Maximising the number of cycles in graphs with forbidden subgraphs

Fix $k \ge 2$ and let $H$ be a graph with $\chi(H) = k+1$ containing a critical edge. We show that for sufficiently large $n,$ the unique $n$-vertex $H$-free graph containing the maximum number of cycles is $T_k(n)$. This resolves both a question and a conjecture of Arman, Gunderson and Tsaturian \cite{Gund1}

Microgravity metal processing: from undercooled liquids to bulk metallic glasses

Bulk metallic glasses (BMGs) are a novel class of metal alloys that are poised for widespread commercialization. Over 30 years of NASA and ESA (as well as other space agency) funding for both ground-based and microgravity experiments has resulted in fundamental science data that have enabled commercial production. This review focuses on the history of microgravity BMG research, which includes experiments on the space shuttle, the ISS, ground-based experiments, commercial fabrication and currently funded efforts

Sensitivity to radiation-induced chromosome damage may be a marker of genetic predisposition in young head and neck cancer patients

We previously showed that levels of chromosome damage induced by ionizing radiation were, on average, higher in G 2 and G 0 lymphocytes of breast cancer patients than of normal healthy controls, but that there was no correlation between the results in the two assays. We proposed that enhanced sensitivity to G 2 or G 0 irradiation was a marker of low-penetrance predisposition to breast cancer, and have recently demonstrated heritability of sensitivity in families of breast cancer cases. We have now applied these assays to patients with head and neck cancers, for whom there is epidemiological evidence of inherited predisposition in addition to environmental causes. The mean frequency of radiation-induced G 2 aberrations was higher in the 42 patients than in 27 normal controls, but not significantly so. However, cases less than 45 years old were significantly more sensitive than normals of the same age range (P = 0.046), whereas there was no difference between patients and normals of less than 45 years. Also, there was an inverse correlation between G 2 sensitivity and age for patients but not for normals. Radiation-induced micronuclei in G 0 cells were more frequent in 49 patients than in 31 normals (P = 0.056) but, as with the G 2 assay, the greatest difference was seen between early-onset patients and young normals. Again there was an inverse correlation with age for patients but not for normals. Six patients with enhanced toxicity to radiotherapy were G 2 tested and four other such patients were G 0 tested; levels of chromosome damage were not significantly greater than in patients with normal reactions. Both assays were used on 64 individuals (39 patients, 25 normals) and there was no significant correlation between the results. We suggest that a proportion of early-onset head and neck cancer patients are genetically predisposed and that each of the two assays detects a different subset of these cases. © 2001 Cancer Research Campaign http://www.bjcancer.co

Random billiards with wall temperature and associated Markov chains

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives the probability distribution of the post-collision velocity for a given pre-collision velocity. A random billiard with microstructure (RBM) is a random billiard for which P is derived from a choice of geometric/mechanical structure on the boundary of the billiard domain. RBMs provide simple and explicit mechanical models of particle-surface interaction that can incorporate thermal effects and permit a detailed study of thermostatic action from the perspective of the standard theory of Markov chains on general state spaces. We focus on the operator P itself and how it relates to the mechanical/geometric features of the microstructure, such as mass ratios, curvatures, and potentials. The main results are as follows: (1) we characterize the stationary probabilities (equilibrium states) of P and show how standard equilibrium distributions studied in classical statistical mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine law, arise naturally as generalized invariant billiard measures; (2) we obtain some basic functional theoretic properties of P. Under very general conditions, we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert space. In a simple but illustrative example, we show that P is a compact (Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of eigenvalues of P to the features of the microstructure;(3) we explore the latter issue both analytically and numerically in a few representative examples;(4) we present a general algorithm for simulating these Markov chains based on a geometric description of the invariant volumes of classical statistical mechanics

Residues: Rethinking Chemical Environments

Boudia S, Creager ANH, Frickel S, et al. Residues: Rethinking Chemical Environments. ENGAGING SCIENCE TECHNOLOGY AND SOCIETY. 2018;4:165-178.This essay offers a new approach for conceptualizing the environmental impact of chemicals production, consumption, disposal, and regulation. Environmental protection regimes tend to be highly segmented according to place, media, substance, and effect. Existing scholarship often reflects this same segmentation, by focusing on a locality, specific chemical, social movement, or regulatory body. In turn, as new environmental measures are introduced to deal with pollution and toxicity, they tend to focus on controlling future effects rather than dealing with the accumulated contamination from past industrial activity and waste. In chemical substances we encounter phenomena that are at the same time voluminous and miniscule, regulated yet unruly. Inspired by recent work on materiality and infrastructures, we focus on the concept of residues as both material and political entities. Following residues, we argue, helps us see how the past has been built into our chemical environments and regulatory systems, and why contaminants seem to always evade control

