The role of authorial context in mathematicians’ evaluations of proof

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians’ responses, leading to four themes in expectations when evaluating the proofs that they read. First, mathematicians’ evaluations of identical arguments were sensitive to researchers’ manipulation of authorship, with most accepting arguments purportedly produced by a colleague while taking a more critical view of that same argument if produced by an undergraduate student. Our thematic analysis of interview responses led to three context-based factors influencing mathematicians’ responses when evaluating student-produced texts: course goals, instructors’ expectations, and assessment type. In the final section, we consider implications for researchers focused on understanding common practice amongst mathematicians as well as the pedagogic consequences of our findings for practice in the classroom

Discovery of a Galaxy Cluster in the Foreground of the Wide-Separation Quasar Pair UM425

We report the discovery of a cluster of galaxies in the field of UM425, a pair of quasars separated by 6.5arcsec. Based on this finding, we revisit the long-standing question of whether this quasar pair is a binary quasar or a wide-separation lens. Previous work has shown that both quasars are at z=1.465 and show broad absorption lines. No evidence for a lensing galaxy has been found between the quasars, but there were two hints of a foreground cluster: diffuse X-ray emission observed with Chandra, and an excess of faint galaxies observed with the Hubble Space Telescope. Here we show, via VLT spectroscopy, that there is a spike in the redshift histogram of galaxies at z=0.77. We estimate the chance of finding a random velocity structure of such significance to be about 5%, and thereby interpret the diffuse X-ray emission as originating from z=0.77, rather than the quasar redshift. The mass of the cluster, as estimated from either the velocity dispersion of the z=0.77 galaxies or the X-ray luminosity of the diffuse emission, would be consistent with the theoretical mass required for gravitational lensing. The positional offset between the X-ray centroid and the expected location of the mass centroid is about 40kpc, which is not too different from offsets observed in lower redshift clusters. However, UM425 would be an unusual gravitational lens, by virtue of the absence of a bright primary lensing galaxy. Unless the mass-to-light ratio of the galaxy is at least 80 times larger than usual, the lensing hypothesis requires that the galaxy group or cluster plays a uniquely important role in producing the observed deflections. Based on observations performed with the Very Large Telescope at the European Southern Observatory, Paranal, Chile.Comment: 12 pages, accepted by ApJ 2005, May 1

Wide Field Imaging. I. Applications of Neural Networks to object detection and star/galaxy classification

[Abriged] Astronomical Wide Field Imaging performed with new large format CCD detectors poses data reduction problems of unprecedented scale which are difficult to deal with traditional interactive tools. We present here NExt (Neural Extractor): a new Neural Network (NN) based package capable to detect objects and to perform both deblending and star/galaxy classification in an automatic way. Traditionally, in astronomical images, objects are first discriminated from the noisy background by searching for sets of connected pixels having brightnesses above a given threshold and then they are classified as stars or as galaxies through diagnostic diagrams having variables choosen accordingly to the astronomer's taste and experience. In the extraction step, assuming that images are well sampled, NExt requires only the simplest a priori definition of "what an object is" (id est, it keeps all structures composed by more than one pixels) and performs the detection via an unsupervised NN approaching detection as a clustering problem which has been thoroughly studied in the artificial intelligence literature. In order to obtain an objective and reliable classification, instead of using an arbitrarily defined set of features, we use a NN to select the most significant features among the large number of measured ones, and then we use their selected features to perform the classification task. In order to optimise the performances of the system we implemented and tested several different models of NN. The comparison of the NExt performances with those of the best detection and classification package known to the authors (SExtractor) shows that NExt is at least as effective as the best traditional packages.Comment: MNRAS, in press. Paper with higher resolution images is available at http://www.na.astro.it/~andreon/listapub.htm

Preference purification and the inner rational agent:A critique of the conventional wisdom of behavioural welfare economics

Neoclassical economics assumes that individuals have stable and context-independent preferences, and uses preference-satisfaction as a normative criterion. By calling this assumption into question, behavioural findings cause fundamental problems for normative economics. A common response to these problems is to treat deviations from conventional rational-choice theory as mistakes, and to try to reconstruct the preferences that individuals would have acted on, had they reasoned correctly. We argue that this preference purification approach implicitly uses a dualistic model of the human being, in which an inner rational agent is trapped in an outer psychological shell. This model is psychologically and philosophically problematic

