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

A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

Diffraction from visible lattice points and k-th power free integers

We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation, see math-ph/9903046 and references therein. Using similar methods we show the same result for the 1-dimensional set of k-th power free integers with k at least 2. Of special interest is the fact that neither of these sets is a Delone set --- each has holes of unbounded inradius. We provide a careful formulation of the mathematical ideas underlying the study of diffraction from infinite point sets.Comment: 45 pages, with minor corrections and improvements; dedicated to Ludwig Danzer on the occasion of his 70th birthda

A rotor technology assessment of the advancing blade concept

A rotor technology assessment of the Advancing Blade Concept (ABC) was conducted in support of a preliminary design study. The analytical methodology modifications and inputs, the correlation, and the results of the assessment are documented. The primary emphasis was on the high-speed forward flight performance of the rotor. The correlation data base included both the wind tunnel and the flight test results. An advanced ABC rotor design was examined; the suitability of the ABC for a particular mission was not considered. The objective of this technology assessment was to provide estimates of the performance potential of an advanced ABC rotor designed for high speed forward flight

Entropy and diffraction of the kk-free points in nn-dimensional lattices

We consider the $k$th-power-free points in $n$-dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these sets have holes of unbounded inradius.Comment: 27 pages, 2 figures; revised version with new references [7,8,23]; latest version with new Theorem 6 and updated reference [7

Breeding to improve meat eating quality in Terminal sire sheep breeds

An economic value for sheep meat eating quality was derived using consumer taste panel sensory trait scores and willingness to pay data. Improving eating quality by one score generated a price premium to commercial producers of $0.15/kg relative to a carcass price of$4.50/kg. Eating quality was included in a breeding objective with growth and lean meat yield. Under selection index scenarios modelled, simultaneous improvement of all traits was only possible with genomic testing of male selection candidates due to antagonistic correlations involving yield, eating quality, intramuscular fat, and shear force. Economic gain could be increased by up to 20% compared to current industry selection indexes

Seminole Voices

In a series of interviews conducted from 1969 to 1971 and again from 1998 to 1999, more than two hundred members of the Florida Seminole community described their lives for the Samuel Proctor Oral History Program at the University of Florida. Some of those interviews, now showcased in this volume, shed light on how the Seminoles’ society, culture, religion, government, health care, and economy had changed during a tumultuous period in Florida’s history. In 1970 the Seminoles lived in relative poverty, dependent on the Bureau of Indian Affairs, tourist trade, cattle breeding, handicrafts, and truck farming. By 2006 they were operating six casinos, and in 2007 they purchased Hard Rock International for $965 million. Within one generation, the tribe moved from poverty and relative obscurity to entrepreneurial success and wealth. Seminole Voices relates how economic changes have affected everyday life and values. The Seminoles’ frank opinions and fascinating stories offer a window into the world of a modern Native community as well as a useful barometer of changes affecting its members at the beginning of the twenty-first century

Defining and Targeting Health Disparities in Chronic Obstructive Pulmonary Disease

The global burden of chronic obstructive pulmonary disease (COPD) continues to grow in part due to better outcomes in other major diseases and in part because a substantial portion of the worldwide population continues to be exposed to inhalant toxins. However, a disproportionate burden of COPD occurs in people of low socioeconomic status (SES) due to differences in health behaviors, sociopolitical factors, and social and structural environmental exposures. Tobacco use, occupations with exposure to inhalant toxins, and indoor biomass fuel (BF) exposure are more common in low SES populations. Not only does SES affect the risk of developing COPD and etiologies, it is also associated with worsened COPD health outcomes. Effective interventions in these people are needed to decrease these disparities. Efforts that may help lessen these health inequities in low SES include 1) better surveillance targeting diagnosed and undiagnosed COPD in disadvantaged people, 2) educating the public and those involved in health care provision about the disease, 3) improving access to cost-effective and affordable health care, and 4) markedly increasing the efforts to prevent disease through smoking cessation, minimizing use and exposure to BF, and decreasing occupational exposures. COPD is considered to be one the most preventable major causes of death from a chronic disease in the world; therefore, effective interventions could have a major impact on reducing the global burden of the disease, especially in socioeconomically disadvantaged populations

Multiple planar coincidences with N-fold symmetry

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.Comment: 13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references update

Local Complexity of Delone Sets and Crystallinity

This paper characterizes when a Delone set X is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. Let N(T) count the number of translation-inequivalent patches of radius T in X and let M(T) be the minimum radius such that every closed ball of radius M(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a `gap in the spectrum' of possible growth rates between being bounded and having linear growth, and that having linear growth is equivalent to X being an ideal crystal. Explicitly, for N(T), if R is the covering radius of X then either N(T) is bounded or N(T) >= T/2R for all T>0. The constant 1/2R in this bound is best possible in all dimensions. For M(T), either M(T) is bounded or M(T) >= T/3 for all T>0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M(T) >= c(n)T for all T>0, for a certain constant c(n) which depends on the dimension n of X and is greater than 1/3 when n > 1.Comment: 26 pages. Uses latexsym and amsfonts package