A Human-Oriented Term Rewriting System

© Springer Nature Switzerland AG 2019. We introduce a fully automatic system, implemented in the Lean theorem prover, that solves equality problems of everyday mathematics. Our overriding priority in devising the system is that it should construct proofs of equality in a way that is similar to that of humans. A second goal is that the methods it uses should be domain independent. The basic strategy of the system is to operate with a subtask stack: whenever there is no clear way of making progress towards the task at the top of the stack, the program finds a promising subtask, such as rewriting a subterm, and places that at the top of the stack instead. Heuristics guide the choice of promising subtasks and the rewriting process. This makes proofs more human-like by breaking the problem into tasks in the way that a human would. We show that our system can prove equality theorems simply, without having to preselect or orient rewrite rules as in standard theorem provers, and without having to invoke heavy duty tools for performing simple reasoning

The Sloan Lens ACS Survey. IX. Colors, Lensing and Stellar Masses of Early-type Galaxies

We present the current photometric dataset for the Sloan Lens ACS (SLACS) Survey, including HST photometry from ACS, WFPC2, and NICMOS. These data have enabled the confirmation of an additional 15 grade `A' (certain) lens systems, bringing the number of SLACS grade `A' lenses to 85; including 13 grade `B' (likely) systems, SLACS has identified nearly 100 lenses and lens candidates. Approximately 80% of the grade `A' systems have elliptical morphologies while ~10% show spiral structure; the remaining lenses have lenticular morphologies. Spectroscopic redshifts for the lens and source are available for every system, making SLACS the largest homogeneous dataset of galaxy-scale lenses to date. We have developed a novel Bayesian stellar population analysis code to determine robust stellar masses with accurate error estimates. We apply this code to deep, high-resolution HST imaging and determine stellar masses with typical statistical errors of 0.1 dex; we find that these stellar masses are unbiased compared to estimates obtained using SDSS photometry, provided that informative priors are used. The stellar masses range from 10^10.5 to 10^11.8 M$_\odot$ and the typical stellar mass fraction within the Einstein radius is 0.4, assuming a Chabrier IMF. The ensemble properties of the SLACS lens galaxies, e.g. stellar masses and projected ellipticities, appear to be indistinguishable from other SDSS galaxies with similar stellar velocity dispersions. This further supports that SLACS lenses are representative of the overall population of massive early-type galaxies with M* >~ 10^11 M$_\odot$, and are therefore an ideal dataset to investigate the kpc-scale distribution of luminous and dark matter in galaxies out to z ~ 0.5.Comment: 20 pages, 18 figures, 5 tables, published in Ap

Mock observations with the Millennium Simulation: cosmological downsizing and intermediate-redshift observations

Only by incorporating various forms of feedback can theories of galaxy formation reproduce the present-day luminosity function of galaxies. It has also been argued that such feedback processes might explain the counterintuitive behaviour of 'downsizing' witnessed since redshifts z ≃ 1–2. To examine this question, observations spanning 0.4 < z < 1.4 from the Deep Extragalactic Evolutionary Probe (DEEP)2/Palomar survey are compared with a suite of equivalent mock observations derived from the Millennium Simulation, populated with galaxies using the galform code. Although the model successfully reproduces the observed total mass function and the general trend of 'downsizing', it fails to accurately reproduce the colour distribution and type-dependent mass functions at all redshifts probed. This failure is shared by other semi-analytical models which collectively appear to 'over-quench' star formation in intermediate-mass systems. These mock lightcones are also a valuable tool for investigating the reliability of the observational results in terms of cosmic variance. Using variance estimates derived from the lightcones, we confirm the significance of the decline since z ∼ 1 in the observed number density of massive blue galaxies which, we argue, provides the bulk of the associated growth in the red sequence. We also assess the limitations arising from cosmic variance in terms of our ability to observe mass-dependent growth since z ∼ 1

Adaptive Optics Imaging of QSOs with Double-Peaked Narrow Lines: Are they Dual AGNs?

