Bridging the Gap:Parent and Child Perspectives of Living With Cerebral Visual Impairments

Cerebral Visual Impairment (CVI) is an umbrella term which includes abnormalities in visual acuity, or contrast sensitivity or colour; ocular motility; visual field and the conscious and unconscious filtering or processing of visual input. Children with CVI have specific needs and problems relating to their development from infancy to adulthood which can impact on their wellbeing. Recent research indicates the complexities of living with CVI but there remains limited information of the full impact of CVI on families’ everyday lives. The qualitative interviews reported here explored families’ experiences to discover the impact of CVI on all aspects of everyday life. Parents and children (aged 6–18) were invited to participate in semi-structured interviews, either face to face, by phone or video call between January 2018 and February 2019. Topics covered everyday practicalities of living with CVI, focusing on challenges and what worked well at school and home. Interviews were audio-recorded and subject to thematic analysis to look for patterns across the data. Twenty families took part in interviews, with eight children/young people within those families contributing interviews of their own. Four themes were developed from the interviews: (1) Assessment and understanding implications of CVI, (2) Education, (3) Family life, (4) Psychological wellbeing and quality of life. The interviews provide valuable insights into the impact of living with CVI and highlight the need for more awareness of the condition among professionals in both health and education settings

Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time harmonic displacement field $\mathbf{u}(r,\theta ,\phi)$ is expanded in a separation of variables form with dependence on $\theta,\phi$ described by vector spherical harmonics with $r$-dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as $\mathbf{u}(r,\theta)$, admit this type of separation of variables solutions for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.Comment: 15 page

Post-AGB Stars in Globular Clusters and Galactic Halos

We discuss three aspects of post-AGB (PAGB) stars in old populations. (1) HST photometry of the nucleus of the planetary nebula (PN) K 648 in the globular cluster (GC) M15 implies a mass of 0.60 Msun, in contrast to the mean masses of white dwarfs in GCs of ~0.5 Msun. This suggests that K 648 is descended from a merged binary, and we infer that single Pop II stars do not produce visible PNe. (2) Yellow PAGB stars are the visually brightest stars in old populations (Mv ~ -3.3) and are easily recognizable because of their large Balmer jumps; thus they show great promise as a Pop II standard candle. Two yellow PAGB stars in the GC NGC 5986 have the same V magnitudes to within +/-0.05 mag, supporting an expected narrow luminosity function. (3) Using CCD photometry and a u filter lying below the Balmer jump, we have detected yellow PAGB stars in the halo of M31 and in its dwarf elliptical companion NGC 205. With the Milky Way zero point, we reproduce the Cepheid distance to M31, and find that NGC 205 is ~100 kpc further away than M31. The star counts imply a yellow PAGB lifetime of about 25,000 yr, and their luminosities imply masses near 0.53 Msun.Comment: 6 pages, 2 figures. To appear in proceedings of Torun, Poland, workshop on "Post-AGB Objects (Proto-Planetary Nebulae) as a Phase of Stellar Evolution," ed. S.K. Gorn

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown

Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random-copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales, and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and simulation results to appear in J Phys