A discrete model for the design sensitivity analysis of multi-layered composite shells of revolution

This paper studies the sensitivity analysis for the optimization of the multi-layered composite axisymmetric shells subjected to arbitrary static loading and free vibrations. The structural analysis is carried out using a two node frustum-cone finite element with 16 degrees of freedom based on Love-Kirchhoff assumptions. The design variables are the angle of orientation of the fibers and/or the vectorial distances from middle surface to upper surface of each ply. The constraint functions are displacements, stresses (Tsai-Hill criterion) and the natural frequency of a specified mode shape. Four types of objective functions can be used: maximum displacement or natural frequency or elastic strain energy and material volume. The design sensitivities are calculated analytically, semi-analytically and by global finite difference. The potentiality of the proposed model and the accuracy of the sensitivities of response are discussed with reference to the applications.info:eu-repo/semantics/publishedVersio

The ALMA Frontier Fields Survey - IV. Lensing-corrected 1.1 mm number counts in Abell 2744, MACSJ0416.1-2403 and MACSJ1149.5+2223

[abridged] Characterizing the number counts of faint, dusty star-forming galaxies is currently a challenge even for deep, high-resolution observations in the FIR-to-mm regime. They are predicted to account for approximately half of the total extragalactic background light at those wavelengths. Searching for dusty star-forming galaxies behind massive galaxy clusters benefits from strong lensing, enhancing their measured emission while increasing spatial resolution. Derived number counts depend, however, on mass reconstruction models that properly constrain these clusters. We estimate the 1.1 mm number counts along the line of sight of three galaxy clusters, i.e. Abell 2744, MACSJ0416.1-2403 and MACSJ1149.5+2223, which are part of the ALMA Frontier Fields Survey. We perform detailed simulations to correct these counts for lensing effects. We use several publicly available lensing models for the galaxy clusters to derive the intrinsic flux densities of our sources. We perform Monte Carlo simulations of the number counts for a detailed treatment of the uncertainties in the magnifications and adopted source redshifts. We find an overall agreement among the number counts derived for the different lens models, despite their systematic variations regarding source magnifications and effective areas. Our number counts span ~2.5 dex in demagnified flux density, from several mJy down to tens of uJy. Our number counts are consistent with recent estimates from deep ALMA observations at a 3$\sigma$ level. Below $\approx$ 0.1 mJy, however, our cumulative counts are lower by $\approx$ 1 dex, suggesting a flattening in the number counts. In our deepest ALMA mosaic, we estimate number counts for intrinsic flux densities $\approx$ 4 times fainter than the rms level. This highlights the potential of probing the sub-10 uJy population in larger samples of galaxy cluster fields with deeper ALMA observations.Comment: 19 pages, 14 figures, 3 tables. Accepted for publication in A&

String Driven Cosmology and its Predictions

We present a minimal model for the Universe evolution fully extracted from effective String Theory. This model is by its construction close to the standard cosmological evolution, and it is driven selfconsistently by the evolution of the string equation of state itself. The inflationary String Driven stage is able to reach enough inflation, describing a Big Bang like evolution for the metric. By linking this model to a minimal but well established observational information, (the transition times of the different cosmological epochs), we prove that it gives realistic predictions on early and current energy density and its results are compatible with General Relativity. Interestingly enough, the predicted current energy density is found Omega = 1 and a lower limit Omega \geq 4/9 is also found. The energy density at the exit of the inflationary stage also gives | Omega |_{inf}=1. This result shows an agreement with General Relativity (spatially flat metric gives critical energy density) within an inequivalent Non-Einstenian context (string low energy effective equations). The order of magnitude of the energy density-dilaton coupled term at the beginning of the radiation dominated stage agrees with the GUT scale. The predicted graviton spectrum is computed and analyzed without any free parameters. Peaks and asymptotic behaviours of the spectrum are a direct consequence of the dilaton involved and not only of the scale factor evolution. Drastic changes are found at high frequencies: the dilaton produces an increasing spectrum (in no string cosmologies the spectrum is decreasing). Without solving the known problems about higher order corrections and graceful exit of inflation, we find this model closer to the observational Universe than the current available string cosmology scenarii.Comment: LaTex, 22 pages, Lectures delivered at the Chalonge School, Nato ASI: Phase Transitions in the Early Universe: Theory and Observations. To appear in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez. (Kluwer Pub