Active galaxies hosting two accreting and merging super-massive black holes (SMBHs) -- dual Active Galactic Nuclei (AGN) -- are predicted by many current and popular models of black hole-galaxy co-evolution. We present here the results of a program that has identified a set of probable dual AGN candidates based on near Infra-red (NIR) Laser Guide-Star Adaptive Optics (LGS AO) imaging with the Keck II telescope. These candidates are selected from a complete sample of radio-quiet Quasi-stellar Objects (QSOs) drawn from the Sloan Digital Sky Survey (SDSS), which show double-peaked narrow AGN emission lines. Of the twelve AGNs imaged, we find six with double galaxy structure, of which four are in galaxy mergers. We measure the ionization of the two velocity components in the narrow AGN lines to test the hypothesis that both velocity components come from an active nucleus. The combination of a well-defined parent sample and high-quality imaging allows us to place constraints on the fraction of SDSS QSOs that host dual accreting black holes separated on kiloparsec (kpc) scales: ~0.3%-0.65%. We derive from this fraction the time spent in a QSO phase during a typical merger and find a value that is much lower than estimates that arise from QSO space densities and galaxy merger statistics. We discuss possible reasons for this difference. Finally, we compare the SMBH mass distributions of single and dual AGN and find little difference between the two within the limited statistics of our program, hinting that most SMBH growth happens in the later stages of a merger process.Comment: 9 pages, 4 figures, 1 table; accepted to the Astrophysical Journa

Identification of hydroxyapatite spherules provides new insight into subretinal pigment epithelial deposit formation in the aging eye.

Accumulation of protein- and lipid-containing deposits external to the retinal pigment epithelium (RPE) is common in the aging eye, and has long been viewed as the hallmark of age-related macular degeneration (AMD). The cause for the accumulation and retention of molecules in the sub-RPE space, however, remains an enigma. Here, we present fluorescence microscopy and X-ray diffraction evidence for the formation of small (0.5-20 μm in diameter), hollow, hydroxyapatite (HAP) spherules in Bruch's membrane in human eyes. These spherules are distinct in form, placement, and staining from the well-known calcification of the elastin layer of the aging Bruch's membrane. Secondary ion mass spectrometry (SIMS) imaging confirmed the presence of calcium phosphate in the spherules and identified cholesterol enrichment in their core. Using HAP-selective fluorescent dyes, we show that all types of sub-RPE deposits in the macula, as well as in the periphery, contain numerous HAP spherules. Immunohistochemical labeling for proteins characteristic of sub-RPE deposits, such as complement factor H, vitronectin, and amyloid beta, revealed that HAP spherules were coated with these proteins. HAP spherules were also found outside the sub-RPE deposits, ready to bind proteins at the RPE/choroid interface. Based on these results, we propose a novel mechanism for the growth, and possibly even the formation, of sub-RPE deposits, namely, that the deposit growth and formation begin with the deposition of insoluble HAP shells around naturally occurring, cholesterol-containing extracellular lipid droplets at the RPE/choroid interface; proteins and lipids then attach to these shells, initiating or supporting the growth of sub-RPE deposits

Eff ect of Revalor- XH, Revalor- 200, and Combination Revalor- IH/Revalor- 200 on Yearling Heifer Growth Performance and Carcass Characteristics

A commercial feedlot trial tested three implant strategies (Revalor- 200 on day 0, Revalor- IH on d 0 and re- implanted with Revalor- 200 on d 56, or Revalor- XH on d 0) on growth performance and carcass characteristics of heifers fed for 138 d. Th ere were no differences observed for final body weight, dry matter intake, or average daily gain on a live basis among implant strategies. Heifers implanted with Revalor- IH/200 combination had greater carcass- adjusted final body weight and improved feed conversion compared to Revalor- 200 and Revalor- XH. Hot carcass weights, dressing percent, and LM area were improved for Revalor- IH/200 implanted heifers relative to Revalor- 200 and Revalor- XH implanted heifers. Marbling score and 12th- rib fat thickness were not different among implant treatments. Heifers implanted with Revalor- IH/200 had a shift to a lower USDA yield grade distribution compared to 200 and XH implanted heifers. Th e greater concentration of trenbolone acetate and estradiol provided by Revalor- IH/200 combination slightly improved growth and carcass performance compared to the non- coated Revalor- 200 implant and partially coated Revalor- XH implant

