Abstract:
Background While prepubertal nutritional influences appear to play a role in sexual maturation, there is a need to clarify the potential contributions of maternal and childhood influences in setting the tempo of reproductive maturation. In the present study we employed an established model of nutritional programming to evaluate the relative influences of prenatal and postnatal nutrition on growth and ovarian function in female offspring. Methods Pregnant Wistar rats were fed either a calorie-restricted diet, a high fat diet, or a control diet during pregnancy and/or lactation. Offspring then were fed either a control or a high fat diet from the time of weaning to adulthood. Pubertal age was monitored and blood samples collected in adulthood for endocrine analyses. Results We report that in the female rat, pubertal timing and subsequent ovarian function is influenced by the animal's nutritional status in utero, with both maternal caloric restriction and maternal high fat nutrition resulting in early pubertal onset. Depending on the offspring's nutritional history during the prenatal and lactational periods, subsequent nutrition and body weight gain did not further influence offspring reproductive tempo, which was dominated by the effect of prenatal nutrition. Whereas maternal calorie restriction leads to early pubertal onset, it also leads to a reduction in adult progesterone levels later in life. In contrast, we found that maternal high fat feeding which also induces early maturation in offspring was associated with elevated progesterone concentrations. Conclusions These observations are suggestive of two distinct developmental pathways leading to the acceleration of pubertal timing but with different consequences for ovarian function. We suggest different adaptive explanations for these pathways and for their relationship to altered metabolic homeostasis.

Abstract:
Two factors have been suggested to play a role in determin ing the limit to inflorescence size within a species: energy limitation and diminishing pollination returns for larger inflorescence sizes. In an effort to assess the significance or pollination limitation we examined the effect or inflorescence size on pol1inator visitation patterns for 2 species, Aconitum columbianum and Delphinium nelsonii. These species are similar in their pollination biology, and both have a racemose inflorescence, but they differ markedly in inflorescence size (A. columbianum has from 1-26 open flowers while D. nelsonii has 1-6 open flowers). For each species the following parameters were examined as a function of inflorescence size: visits per inflorescence, flowers visited per visit, and visits per flower. For D. nelsonii all 3 parameters increased with increasing inflorescence size although for large inflorescences the rate of increase slowed slightly for flowers per visit and visits per flower. For A. columbianum all 3 parameters also generally increased with increasing inflorescence size but for the largest sizes there was no further increase in visits per inflorescence or flowers per visit and there was a decrease in visits per flower. The pattern of a smaller increase in attractiveness with progressively larger inflorescences corresponds to what would be expected if inflorescence attractiveness were based on the concept of just noticeable difference. The observed pattern of a smaller increase in flowers per visit with increasing inflorescence size can be described accurately by a model in which there is, on average, a fixed probability of moving from one flower to another on an inflorescence. The number of visits per flower is simply the consequence of the other 2 parameters. The lack of any significant decrease in pollinator visitation with increasing inflorescence size for D. nelsonii suggests that energy is probably the factor limiting inflorescence size. For A. columbianum, the largest Inflorescences have a reduced number of visits per flower and the total number of visits per inflorescence for the very largest inflorescences is reduced. This, in conjunction with a possible reduction in visit quality for large inflorescences, raises the possibility that inflorescence size in A. columbianum may be pollination limited. [ca] S'han suggerit do s factors que juguen un paper en la determinació de la mida de la inflorescència a l'interior d'una espècie: la limitació d'energia i la disminució de la recompensa de la pol-linització per a inflorescències llargues. En un es

Abstract:
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".

Abstract:
The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over real algebraic number fields.

Abstract:
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.

Abstract:
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.

Abstract:
Background: Comparisons of health-related quality of life (HRQOL) between persons with chronic obstructive pulmonary disease (COPD) and adults in the general population are not well described. Aims: To examine associations between COPD and four measures of HRQOL in a population-based sample. Patients & Methods: These relationships were examined using data from 13,887 adults aged >18 years who participated in the 2007 Behavioral Risk Factor Surveillance System (BRFSS) conducted in North Carolina (NC). Logistic regression was used to obtain adjusted relative odds (aOR). Results: The age-adjusted prevalence of COPD among NC adults was 5.4% (standard error 0.27). Nearly half of adults with COPD reported fair/poor health compared with 15% of those without the condition (age-aOR, 5.5; 95% confidence interval [CI], 4.4 to 6.8). On average, adults with COPD reported twice as many unhealthy days (physical/mental) as those without the condition. The age-adjusted prevalence of >14 unhealthy days during the prior 30 days was 45% for adults with COPD and 17% for those without. The aOR of >14 unhealthy days was 1.7 (95% CI, 1.4 to 2.2) times greater among adults with COPD compared with those without. Conclusions: These results suggest COPD is independently associated with lower levels of HRQOL and reinforce the importance of preventing COPD and its complications through health education messages stressing efforts to reduce total personal exposure to tobacco smoke, occupational dusts and chemicals, and other indoor and outdoor air pollutants linked to COPD and early disease recognition. Our findings represent one of the few statewide efforts in the US and provide guidance for disease management and policy decision making.

Abstract:
X-ray reflectivity and fluorescence near total reflection experiments were performed to examine the affinities of divalent ions ($\mathrm{Ca^{2+}}$ and $\mathrm{Ba^{2+}}$) from aqueous solution to a charged phosphatidic-acid (PA) surface. A phospholipid (1,2-Dimyristoyl-sn-Glycero-3-Phosphate, DMPA), spread as a monolayer at the air/water interface, was used to form and control the charge density at the interface. We find that for solutions of the pure salts (i.e., $\mathrm{CaCl_{2}}$ and $\mathrm{BaCl_{2}}$), the number of bound ions per DMPA at the interface is saturated at concentrations that exceed $\mathrm{10^{-3}M}$. For a 1:1 $\mathrm{Ca^{2+}/Ba^{2+}}$ mixed solutions, we find that the bound $\mathrm{Ca^{2+}/Ba^{2+}}$ ratio at the interface is 4:1. If the only property determining charge accumulation near PA were the ionic charges, the concentration of mixed $\mathrm{Ca^{2+}/Ba^{2+}}$ at the interface would equal that of the bulk. Our results show a clear specific affinity of PA for Ca compared to Ba. We provide some discussion on this issues as well as some implications for biological systems. Although our results indicate an excess of counterion charge with respect to the surface charge, that is, charge inversion, the analysis of both reflectivity and fluorescence do not reveal excess of co-ions (namely, $\mathrm{Cl^{-}}$ or $\mathrm{I}^{-}$).

Abstract:
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.

Abstract:
The coincidence problem for planar patterns with $N$-fold symmetry is considered. For the N-fold symmetric module with $N<46$, all isometries of the plane are classified that result in coincidences of finite index. This is done by reformulating the problem in terms of algebraic number fields and using prime factorization. The more complicated case $N \ge 46$ is briefly discussed and N=46 is described explicitly. The results of the coincidence problem also solve the problem of colour lattices in two dimensions and its natural generalization to colour modules.