Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most $k$. Ban and Linial conjectured that every bridgeless cubic graph admits a $2$-bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph $G$ with $|E(G)| \equiv 0 \pmod 2$ has a $2$-edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we give a detailed insight into the conjectures of Ban-Linial and Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above mentioned conjectures. Moreover, we prove Ban-Linial's conjecture for cubic cycle permutation graphs. As a by-product of studying $2$-edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.Comment: 33 pages; submitted for publicatio

A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation

The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible "planetary" parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.Comment: Submitted to Ap

Experiment K-6-03. Gravity and skeletal growth, part 1. Part 2: Morphology and histochemistry of bone cells and vasculature of the tibia; Part 3: Nuclear volume analysis of osteoblast histogenesis in periodontal ligament cells; Part 4: Intervertebral disc swelling pressure associated with microgravity

Bone area, bone electrophysiology, bone vascularity, osteoblast morphology, and osteoblast histogenesis were studied in rats associated with Cosmos 1887. The results suggest that the synchronous animals were the only group with a significantly larger bone area than the basal group, that the bone electrical potential was more negative in flight than in the synchronous rats, that the endosteal osteoblasts from flight rats had greater numbers of transitional Golgi vesicles but no difference in the large Golgi saccules or the alkaline phosphatase activity, that the perioteal vasculature in the shaft of flight rats often showed very dense intraluminal deposits with adjacent degenerating osteocytes as well as lipid accumulations within the lumen of the vessels and sometimes degeneration of the vascular wall (this change was not present in the metaphyseal region of flight animals), and that the progenitor cells decreased in flight rats while the preosteoblasts increased compared to controls. Many of the results suggest that the animals were beginning to recover from the effects of spaceflight during the two day interval between landing and euthanasia; flight effects, such as the vascular changes, did not appear to recover

Socioecology Explains Individual Variation in Urban Space Use in Response to Management in Cape Chacma Baboons (Papio ursinus)

The presence of wildlife adjacent to and within urban spaces is a growing phenomenon globally. When wildlife’s presence in urban spaces has negative impacts for people and wildlife, nonlethal and lethal interventions on animals invariably result. Recent evidence suggests that individuals in wild animal populations vary in both their propensity to use urban space and their response to nonlethal management methods. Understanding such interindividual differences and the drivers of urban space use could help inform management strategies. We use direct observation and high-resolution GPS (1 Hz) to track the space use of 13 adult individuals in a group of chacma baboons (Papio ursinus) living at the urban edge in Cape Town, South Africa. The group is managed by a dedicated team of field rangers, who use aversive conditioning to reduce the time spent by the group in urban spaces. Adult males are larger, more assertive, and more inclined to enter houses, and as such are disproportionately subject to “last resort” lethal management. Field rangers therefore focus efforts on curbing the movements of adult males, which, together with high-ranking females and their offspring, comprise the bulk of the group. However, our results reveal that this focus allows low-ranking, socially peripheral female baboons greater access to urban spaces. We suggest that movement of these females into urban spaces, alone or in small groups, is an adaptive response to management interventions, especially given that they have no natural predators. These results highlight the importance of conducting behavioral studies in conjunction with wildlife management, to ensure effective mitigation techniques

A real Lorentz-FitzGerald contraction

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their `absolute ' state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity.Comment: 6 pages, no figures. Minor changes reflect published versio

'I would rather die': reasons given by 16-year-olds for not continuing their study of mathematics

Improving participation rates in specialist mathematics after the subject ceases to be compulsory at age 16 is part of government policy in England. This article provides independent and recent support for earlier findings concerning reasons for non- participation, based on free response and closed items in a questionnaire with a sample of over 1500 students in 17 schools, close to the moment of choice. The analysis supports findings that perceived difficulty and lack of confidence are important reasons for students not continuing with mathematics, and that perceived dislike and boredom, and lack of relevance, are also factors. There is a close relationship between reasons for non-participation and predicted grade, and a weaker relation to gender. An analysis of the effects of schools, demonstrates that enjoyment is the main factor differentiating schools with high and low participation indices. Building on discussion of these findings, ways of improving participation are briefly suggested

TDP-43 pathology in a patient carrying G2019S LRRK2 mutation and a novel p.Q124E MAPT.

Leucine-rich repeat kinase 2 (LRRK2) mutation is the most common cause of genetic-related parkinsonism and is usually associated with Lewy body pathology; however, tau, α-synuclein, and ubiquitin pathologies have also been reported. We report the case of a patient carrying the LRRK2 G2019S mutation and a novel heterozygous variant c.370C>G, p.Q124E in exon 4 of the microtubule-associated protein tau (MAPT). The patient developed parkinsonism with good levodopa response in her 70s. Neuropathological analysis revealed nigral degeneration and Alzheimer-type tau pathology without Lewy bodies. Immunohistochemical staining using phospho-TDP-43 antibodies identified occasional TDP-43 pathology in the hippocampus, temporal neocortex, striatum, and substantia nigra. However, TDP-43 pathology was not identified in another 4 archival LRRK2 G2019S cases with Lewy body pathology available in the Queen Square Brain Bank. Among other published cases of patients carrying LRRK2 G2019S mutation, only 3 were reportedly evaluated for TDP-43 pathology, and the results were negative. The role of the MAPT variant in the clinical and pathological manifestation in LRRK2 cases remains to be determined

Physical theory of the twentieth century and contemporary philosophy

It has been shown that the criticism of Pauli as well as of Susskind and Glogover may be avoided if the standard quantum-mechanical mathematical model has been suitably extended. There is not more any reason for Einstein's citicism, either, if in addition to some new results concerning Bell's inequalities and Belifante's argument are taken into account. The ensemble interpretation of quantum mechanics (or the hidden-variable theory) should be preferred, which is also supported by the already published results of experiments with three polarizers. Greater space in the text has been devoted also to the discussion of epistemological problems and some philosophical consequences.Comment: 12 page

An optically driven quantum dot quantum computer

We propose a quantum computer structure based on coupled asymmetric single-electron quantum dots. Adjacent dots are strongly coupled by means of electric dipole-dipole interactions enabling rapid computation rates. Further, the asymmetric structures can be tailored for a long coherence time. The result maximizes the number of computation cycles prior to loss of coherence.Comment: 4 figure