Towards a theory of singular thought about abstract mathematical objects

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects

Collisions and close encounters involving massive main-sequence stars

We study close encounters involving massive main sequence stars and the evolution of the exotic products of these encounters as common--envelope systems or possible hypernova progenitors. We show that parabolic encounters between low-- and high--mass stars and between two high--mass stars with small periastrons result in mergers on timescales of a few tens of stellar freefall times (a few tens of hours). We show that such mergers of unevolved low--mass stars with evolved high--mass stars result in little mass loss ($\sim0.01$ M$_{\odot}$) and can deliver sufficient fresh hydrogen to the core of the collision product to allow the collision product to burn for several million years. We find that grazing encounters enter a common--envelope phase which may expel the envelope of the merger product. The deposition of energy in the envelopes of our merger products causes them to swell by factors of $\sim100$. If these remnants exist in very densely-populated environments ($n\gtrsim10^{7}$ pc$^{-3}$), they will suffer further collisions which may drive off their envelopes, leaving behind hard binaries. We show that the products of collisions have cores rotating sufficiently rapidly to make them candidate hypernova/gamma--ray burst progenitors and that $\sim0.1$ of massive stars may suffer collisions, sufficient for such events to contribute significantly to the observed rates of hypernovae and gamma--ray bursts.Comment: 15 pages, 13 figures, LaTeX, to appear in MNRAS (in press

Influence of organic films on the evaporation and condensation of water in aerosol

Uncertainties in quantifying the kinetics of evaporation and condensation of water from atmospheric aerosol are a significant contributor to the uncertainty in predicting cloud droplet number and the indirect effect of aerosols on climate. The influence of aerosol particle surface composition, particularly the impact of surface active organic films, on the condensation and evaporation coefficients remains ambiguous. Here, we report measurements of the influence of organic films on the evaporation and condensation of water from aerosol particles. Significant reductions in the evaporation coefficient are shown to result when condensed films are formed by monolayers of long-chain alcohols [C(n)H((2n+1))OH], with the value decreasing from 2.4 × 10(−3) to 1.7 × 10(−5) as n increases from 12 to 17. Temperature-dependent measurements confirm that a condensed film of long-range order must be formed to suppress the evaporation coefficient below 0.05. The condensation of water on a droplet coated in a condensed film is shown to be fast, with strong coherence of the long-chain alcohol molecules leading to islanding as the water droplet grows, opening up broad areas of uncoated surface on which water can condense rapidly. We conclude that multicomponent composition of organic films on the surface of atmospheric aerosol particles is likely to preclude the formation of condensed films and that the kinetics of water condensation during the activation of aerosol to form cloud droplets is likely to remain rapid

Virtual patient design : exploring what works and why : a grounded theory study

Objectives: Virtual patients (VPs) are online representations of clinical cases used in medical education. Widely adopted, they are well placed to teach clinical reasoning skills. International technology standards mean VPs can be created, shared and repurposed between institutions. A systematic review has highlighted the lack of evidence to support which of the numerous VP designs may be effective, and why. We set out to research the influence of VP design on medical undergraduates. Methods: This is a grounded theory study into the influence of VP design on undergraduate medical students. Following a review of the literature and publicly available VP cases, we identified important design properties. We integrated them into two substantial VPs produced for this research. Using purposeful iterative sampling, 46 medical undergraduates were recruited to participate in six focus groups. Participants completed both VPs, an evaluation and a 1-hour focus group discussion. These were digitally recorded, transcribed and analysed using grounded theory, supported by computer-assisted analysis. Following open, axial and selective coding, we produced a theoretical model describing how students learn from VPs. Results: We identified a central core phenomenon designated ‘learning from the VP’. This had four categories: VP Construction; External Preconditions; Student–VP Interaction, and Consequences. From these, we constructed a three-layer model describing the interactions of students with VPs. The inner layer consists of the student's cognitive and behavioural preconditions prior to sitting a case. The middle layer considers the VP as an ‘encoded object’, an e-learning artefact and as a ‘constructed activity’, with associated pedagogic and organisational elements. The outer layer describes cognitive and behavioural change. Conclusions: This is the first grounded theory study to explore VP design. This original research has produced a model which enhances understanding of how and why the delivery and design of VPs influence learning. The model may be of practical use to authors, institutions and researchers

NuSTAR hard X-ray data and Gemini 3D spectra reveal powerful AGN and outflow histories in two low-redshift Lyman-α\alpha blobs

