A note on the probability of generating alternating or symmetric groups

We improve on recent estimates for the probability of generating the alternating and symmetric groups $\mathrm{Alt}(n)$ and $\mathrm{Sym}(n)$. In particular we find the sharp lower bound, if the probability is given by a quadratic in $n^{-1}$. This leads to improved bounds on the largest number $h(\mathrm{Alt}(n))$ such that a direct product of $h(\mathrm{Alt}(n))$ copies of $\mathrm{Alt}(n)$ can be generated by two elements

Breaking the Grenville–Sveconorwegian link in Rodinia reconstructions

The Grenville, Sveconorwegian, and Sunsas orogens are typically inferred to reflect collision between Laurentia, Baltica, and Amazonia at ca. 1.0 Ga, forming a central portion of the Rodinia supercontinent. This triple‐junction configuration is often nearly identical in otherwise diverse Rodinia reconstructions. However, available geological data suggest that although the Grenville and Sveconorwegian provinces shared a similar tectonic evolution from pre‐1.8 to ca. 1.5 Ga, they record distinctly different tectonic histories leading up to, during, and possibly following Grenville–Sveconorwegian orogenesis. Moreover, palaeomagnetic data suggest the two continents were separated at peak orogenesis, further invalidating any direct correlation. A number of possible interpretations are permissible with available geological and palaeomagnetic data, of which a “classic” triple‐junction configuration appears least likely. In contrast to the commonly inferred intertwined Proterozoic evolution of Baltica and Laurentia, the possibility remains that they were unrelated for a billion years between 1.5 and 0.45 Ga

What influences healthcare professionals' treatment preferences for older women with operable breast cancer?: an application of the discrete choice experiment

Introduction Primary endocrine therapy (PET) is used variably in the UK as an alternative to surgery for older women with operable breast cancer. Guidelines state that only patients with “significant comorbidity” or “reduced life expectancy” should be treated this way and age should not be a factor. Methods A Discrete Choice Experiment (DCE) was used to determine the impact of key variables (patient age, comorbidity, cognition, functional status, cancer stage, cancer biology) on healthcare professionals' (HCP) treatment preferences for operable breast cancer among older women. Multinomial logistic regression was used to identify associations. Results 40% (258/641) of questionnaires were returned. Five variables (age, co-morbidity, cognition, functional status and cancer size) independently demonstrated a significant association with treatment preference (p < 0.05). Functional status was omitted from the multivariable model due to collinearity, with all other variables correlating with a preference for operative treatment over no preference (p < 0.05). Only co-morbidity, cognition and cancer size correlated with a preference for PET over no preference (p < 0.05). Conclusion The majority of respondents selected treatment in accordance with current guidelines, however in some scenarios, opinion was divided, and age did appear to be an independent factor that HCPs considered when making a treatment decision in this population

Age and growth in the Australian freshwater mussel, Westralunio carteri, with an evaluation of the fluorochrome calcein for validating the assumption of annulus formation

Growth and longevity of freshwater mussels (Unionida) are important for defining life-history strategies and assessing vulnerability to human impacts. We used mark-recapture and analysis of shell rings to investigate age and growth of the hyriid, Westralunio carteri, at 5 sites in southwestern Australia. We tested the utility of the in situ marker calcein for validating the assumption of annulus formation in adults. Calcein was incorporated into the shells of all recovered individuals, but it provided an interpretable reference mark in only 4 of 16 individuals. These 4 individuals produced 1 shell ring subsequent to the mark, supporting the assumption of annulus production during the austral winter. Maximum age ranged among populations from 36 to 52 y and maximum size ranged from 72.9 to 82.8 mm. Mean age and length did not differ between sexes, and growth trajectories differed between sexes at only 1 site. Estimates of growth measured by the von Bertalanffy growth constant, K, ranged from 0.021 to 0.336 among sites. Estimates from mark-recapture experiments were 20 to 52% lower than values from shell annuli at all sites except 1 where K from shell annuli was similar to 1/2 that estimated from mark-recapture. Both methods showed a positive relationship between K and mean water temperature among sites, suggesting a role of riparian shading in regulating stream temperature, and hence, indirectly influencing mussel growth. Mussel growth and mean N or P concentrations were not related among sites, but total N at the site with highest mussel growth was >2x higher than at any other site. Westralunio carteri is a long-lived, slow-growing bivalve. Maximum age, K, and probable age at maturity (4-6 y) are similar to other slow-growing freshwater bivalve groups. This suite of life-history traits is considered an adaptation for stable aquatic habitats. Therefore, W. carteri can be expected to adapt poorly to human impacts, such as riparian clearing and water extraction, which increase the temporal variability of environmental conditions in streams

