Biphasic behaviour in malignant invasion

Invasion is an important facet of malignant growth that enables tumour cells to colonise adjacent regions of normal tissue. Factors known to influence such invasion include the rate at which the tumour cells produce tissue-degrading molecules, or proteases, and the composition of the surrounding tissue matrix. A common feature of experimental studies is the biphasic dependence of the speed at which the tumour cells invade on properties such as protease production rates and the density of the normal tissue. For example, tumour cells may invade dense tissues at the same speed as they invade less dense tissue, with maximal invasion seen for intermediate tissue densities. In this paper, a theoretical model of malignant invasion is developed. The model consists of two coupled partial differential equations describing the behaviour of the tumour cells and the surrounding normal tissue. Numerical methods show that the model exhibits steady travelling wave solutions that are stable and may be smooth or discontinuous. Attention focuses on the more biologically relevant, discontinuous solutions which are characterised by a jump in the tumour cell concentration. The model also reproduces the biphasic dependence of the tumour cell invasion speed on the density of the surrounding normal tissue. We explain how this arises by seeking constant-form travelling wave solutions and applying non-standard phase plane methods to the resulting system of ordinary differential equations. In the phase plane, the system possesses a singular curve. Discontinuous solutions may be constructed by connecting trajectories that pass through particular points on the singular curve and recross it via a shock. For certain parameter values, there are two points at which trajectories may cross the singular curve and, as a result, two distinct discontinuous solutions may arise

Common envelope ejection in massive binary stars - Implications for the progenitors of GW150914 and GW151226

The recently detected gravitational wave signals (GW150914 and GW151226) of the merger event of a pair of relatively massive stellar-mass black holes (BHs) calls for an investigation of the formation of such progenitor systems in general. We analyse the common envelope (CE) stage of the "traditional" formation channel in binaries where the first-formed compact object undergoes an in-spiral inside the envelope of its evolved companion star and ejects the envelope in that process. We calculate envelope binding energies of donor stars with initial masses between 4 and 115 Msun for metallicities of Z=Zsun/2 and Z=Zsun/50, and derive minimum masses of in-spiralling objects needed to eject these envelopes. We find that CE evolution, besides from producing WD-WD and NS-NS binaries, may, in principle, also produce massive BH-BH systems with individual BH component masses up to ~50-60 Msun, in particular for donor stars evolved to giants. However, the physics of envelope ejection of massive stars remains uncertain. We discuss the applicability of the energy-budget formalism, the location of the bifurcation point, the recombination energy and the accretion energy during in-spiral as possible energy sources, and also comment on the effect of inflated helium cores. Massive stars in a wide range of metallicities and with initial masses up to at least 115 Msun may possibly shed their envelopes and survive CE evolution, depending on their initial orbital parameters, similarly to the situation for intermediate mass and low-mass stars with degenerate cores. We conclude that based on stellar structure calculations, and in the view of the usual simple energy budget analysis, events like GW150914 and GW151226 could possibly be produced from the CE channel. Calculations of post-CE orbital separations, however, and thus the estimated LIGO detection rates, remain highly uncertain. [Abridged]Comment: 13 pages, 7 figures, A&A accepte

Adolescent reproductive health and awareness of HIV among rural high school students, North Western Ethiopia.

Ethiopia is faced with an increasing problem from HIV infection, and the vulnerability of adolescents is a key concern. There is little information on the knowledge, attitudes and practices of this age group with respect to HIV, sexually transmitted diseases and preventive measures. We conducted a cross-sectional study among 260 students from two rural high schools in North Western Ethiopia. We found that although the general awareness of HIV was high, correct knowledge of the virus and its modes of transmission was shown in only 44% of adolescent boys and 41% of adolescent girls. Knowledge of HIV and condoms was lower among students whose parents were farmers, significant so among girls (p=0.02). Use of condoms among sexually active single male students (49%) was insufficient but was higher than among adolescents in many other African settings. Knowledge of STDs was generally low: 82% of adolescent males and 37% of adolescent females had some awareness of STDs. Almost 20% of sexually active males in the study had previously experienced an STD, almost all of whom had visited a commercial sex worker. Targeted interventions are warranted among adolescents and sex workers in Ethiopia complemented by STD treatment services

The self-care for people initiative: the outcome evaluation.

