Estimation under group actions: recovering orbits from invariants

Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe very noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action in the high-noise regime. This generalizes problems of interest such as multi-reference alignment (MRA) and the reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain matching lower and upper bounds on the sample complexity of these problems in high generality, showing that the statistical difficulty is intricately determined by the invariant theory of the underlying symmetry group. In particular, we determine that for cryo-EM with noise variance $\sigma^2$ and uniform viewing directions, the number of samples required scales as $\sigma^6$. We match this bound with a novel algorithm for ab initio reconstruction in cryo-EM, based on invariant features of degree at most 3. We further discuss how to recover multiple molecular structures from heterogeneous cryo-EM samples.Comment: 54 pages. This version contains a number of new result

The hydrology of prehistoric farming systems in a central Arizona ecotone

The prehistoric land use and water management in the semi-arid Southwest was examined. Remote sensing data, geology, hydrology and biology are discussed along with an evaluation of remote sensing contributions, recommendations for applications, and proposed future remote sensing studies

Archaeological Testing and Collecting at Choke Canyon Reservoir, Nueces River Project, Texas

This monograph reports the findings made during the summer of 1977 of test excavations and/or surface collections at 17 prehistoric archaeological sites in the Choke Canyon Reservoir area. The work was carried out by Texas A&M University for the Center for Archaeological Research, The University of Texas at San Antonio. The field work was conducted to assess the archaeological potential of each site in order to advance recommendations for further investigations. The artifact samples, although meager, are described and these data are incorporated with other information from each site towards an overall site evaluation. Recommendations for further work are also included at the end of the report

Implications of the problem orientated medical record (POMR) for research using electronic GP databases: a comparison of the Doctors Independent Network Database (DIN) and the General Practice Research Database (GPRD).

Background The General Practice Research Database (GPRD) and Doctor's Independent Network Database (DIN), are large electronic primary care databases compiled in the UK during the 1990s. They provide a valuable resource for epidemiological and health services research. GPRD (based on VAMP) presents notes as a series of discrete episodes, whereas DIN is based on a system (MEDITEL) that used a Problem Orientated Medical Record (POMR) which links prescriptions to diagnostic problems. We have examined the implications for research of these different underlying philosophies. Methods Records of 40,183 children from 141 practices in DIN and 76,310 from 464 practices in GRPD who were followed to age 5 were used to compare the volume of recording of prescribing and diagnostic codes in the two databases. To assess the importance and additional value of the POMR within DIN, the appropriateness of diagnostic linking to skin emollient prescriptions was investigated. Results Variation between practices for both the number of days on which prescriptions were issued and diagnoses were recorded was marked in both databases. Mean number of "prescription days" during the first 5 years of life was similar in DIN (19.5) and in GPRD (19.8), but the average number of "diagnostic days" was lower in DIN (15.8) than in GPRD (22.9). Adjustment for linkage increased the average "diagnostic days" to 23.1 in DIN. 32.7% of emollient prescriptions in GPRD appeared with an eczema diagnosis on the same day compared to only 19.4% in DIN; however, 86.4% of prescriptions in DIN were linked to an earlier eczema diagnosis. More specifically 83% of emollient prescriptions appeared under a problem heading of eczema in the 121 practices that were using problem headings satisfactorily. Conclusion Prescribing records in DIN and GPRD are very similar, but the usage of diagnostic codes is more parsimonious in DIN because of its POMR structure. Period prevalence rates will be underestimated in DIN unless this structure is taken into account. The advantage of the POMR is that in 121 of 141 practices using problem headings as intended, most prescriptions can be linked to a problem heading providing a specific reason for their issue

Modern ‘live’ football: moving from the panoptican gaze to the performative, virtual and carnivalesque

Drawing on Redhead's discussion of Baudrillard as a theorist of hyperreality, the paper considers the different ways in which the mediatized ‘live’ football spectacle is often modelled on the ‘live’ however eventually usurps the ‘live’ forms position in the cultural economy, thus beginning to replicate the mediatized ‘live’. The blurring of the ‘live’ and ‘real’ through an accelerated mediatization of football allows the formation of an imagined community mobilized by the working class whilst mediated through the sanitization, selling of ‘events’ and the middle classing of football, through the re-encoding of sporting spaces and strategic decision-making about broadcasting. A culture of pub supporting then allows potential for working-class supporters to remove themselves from the panoptican gazing systems of late modern hyperreal football stadia and into carnivalesque performative spaces, which in many cases are hyperreal and simulated themselves

Nano-porosity in GaSb induced by swift heavy ion irradiation

Nano-porous structures form in GaSb after ion irradiation with 185 MeV Au ions. The porous layer formation is governed by the dominant electronic energy loss at this energy regime. The porous layer morphology differs significantly from that previously reported for low-energy, ion-irradiated GaSb. Prior to the onset of porosity, positron annihilation lifetime spectroscopy indicates the formation of small vacancy clusters in single ion impacts, while transmission electron microscopy reveals fragmentation of the GaSb into nanocrystallites embedded in an amorphous matrix. Following this fragmentation process, macroscopic porosity forms, presumably within the amorphous phase.The authors thank the Australian Research Council for support and the staff at the ANU Heavy Ion Accelerator Facility for their continued technical assistance. R.C.E. acknowledges the support from the Office of Basic Energy Sciences of the U.S. DOE (Grant No. DE-FG02-97ER45656)

Factors influencing the inspirational effect of major sports events on audience sport participation behaviour

The purpose of this paper is to elucidate the factors that determine the extent to which spectators attending one-off sports events feel inspired to increase their own participation in sport. The research considers both the socio-demographic and sport participation profile of the audience as well as the characteristics of an event as predictors of inspiration. The methodological approach involved secondary analysis of data collected from audiences across 10 events held in England since 2010. The findings are based on an aggregate sample of 7458 respondents. The statistical method used to analyse the data was multinomial logistic regression. The results show that the majority of respondents were inspired by the event that they attended, but the strength of the inspiration effect varied significantly according to their age; place of residence; ethnic origin; sport participation profile; and whether or not they had been exposed to information about opportunities to undertake sport. Moreover, events featuring team sports, non-age restricted events and elite events incorporating a mass participation component were also found to be positively related to inspiration. Several policy implications are identified for event organizers and public funders of both elite and community sport