Cyclic labellings with constraints at two distances

Motivated by problems in radio channel assignment, we consider the vertex-labelling of graphs with non-negative integers. The objective is to minimise the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with associated optimal assignments, for trees and cycles

Extremism propagation in social networks with hubs

One aspect of opinion change that has been of academic interest is the impact of people with extreme opinions (extremists) on opinion dynamics. An agent-based model has been used to study the role of small-world social network topologies on general opinion change in the presence of extremists. It has been found that opinion convergence to a single extreme occurs only when the average number of network connections for each individual is extremely high. Here, we extend the model to examine the effect of positively skewed degree distributions, in addition to small-world structures, on the types of opinion convergence that occur in the presence of extremists. We also examine what happens when extremist opinions are located on the well-connected nodes (hubs) created by the positively skewed distribution. We find that a positively skewed network topology encourages opinion convergence on a single extreme under a wider range of conditions than topologies whose degree distributions were not skewed. The importance of social position for social influence is highlighted by the result that, when positive extremists are placed on hubs, all population convergence is to the positive extreme even when there are twice as many negative extremists. Thus, our results have shown the importance of considering a positively skewed degree distribution, and in particular network hubs and social position, when examining extremist transmission

An Examination of the Space Weathering Patina of Lunar Rock 76015

Space weathering discussions have generally centered around soils but exposed rocks will also incur the effects of weathering. Rocks have much longer surface lifetimes than an individual soil grain and thus record a longer history of exposure. By studying the weathering products which have built up on a rock surface, we can gain a deeper perspective on the weathering process and better assess the relative importance of various weathering components. The weathered coating, or patina, of the lunar rock 76015 has been previously studied under SEM and also by TEM using ultramicrotome sample preparation methods. However, to really understand the products involved in creating these coatings, it is helpful to examine the patina in cross section, something which is now possible though the use of Focused Ion Beam (FIB) sample prep techniques, which allows us to preserve intact the delicate stratigraphy of the patina coating and provides a unique cross-sectional view of the space weathering process. Several samples have been prepared from the rock and the coatings are found to be quite variable in thickness and composition from one sample to the next

A Hypothesis to Explain Cancers in Confined Colonies of Naked Mole Rats

Abstract: Naked mole rats (NMRs) are subterranean eusocial mammals, known for their virtual absence of aging in their first 20 to 30 years of life, and their apparent resistance to cancer development. As such, this species has become an important biological model for investigating the physiological and molecular mechanisms behind cancer resistance. Two recent studies have discovered middle and late-aged worker (that is, non-breeding) NMRs in captive populations exhibiting neoplasms, consistent with cancer development, challenging the claim that NMRs are cancer resistant. These cases are possibly artefacts of inbreeding or certain rearing conditions in captivity, but they are also consistent with evolutionary theory.We present field data showing that worker NMRs live on average for 1 to 2 years. This, together with considerable knowledge about the biology of this species, provides the basis for an evolutionary explanation for why debilitating cancers in NMRs should be rare in captive populations and absent in the wild. Whereas workers are important for maintaining tunnels, colony defence, brood care, and foraging, they are highly vulnerable to predation. However, surviving workers either replace dead breeders, or assume other less active functions whilst preparing for possible dispersal. These countervailing forces (selection resulting in aging due to early-life investments in worker function, and selection for breeder longevity) along with the fact that all breeders derive from the worker morph, can explain the low levels of cancer observed by these recent studies in captive colonies. Because workers in the field typically never reach ages where cancer becomes a risk to performance or mortality, those rare observations of neoplastic growth should be confined to the artificial environments where workers survive to ages rarely if ever occurring in the wild. Thus, we predict that the worker phenotype fortuitously benefits from anti-aging and cancer protection in captive populations

Sampling the Uppermost Surface of Airless Bodies

The uppermost surface of an airless body is a critical source of ground-truth information for the various remote sensing techniques that only penetrate nanometers to micrometers into the surface. Such samples will also be vital for understanding conditions at the surface and acquiring information about how the body interacts with its environment, including solar wind interaction, grain charging and levitation [1]. Sampling the uppermost surface while preserving its structure (e.g. porosity, grain-to-grain contacts) however, is a daunting task that has not been achieved on any sample return mission to date