Virtual risk management—exploring effects of childhood risk experiences through innovative methods (ViRMa) for primary school children in Norway: study protocol for the ViRMa project

Background: Research indicates that risky play benefits children’s risk assessment and risk management skills and offers several positive health effects such as resilience, social skills, physical activity, well-being, and involvement. There are also indications that the lack of risky play and autonomy increases the likelihood of anxiety. Despite its well-documented importance, and the willingness of children to engage in risky play, this type of play is increasingly restricted. Assessing long-term effects of risky play has been problematic because of ethical issues with conducting studies designed to allow or encourage children to take physical risks with the potential of injury. Objective: The Virtual Risk Management project aims to examine children’s development of risk management skills through risky play. To accomplish this, the project aims to use and validate newly developed and ethically appropriate data collection tools such as virtual reality, eye tracking, and motion capturing, and to provide insight into how children assess and handle risk situations and how children’s past risky play experiences are associated with their risk management. Methods: We will recruit 500 children aged 7-10 years and their parents from primary schools in Norway. Children’s risk management will be measured through data concerning their risk assessment, risk willingness, and risk handling when completing a number of tasks in 3 categories of virtual reality scenarios: street crossing, river crossing, and playing on playground equipment. The children will move around physically in a large space while conducting the tasks and wear 17 motion-capturing sensors that will measure their movements to analyze motor skills. We will also collect data on children’s perceived motor competence and their sensation-seeking personality. To obtain data on children’s risk experiences, parents will complete questionnaires on their parental style and risk tolerance, as well as information about the child’s practical risk experience. Results: Four schools have been recruited to participate in data collection. The recruitment of children and parents for this study started in December 2022, and as of April 2023, a total of 433 parents have consented for their children to participate. Conclusions: The Virtual Risk Management project will increase our understanding of how children’s characteristics, upbringing, and previous experiences influence their learning and ability to handle challenges. Through development and use of cutting-edge technology and previously developed measures to describe aspects of the children’s past experiences, this project addresses crucial topics related to children’s health and development. Such knowledge may guide pedagogical questions and the development of educational, injury prevention, and other health-related interventions, and reveal essential areas for focus in future studies. It may also impact how risk is addressed in crucial societal institutions such as the family, early childhood education, and schools

The Sloan Lens ACS Survey. X. Stellar, Dynamical, and Total Mass Correlations of Massive Early-type Galaxies

We use stellar masses, photometry, lensing, and velocity dispersions to investigate empirical correlations for the final sample of 73 early-type lens galaxies (ETGs) from the SLACS survey. The traditional correlations (Fundamental Plane [FP] and its projections) are consistent with those found for non-lens galaxies, supporting the thesis that SLACS lens galaxies are representative of massive ETGs. The addition of strong lensing estimates of the total mass allows us to gain further insights into their internal structure: i) the mean slope of the total mass density profile is = 2.078+/-0.027 with an intrinsic scatter of 0.16+/-0.02; ii) gamma' correlates with effective radius and central mass density, in the sense that denser galaxies have steeper profiles; iii) the dark matter fraction within reff/2 is a monotonically increasing function of galaxy mass and size; iv) the dimensional mass M_dim is proportional to the total mass, and both increase more rapidly than stellar mass M*; v) the Mass Plane (MP), obtained by replacing surface brightness with surface mass density in the FP, is found to be tighter and closer to the virial relation than the FP and the M*P, indicating that the scatter of those relations is dominated by stellar population effects; vi) we construct the Fundamental Hyper-Plane by adding stellar masses to the MP and find the M* coefficient to be consistent with zero and no residual intrinsic scatter. Our results demonstrate that the dynamical structure of ETGs is not scale invariant and that it is fully specified by the total mass, r_eff, and sigma. Although the basic trends can be explained qualitatively in terms of varying star formation efficiency as a function of halo mass and as the result of dry and wet mergers, reproducing quantitatively the observed correlations and their tightness may be a significant challenge for galaxy formation models.Comment: 16 pages, 9 figures; submitted to ApJ after responding to the referee comment