supplier

\u3ci\u3eIn Vivo\u3c/i\u3e Human Skeletal Muscle Glycogen Measured by Chemical Exchange Saturation Transfer (GlycoCEST) and \u3csup\u3e13\u3c/sup\u3eC MRS at 7T

CEST is a molecular imaging technique that allows indirect detection of protons associated with mobile proteins. GlycoCEST is a variant of CEST for imaging tissue glycogen, the storage form of glucose. With glycoCEST, the -OH protons of glycogen are saturated, transfer the saturation to bulk water by way of chemical exchange which reduces the bulk water signal in proportion to the glycogen content. the purpose of this study was to determine the feasibility of glycoCEST imaging in human skeletal muscle at 7T. Our findings, although preliminary, suggest that glycoCEST imaging at 7T can be used to image muscle glycogen

Cold exposure induces dynamic, heterogeneous alterations in human brown adipose tissue lipid content

Brown adipose tissue undergoes a dynamic, heterogeneous response to cold exposure that can include the simultaneous synthesis, uptake, and oxidation of fatty acids. The purpose of this work was to quantify these changes in brown adipose tissue lipid content (fat-signal fraction (FSF)) using fat-water magnetic resonance imaging during individualized cooling to 3 °C above a participant’s shiver threshold. Eight healthy men completed familiarization, perception-based cooling, and MRI-cooling visits. FSF maps of the supraclavicular region were acquired in thermoneutrality and during cooling (59.5 ± 6.5 min). Brown adipose tissue regions of interest were defined, and voxels were grouped into FSF decades (0–10%, 10–20%…90–100%) according to their initial value. Brown adipose tissue contained a heterogeneous morphology of lipid content. Voxels with initial FSF values of 60–100% (P \u3c 0.05) exhibited a significant decrease in FSF while a simultaneous increase in FSF occurred in voxels with initial FSF values of 0–30% (P \u3c 0.05). These data suggest that in healthy young men, cold exposure elicits a dynamic and heterogeneous response in brown adipose tissue, with areas initially rich with lipid undergoing net lipid loss and areas of low initial lipid undergoing a net lipid accumulation

The lesbian, gay, bisexual and transgender community online: discussions of bullying and self-disclosure in YouTube videos

Computer-mediated communication has become a popular platform for identity construction and experimentation as well as social interaction for those who identify as lesbian, gay, bisexual or transgender (LGBT). The creation of user-generated videos has allowed content creators to share experiences on LGBT topics. With bullying becoming more common amongst LGBT youth, it is important to obtain a greater understanding of this phenomenon. In our study, we report on the analysis of 151 YouTube videos which were identified as having LGBT- and bullying-related content. The analysis reveals how content creators openly disclose personal information about themselves and their experiences in a non-anonymous rhetoric with an unknown public. These disclosures could indicate a desire to seek friendship, support and provide empathy

Initial Response of Mature, Experienced Runners to Barefoot Running: Transition to Forefoot Strike

Introduction Forefoot strike has been advocated for many runnersbecause of the relatively lower impact and push-off forces comparedto a heel strike. The purpose of this study was to explore the abilityof mature (> 30 years old), experienced runners to transition from aheel foot strike to a forefoot strike when first introduced to barefootrunning on a treadmill. We hypothesized: 1) mature runners who heelstrike while wearing traditional training shoes would persist in heelstriking immediately following a switch to barefoot, 2) mean shoeheel-to-toe drop would be significantly greater in runners who persistin heel striking when running barefoot compared to those who transitionto a forefoot strike pattern, and 3) there would be a significantdecrease in heel striking in the barefoot condition as running speedsincreased. Methods This was a controlled crossover laboratory study. Thirty-three experienced runners (average 23.4 miles per week) withan average age of 45.6 years were recruited for this study. The participantsfirst ran in their standard running shoes and subsequentlybarefoot. A motion capture system was utilized to detect and analyzeany transition from heel strike to forefoot strike made by study participants. Results Of the 26 participants who were classified as heel strikerunners in their running shoes, 50% (13/26, p = 0.001) transitionedto forefoot strike when changing from running in shoes to runningbarefoot. Conclusions The injuries associated with transition from standardrunning shoes to barefoot running or minimalist shoes may be influencedby the persistence of heel striking in mature runners. Olderexperienced runners may have limited ability to transition from heelto forefoot striking when first introduced to barefoot running. Maturerunners should be cautious when beginning a minimalist shoe orbarefoot running regimen

Pilot Weather Advisor System

The Pilot Weather Advisor (PWA) system is an automated satellite radio-broadcasting system that provides nearly real-time weather data to pilots of aircraft in flight anywhere in the continental United States. The system was designed to enhance safety in two distinct ways: First, the automated receipt of information would relieve the pilot of the time-consuming and distracting task of obtaining weather information via voice communication with ground stations. Second, the presentation of the information would be centered around a map format, thereby making the spatial and temporal relationships in the surrounding weather situation much easier to understan