To determine the effects of a community-based training programme in self-care on the lay population

Convention emergence in partially observable topologies

In multi-agent systems it is often desirable for agents to adhere to standards of behaviour that minimise clashes and wasting of (limited) resources. In situations where it is not possible or desirable to dictate these standards globally or via centralised control, convention emergence offers a lightweight and rapid alternative. Placing fixed strategy agents within a population has been shown to facilitate faster convention emergence with some degree of control. Placing these fixed strategy agents at topologically influential locations (such as high-degree nodes) increases their effectiveness. However, finding such influential locations often assumes that the whole network is visible or that it is feasible to inspect the whole network in a computationally practical time, a fact not guaranteed in many real-world scenarios. We present an algorithm, PO-Place, that finds influential nodes given a finite number of network observations. We show that PO-Place finds sets of nodes with similar reach and influence to the set of high-degree nodes and we then compare the performance of PO-Place to degree placement for convention emergence in several real-world topologies

Asteroseismic test of rotational mixing in low-mass white dwarfs

We exploit the recent discovery of pulsations in mixed-atmosphere (He/H), extremely low-mass white dwarf precursors (ELM proto-WDs) to test the proposition that rotational mixing is a fundamental process in the formation and evolution of low-mass helium core white dwarfs. Rotational mixing has been shown to be a mechanism able to compete efficiently against gravitational settling, thus accounting naturally for the presence of He, as well as traces of metals such as Mg and Ca, typically found in the atmospheres of ELM proto-WDs. Here we investigate whether rotational mixing can maintain a sufficient amount of He in the deeper driving region of the star, such that it can fuel, through HeII-HeIII ionization, the observed pulsations in this type of stars. Using state-of-the-art evolutionary models computed with MESA, we show that rotational mixing can indeed explain qualitatively the very existence and general properties of the known pulsating, mixed-atmosphere ELM proto-WDs. Moreover, such objects are very likely to pulsate again during their final WD cooling phase.Comment: accepted for publication in A&A Letter

Ultra-luminous X-ray sources and neutron-star-black-hole mergers from very massive close binaries at low metallicity

Gravitational waves from the binary black hole (BH) merger GW150914 may enlighten our understanding of ultra-luminous X-ray sources (ULXs), as BHs>30Msun can reach luminosities>4x10^39 erg s^-1 without exceeding their Eddington limit. It is then important to study variations of evolutionary channels for merging BHs, which might instead form accreting BHs and become ULXs. It was recently shown that massive binaries with mass ratios close to unity and tight orbits can undergo efficient rotational mixing and evolve chemically homogeneously, resulting in a compact BH binary. We study similar systems by computing ~120000 detailed binary models with the MESA code covering a wide range of initial parameters. For initial mass ratios M2/M1~0.1-0.4, primaries >40Msun can evolve chemically homogeneously, remaining compact and forming a BH without undergoing Roche-lobe overflow. The secondary then expands and transfers mass to the BH, initiating a ULX phase. We predict that ~1 out of 10^4 massive stars evolves this way, and that in the local universe 0.13 ULXs per Msun yr^-1 of star-formation rate are observable, with a strong preference for low-metallicities. At metallicities log Z>-3, BH masses in ULXs are limited to 60Msun due to the occurrence of pair-instability supernovae which leave no remnant, resulting in an X-ray luminosity cut-off. At lower metallicities, very massive stars can avoid exploding as pair-instability supernovae and instead form BHs with masses above 130Msun, producing a gap in the ULX luminosity distribution. After the ULX phase, neutron-star-BH binaries that merge in less than a Hubble time are produced with a formation rate <0.2 Gpc^-3 yr^-1. We expect that upcoming X-ray observatories will test these predictions, which together with additional gravitational wave detections will provide strict constraints on the origin of the most massive BHs that can be produced by stars.Comment: Accepted for publication in A&A. 19 Pages plus 16 pages of appendices. Abstract abridge