Repetitive Delone Sets and Quasicrystals

This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is called repetitive if there is a function M(T) such that every ball of radius M(T)+T contains a copy of each kind of patch of radius T that occurs in the set. This is equivalent to the minimality of an associated topological dynamical system with R^n-action. There is a lower bound for M(T) in terms of N(T), namely N(T) = O(M(T)^n), but no general upper bound. The complexity of a repetitive Delone set can be measured by the growth rate of its repetitivity function M(T). For example, M(T) is bounded if and only if the set is a crystal. A set is called is linearly repetitive if M(T) = O(T) and densely repetitive if M(T) = O(N(T))^{1/n}). We show that linearly repetitive sets and densely repetitive sets have strict uniform patch frequencies, i.e. the associated topological dynamical system is strictly ergodic. It follows that such sets are diffractive. In the reverse direction, we construct a repetitive Delone set in R^n which has M(T) = O(T(log T)^{2/n}(log log log T)^{4/n}), but does not have uniform patch frequencies. Aperiodic linearly repetitive sets have many claims to be the simplest class of aperiodic sets, and we propose considering them as a notion of "perfectly ordered quasicrystal".Comment: To appear in "Ergodic Theory and Dynamical Systems" vol.23 (2003). 37 pages. Uses packages latexsym, ifthen, cite and files amssym.def, amssym.te

Bridge Damage Models for Seismic Risk Assessment of Oregon Highway Network

The highway transportation network of the United States relies on the health and integrity of major infrastructure elements such as bridges. Frequently traveled parts of Oregon are within the seismically active Pacific Northwest and many of the bridges were designed and built to lateral demands that were assumed to be less than the current expectation, a deficiency caused by our growing awareness of seismic hazard and our enhanced understanding of the non-linear response of bridges. This vulnerability to damage from earthquakes can result in not only immediate damage, but also in potentially lingering economic impact caused by the disruption to traffic and freight mobility. Using analytical methods, fragility curves were constructed assuming lognormal capacity and demand distributions. Probability of failure was determined for the four damage state conditions of slight, moderate, extensive, and complete levels of damage. These statistical values were compared to the median and dispersion values proposed by other researchers, in addition to those calculated using guidelines from the HAZUS Technical Manual. Older multiple-span Oregon bridges were found to be significantly more fragile than the HAZUS models. As a result of this modeling and analysis effort, the relative fragility of the modeled typical 3-span and 5-span bridges was determined and quantified. Possible causes of the relatively high fragilities were also considered

The reconstruction of primary teachers' identitities

Primary teachers have had to reconstruct their identities in response to the reconstruction of the education system. The holism, humanism and vocationalism of the old Plowden self-identity has been challenged by a new assigned social identity signalled in the assault on child-centred philosophy, the diminution of elementary trust, and changes in the teacher role. These challenges have thrown up new dilemmas for teachers, and represent 'fateful moments' in the careers of their identities. In trying to resolve the dilemmas, teachers have engaged in identity work, characterised mainly by identity talk, and a number of emotional and intellectual strategies. The result has been a partitioning of the old Plowden self-identity, with the 'real self' being largely withheld from the new personal identity and the sense of vocationalism being set to one side. The new personal identity in teaching represents a more instrumental and situational outlook, with the substantial self finding more expression elsewhere. Identity work is still in progress and seems set to continue while teachers have to find ways of relating to two or more competing discourses

Quantitative Spectroscopy of Supernovae for Dark Energy Studies

Detailed quantitative spectroscopy of Type Ia supernovae (SNe~Ia) provides crucial information needed to minimize systematic effects in both ongoing SNe Ia observational programs such as the Nearby Supernova Factory, ESSENCE, and the SuperNova Legacy Survey (SNLS) and in proposed JDEM missions such as SNAP, JEDI, and DESTINY. Quantitative spectroscopy is mandatory to quantify and understand the observational strategy of comparing ``like versus like''. It allows us to explore evolutionary effects, from variations in progenitor metallicity to variations in progenitor age, to variations in dust with cosmological epoch. It also allows us to interpret and quantify the effects of asphericity, as well as different amounts of mixing in the thermonuclear explosion.Comment: White paper submitted to the Dark Energy Task Force, 13 pages, 5 figure