A Pseudo-Two-Dimensional (P2D) Model for FeS2 Conversion Cathode Batteries

Conversion cathode materials are gaining interest for secondary batteries due to their high theoretical energy and power density. However, practical application as a secondary battery material is currently limited by practical issues such as poor cyclability. To better understand these materials, we have developed a pseudo-two-dimensional model for conversion cathodes. We apply this model to FeS2 - a material that undergoes intercalation followed by conversion during discharge. The model is derived from the half-cell Doyle-Fuller-Newman model with additional loss terms added to reflect the converted shell resistance as the reaction progresses. We also account for polydisperse active material particles by incorporating a variable active surface area and effective particle radius. Using the model, we show that the leading loss mechanisms for FeS2 are associated with solid-state diffusion and electrical transport limitations through the converted shell material. The polydisperse simulations are also compared to a monodisperse system, and we show that polydispersity has very little effect on the intercalation behavior yet leads to capacity loss during the conversion reaction. We provide the code as an open-source Python Battery Mathematical Modelling (PyBaMM) model that can be used to identify performance limitations for other conversion cathode materials

Learning beyond a single field of nursing through a virtual case-based approach to pre-registration nurse education.

Ensuring that pre-registration student nurses gain the richness of clinical practice to allow them to feel confident and knowledgeable to care for patients of the 21st century is often a challenge. Clinical practice challenges often mean that students will be strategic learners. This article discusses the development of a virtual case-based learning site to provide a rich experience for students to learn

Abnormal dorsal attention network activation in memory impairment after traumatic brain injury

Memory impairment is a common, disabling effect of traumatic brain injury. In healthy individuals, successful memory encoding is associated with activation of the dorsal attention network as well as suppression of the default mode network. Here, in traumatic brain injurypatients we examined whether: i) impairments in memory encoding are associated with abnormal brain activation in these networks; ii) whether changes in this brain activity predict subsequent memory retrieval; and iii) whether abnormal white matter integrity underpinningfunctional networks is associated with impaired subsequent memory. 35 patients with moderate-severetraumatic brain injury aged 23-65 years (74% males) in the post-acute/chronic phase after injury and 16 healthy controls underwent functional MRI during performance of an abstract image memory encoding task. Diffusion tensor imaging was used to assess structural abnormalities across patient groups compared to 28 age-matched healthy controls. Successful memory encoding across all participants was associated with activation of the dorsal attention network, the ventral visual stream and medial temporal lobes. Decreased activation was seen in the default mode network. Patients with preserved episodic memory demonstrated increased activation in areas of the dorsal attention network.Patients with impaired memory showed increased left anterior prefrontal activity. White matter microstructure underpinning connectivity between core nodes of the encoding networks was significantly reduced in patients with memory impairment. Our results show for the first time that patients with impaired episodic memory show abnormal activation of key nodes within the dorsal attention network and regions regulating default mode network activity during encoding. Successful encoding was associated with an opposite direction of signal change between patients with and without memory impairment, suggesting that memory encoding mechanisms could be fundamentally altered in this population. We demonstrate a clear relationship between functional networks activated during encoding and underlying abnormalities within the structural connectome in patients with memory impairment. We suggest that encoding failures in this group are likely due to failed control of goal-directed attentional resources

Runaway Massive Binaries and Cluster Ejection Scenarios

The production of runaway massive binaries offers key insights into the evolution of close binary stars and open clusters. The stars HD 14633 and HD 15137 are rare examples of such runaway systems, and in this work we investigate the mechanism by which they were ejected from their parent open cluster, NGC 654. We discuss observational characteristics that can be used to distinguish supernova ejected systems from those ejected by dynamical interactions, and we present the results of a new radio pulsar search of these systems as well as estimates of their predicted X-ray flux assuming that each binary contains a compact object. Since neither pulsars nor X-ray emission are observed in these systems, we cannot conclude that these binaries contain compact companions. We also consider whether they may have been ejected by dynamical interactions in the dense environment where they formed, and our simulations of four-body interactions suggest that a dynamical origin is possible but unlikely. We recommend further X-ray observations that will conclusively identify whether HD 14633 or HD 15137 contain neutron stars.Comment: Accepted to ApJ, 11 page