We have shown that Lyman-$\alpha$ blobs (LABs) may still exist even at $z\sim0.3$, about 7 billion years later than most other LABs known (Schirmer et al. 2016). Their luminous Ly$\alpha$ and [OIII] emitters at $z\sim0.3$ offer new insights into the ionization mechanism. This paper focuses on the two X-ray brightest LABs at $z\sim0.3$, SDSS J0113$+$0106 (J0113) and SDSS J1155$-$0147 (J1155), comparable in size and luminosity to `B1', one of the best-studied LABs at $z \gtrsim$ 2. Our NuSTAR hard X-ray (3--30 keV) observations reveal powerful active galactic nuclei (AGN) with $L_{2-10{\;\rm keV}}=(0.5$--$3)\times10^{44}$ erg cm$^{-2}$ s$^{-1}$. J0113 also faded by a factor of $\sim 5$ between 2014 and 2016, emphasizing that variable AGN may cause apparent ionization deficits in LABs. Joint spectral analyses including Chandra data constrain column densities of $N_{\rm H}=5.1^{+3.1}_{-3.3}\times10^{23}$ cm$^{-2}$ (J0113) and $N_{\rm H}=6.0^{+1.4}_{-1.1}\times10^{22}$ cm$^{-2}$ (J1155). J0113 is likely buried in a torus with a narrow ionization cone, but ionizing radiation is also leaking in other directions as revealed by our Gemini/GMOS 3D spectroscopy. The latter shows a bipolar outflow over $10$ kpc, with a peculiar velocity profile that is best explained by AGN flickering. X-ray analysis of J1155 reveals a weakly absorbed AGN that may ionize over a wide solid angle, consistent with our 3D spectra. Extinction corrected [OIII] log-luminosities are high, $\sim43.6$. The velocity dispersions are low, $\sim100$--$150$ km s$^{-1}$, even at the AGN positions. We argue that this is a combination of high extinction hiding the turbulent gas, and previous outflows that have cleared the escape paths for their successors.Comment: 15 pages, 17 Figures, accepted for publication in Ap

A Survey for Low-Surface-Brightness Galaxies Around M31. I. The Newly Discovered Dwarf Andromeda V

We present images and a color-magnitude diagram for And V, a new dwarf spheroidal companion to M31 that was found using a digital filtering technique applied to 1550 square degrees of the second Palomar Sky Survey. And V resolves into stars easily in follow-up 4-m V- and I-band images, from which we deduce a distance of 810 +/- 45 kpc using the tip of the red giant branch method. Within the uncertainties, this distance is identical to the Population II distances for M31 and, combined with a projected separation of 112 kpc, provides strong support for a physical association between the two galaxies. There is no emission from And V detected in H alpha, 1.4 GHz radio continuum, or IRAS bandpasses, and there is no young population seen in the color-magnitude diagram that might suggest that And V is an irregular. Thus, the classification as a new dwarf spheroidal member of the Local Group seems secure. With an extinction-corrected central surface brightness of 25.2 V mag per square arcsec, a mean metal abundance of [Fe/H] approximately -1.5, and no evidence for upper AGB stars, And V resembles And I & III.Comment: Accepted for publication in The Astronomical Journal, November 1998 issue; 4 embedded PostScript figures, 4 JPEG figures; see http://aloe.tuc.noao.edu/jacoby/dwarfs.html for a complete full-resolution PostScript versio

Dark-Ages Reionisation & Galaxy Formation Simulation XVI: The Thermal Memory of Reionisation

Intergalactic medium temperature is a powerful probe of the epoch of reionisation, as information is retained long after reionisation itself. However, mean temperatures are highly degenerate with the timing of reionisation, with the amount heat injected during the epoch, and with the subsequent cooling rates. We post-process a suite of semi-analytic galaxy formation models to characterise how different thermal statistics of the intergalactic medium can be used to constrain reionisation. Temperature is highly correlated with redshift of reionisation for a period of time after the gas is heated. However as the gas cools, thermal memory of reionisation is lost, and a power-law temperature-density relation is formed, $T = T_0(1+\delta)^{1-\gamma}$ with $\gamma \approx 1.5$. Constraining our model against observations of electron optical depth and temperature at mean density, we find that reionisation likely finished at $z_{\rm{reion}} = 6.8 ^{+ 0.5} _{-0.8}$ with a soft spectral slope of $\alpha = 2.8 ^{+ 1.2} _{-1.0}$. By restricting spectral slope to the range $[0.5,2.5]$ motivated by population II synthesis models, reionisation timing is further constrained to $z_{\rm{reion}} = 6.9 ^{+ 0.4} _{-0.5}$. We find that, in the future, the degeneracies between reionisation timing and background spectrum can be broken using the scatter in temperatures and integrated thermal history.Comment: 17 pages, 17 figures, Accepted for publication in MNRA

Dynamics of particle size on inhalation of environmental aerosol and impact on deposition fraction

Inhalation of elevated levels of particulate air pollution has been shown to elicit the onset of adverse health effects in humans, where the magnitude of the response is a product of where in the lung the particulate dose is delivered. At any point in time during inhalation the depositional flux of the aerosol is a function of the radius of the droplet, thus a detailed understanding of the rate and magnitude of the mass flux of water to the droplet during inhalation is crucial. In this study, we assess the impact of aerosol hygroscopicity on deposited dose through the inclusion of a detailed treatment of the mass flux of water to account for the dynamics of particle size in a modified version of the standard International Commission on Radiological Protection (ICRP) whole lung deposition model. The ability to account for the role of the relative humidity (RH) of the aerosol prior to, and during, inhalation on the deposition pattern is explored, and found to have a significant effect on the deposition pattern. The model is verified by comparison to previously published measurements, and used to demonstrate that ambient RH affects where in the lung indoor particulate air pollution is delivered

On the Varieties of Abstract Objects

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and causal powers