Oral and Written Transmission in Ethiopian Christian Chant

Of all the musical traditions in the world among which fruitful comparisons with medieval European chant might be made, the chant tradition of the Ethiopian Orthodox Church promises to be especially informative. In Ethiopia one can actually witness many of the same processes of oral and written transmission as were or may have been active in medieval Europe. Music and literacy are taught in a single curriculum in ecclesiastical schools. Future singers begin to acquire the repertory by memorising chants that serve both as models for whole melodies and as the sources of the melodic phrases linked to individual notational signs. At a later stage of training each one copies out a complete notated manuscript on parchment using medieval scribal techniques. But these manuscripts are used primarily for study purposes; during liturgical celebrations the chants are performed from memory without books, as seems originally to have been the case also with Gregorian and Byzantine chant. Finally, singers learn to improvise sung liturgical poetry according to a structured system of rules. If one desired to imitate the example of Parry and Lord, who investigated the modern South Slavic epic for possible clues to Homeric poetry, it would be difficult to find a modern culture more similar to the one that spawned Gregorian chant.African and African American StudiesMusi

Classificatory struggles in the midst of austerity: policing or politics?

This article reports findings on class identities amongst a small sample of mainly working-class residents in the City of Salford. We attempt to develop a Rancièrian framework for understanding class identities, centred on his key concept of dissensus, and how these ideas have been developed by Imogen Tyler through the notion of ‘classificatory struggles’. From this, we identify a continuum of responses that are discernible in relation to the neoliberal order of classifications: from those orientated to a ‘policing’ function, either accepting and internalising dominant discourses or attempting to displace abjection onto others, to those that tend more towards ‘politics’ in either asserting alternative circuits of value or through an appeal to the name of the proletariat as a political claim to radical equality. In examining our data, we note that although a majority disavowed an explicit working-class identity, they nonetheless engaged in a range of classificatory struggles

Phenology of Apothecium Production in Populations of Monilinia vaccinii-corymbosi from Early- and Late-Maturing Blueberry Cultivars

Pseudosclerotia were evaluated for differences in timing of apothecium development in four controlled experiments conducted over a 2-year period. In a separate experiment, conidia from 10 randomly selected isolates from both of the fungal populations were used to inoculate open flowers. Germination of pseudosclerotia produced from these artificial inoculations also was evaluated. The timing and rate of shoot elongation for cvs. Weymouth and Jersey were assessed in one greenhouse and two field experiments. Average development times for the fungal population from cv. Weymouth were 8 to 15 days earlier or 33 to 42% less than those for the population from cv. Jersey. The fungal population from Weymouth also exhibited less variation in development times for each developmental stage measured. Similarly, germination of pseudosclerotia produced in artificial inoculations differed between populations. On average, pseudosclerotia derived from the Weymouth population produced apothecia 16 days earlier. During spring 1995 and 1996, vegetative and truss buds on cv. Weymouth developed 4 to 16 days earlier than those on cv. Jersey. These results demonstrate that M. vaccinii-corymbosi exhibits variation in timing of pseudosclerotia germination and apothecium development within and between populations. We hypothesize that differences observed in the timing of apothecium development are related to the fitness of the populations on their original host cultivars and were selected by host phenolog

Variation and Heritability of Phenology in the Fungus Monilinia vaccinii-corymbosi on Blueberry

The germination of field-collected pseudosclerotia and the development of apothecia from eight New Jersey populations of the mummy berry fungus Monilinia vaccinii-corymbosi were evaluated under controlled conditions in the greenhouse. Development data for apothecia were used to describe the timing of apothecium formation and to estimate broad- and narrow-sense heritabilities of fungal phenology. Mean development times for the formation of apothecia ranged from 35.4 to 54.7 days. The mean development times for populations collected from early-season cv. Weymouth ranged from 35.4 to 39.6 days and were significantly shorter than the development times for three of the four populations collected from late-season cv. Jersey (46.9 to 54.7 days) or for the population collected from mixed stands of cultivated blueberries (42.7 days). The development of populations from late cultivars planted in very close proximity to early cv. Weymouth was early (36.5 to 39.0 days) and not significantly different from the development of populations collected from cv. Weymouth. Phenotypic and genetic variances of apothecium development for individual populations ranged from 18.9 to 44.8 and 7.2 to 30.9, respectively. Broad-sense heritabilities of apothecia development for each fungal population, calculated by partitioning phenotypic variation into genetic and environmental components, ranged from 0.31 to 0.78. Narrow-sense heritabilities of apothecia development, based on parent-offspring regression, ranged from 0.58 to 0.78. These results indicate that populations ofM. vaccinii-corymbosi differ in phenology and that a significant portion of the phenological variation within populations is genetic. Thus, it is plausible to propose that the phenology of apothecium development is a component of fungal fitness and that host phenology can influence the timing of pathogen development