The Sveconorwegian orogeny: reamalgamation of the fragmented southwestern margin of Fennoscandia

The Sveconorwegian orogeny encompasses magmatic, metamorphic and deformational events between ca. 1140 and 920 Ma at the southwestern margin of Fennoscandia. In recent years, the tectonic setting of this nearly 200 Myr-long evolution has been debated, with some workers arguing for collision with an unknown continent off the present-day southwest coast of Norway, and others advocating accretionary processes inboard of an active margin. Recently, it has been suggested that orogeny may have been gravity-driven by delamination and foundering of heavy subcontinental lithospheric mantle in an intraplate setting, in some ways similar to proposed sagduction processes in the Archaean. Resolving the tectonic setting of the Sveconorwegian orogen has implications for correlation with other orogens and Rodinia supercontinent reconstructions and for assessments of the evolution of plate tectonics on Earth, from the Archaean to the present. Here, we present new mapping and geochronological data from the Bamble and Telemark lithotectonic units in the central and western Sveconorwegian orogen – the former representing a critical region separating western parts of the orogen that underwent long-lived high- to ultrahigh-temperature metamorphism and magmatism from parts closer to the orogenic foreland that underwent episodic high-pressure events. The data show that the units constituting the Sveconorwegian orogen most likely formed at the southwestern margin of Fennoscandia between ca. 1800 and 1480 Ma, followed by fragmentation during widespread extension between ca. 1340 and 1100 Ma marked by bimodal magmatism and sedimentation. A summary of Sveconorwegian magmatic, metamorphic and depositional events in the different units shows disparate histories prior to their assembly with adjacent units. The most likely interpretation of this record seems to be that episodic, Sveconorwegian metamorphic and deformational events in the central and eastern parts of the orogen represent accretion and assembly of these units. This process most likely took place behind an active margin to the southwest that sustained mafic underplating in the proximal back-arc, resulting in high- to ultrahigh-temperature metamorphism in the western parts. In this interpretation, all features of the Sveconorwegian orogen are readily explained by modern-style plate tectonic processes and hypotheses involving some form of vertical, intraplate tectonics are not supported

Adiabatic Output Coupling of a Bose Gas at Finite Temperatures

We develop a general theory of adiabatic output coupling from trapped atomic Bose-Einstein Condensates at finite temperatures. For weak coupling, the output rate from the condensate, and the excited levels in the trap, settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state where the population in the trap is not appreciably depleted. We show how the composition of the output beam, containing condensate and thermal component, may be controlled by changing the frequency of the output coupler. This composition determines the first and second order coherence of the output beam. We discuss the changes in the composition of the bose gas left in the trap and show how nonresonant output coupling can stimulate either the evaporation of thermal excitations in the trap or the growth of non-thermal excitations, when pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from the previous submission have been fixe

Genes in the postgenomic era

We outline three very different concepts of the gene - 'instrumental', 'nominal', and 'postgenomic'. The instrumental gene has a critical role in the construction and interpretation of experiments in which the relationship between genotype and phenotype is explored via hybridization between organisms or directly between nucleic acid molecules. It also plays an important theoretical role in the foundations of disciplines such as quantitative genetics and population genetics. The nominal gene is a critical practical tool, allowing stable communication between bioscientists in a wide range of fields grounded in well-defined sequences of nucleotides, but this concept does not embody major theoretical insights into genome structure or function. The post-genomic gene embodies the continuing project of understanding how genome structure supports genome function, but with a deflationary picture of the gene as a structural unit. This final concept of the gene poses a significant challenge to conventional assumptions about the relationship between genome structure and function, and between genotype and phenotype