More on Geometric Morphisms between Realizability Toposes

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\em computationally dense\/} ones) are seen to be the ones whose `lifts' to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize pcas whose realizability topos admits a geometric morphism to the effective topos.Comment: 20 page

Unequal Exposure to Ecological Hazards 2005: Environmental Injustices in the Commonwealth of Massachusetts

Unequal Exposure to Ecological Hazards 2005 documents Massachusetts residents' unequal exposure to environmental hazards. More specifically, the report analyzes both income basedand racially-based disparities in the geographic distribution of some 17 different types ofenvironmentally hazardous sites and industrial facilities in the Commonwealth of Massachusetts. This report provides evidence that working class communities and communities of color are disproportionately impacted by toxic waste disposal, incinerators, landfills, trash transfer stations, power plants, and polluting industrial facilities. In some cases, not only are new toxic facilities and dump sites located in poorer neighborhoods and communities of color, but as in the case of the public housing development and playgrounds near the Alewife station in Cambridge, housing for people of color and low income populations is sometimes located on top of preexisting hazardous waste sites and/or nearby polluting facilities. We conclude that striking inequities in the distribution of these environmentally hazardous sites and facilities are placing working class families and people of color at substantially greater risk of exposure to human health risks. We advocate the adoption of a number of measures, including a comprehensive environmental justice act, to reduce pollution and address unequal exposure to ecological threats

The Relationship of STEM Attitudes and Career Interest

This study examines the relationships between attitudes toward all core STEM subjects and interest in STEM careers among 4th through 12th grade US students through the administration of the Student Attitudes toward STEM (S-STEM) Survey to over 15,000 public school students. The research developed a model based on expectancy-value theory that incorporates key demographic factors of age, gender, and race/ethnicity. Our findings reinforce prior research that students across key demographic factors perceive biological/clinical and physical science career paths differently, resulting in two career clusters. Of interest, the relationship of mathematics attitudes to career interest varied by STEM career cluster. Findings were also supportive of the conclusion that students’ attitudes towards STEM careers are not static over their primary and secondary grades, stabilizing and leveling during their secondary years. Gender showed significantly different interest levels for the two career clusters: males higher for physical sciences and females higher for biological/clinical sciences. Racial/ethnic disparity in STEM career interests can be seen more readily in physical sciences and engineering than in the biological sciences. Overall, our work reinforces findings that students, as young as elementary grades, are forming attitudinal associations between their academic and life experience and future STEM careers

Effective Kan fibrations in simplicial sets

We introduce the notion of an effective Kan fibration, a new mathematical structure that can be used to study simplicial homotopy theory. Our main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. This contrasts with the ordinary, unstructured notion of a Kan fibration. We show that fundamental properties of Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, we give a constructive (explicit) proof showing that effective Kan fibrations are stable under push forward, or fibred exponentials. This is known to be impossible for ordinary Kan fibrations. We further show that effective Kan fibrations are local, or completely determined by their fibres above representables. We also give an (ineffective) proof saying that the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. By showing that the effective Kan fibrations combine all these properties, we solve an open problem in homotopy type theory. In this way our work provides a first step in giving a constructive account of Voevodsky's model of univalent type theory in simplicial sets.Comment: 170 page

Answering Dreyfus's Challenge: Toward a Theory of Concepts without Intellectualism

John McDowell’s debates about concepts with Robert Brandom and Hubert Dreyfus over the past two decades reveal key commitments each philosopher makes. McDowell is committed to giving concepts a role in our embodied coping, extending rational form to human experience. Brandom is committed to defining concepts in a way that helps make rationality distinct. And Dreyfus is committed to explaining how rational understanding develops out of lesser abilities we share with human infants and other animals (I call this “Dreyfus’s challenge”). These commitments appear irreconcilable. I argue to the contrary that they are, in principle, reconcilable, provided we give up their shared “rationalist” commitment to the idea that the rational use of language is necessary for having concepts. First, I exploit Brandom and McDowell’s debate to motivate abandoning the rationalist commitment. Next, I exploit Dreyfus and McDowell’s debate to establish the need for a broader notion of concepts to answer Dreyfus’s challenge. I turn to Elizabeth Camp’s broader notion of concepts as spontaneously, systematically recombinable representations, and establish that it lacks resources for distinguishing human rationality. To resolve that weakness, I integrate Camp’s notion of concepts with John Haugeland’s theory of objectivity, which does make rationality distinct. Finally, drawing my integration of Camp and Haugeland, I propose a way to answer Dreyfus’s challenge, which I call “relaxed holism.” The core of relaxed holism is a cumulative, developmental sequence of three related cognitive abilities: representation, concepts, and metacognition. I argue that relaxed holism also reconciles both McDowell’s commitment to giving normatively governed concepts a role in embodied coping, and Brandom’s commitment to defining concepts in a way that helps make rationality distinct

The Bursty Star Formation Histories of Low-mass Galaxies at 0.4<z<10.4<z<1 Revealed by Star Formation Rates Measured from Hβ\beta and FUV

We investigate the burstiness of star formation histories (SFHs) of galaxies at $0.4<z<1$ by using the ratio of star formation rates (SFRs) measured from H$\beta$ and FUV (1500 \AA) (H$\beta$--to--FUV ratio). Our sample contains 164 galaxies down to stellar mass (M*) of $10^{8.5} M_\odot$ in the CANDELS GOODS-N region, where Team Keck Redshift Survey DEIMOS spectroscopy and HST/WFC3 F275W images from CANDELS and Hubble Deep UV Legacy Survey are available. When the {\it ratio} of H$\beta$- and FUV-derived SFRs is measured, dust extinction correction is negligible (except for very dusty galaxies) with the Calzetti attenuation curve. The H$\beta$--to--FUV ratio of our sample increases with M* and SFR. The median ratio is $\sim$0.7 at M*$\sim10^{8.5} M_\odot$ (or SFR$\sim 0.5 M_\odot/yr$) and increases to $\sim$1 at M*$\sim10^{10} M_\odot$ (or SFR $\sim 10 M_\odot/yr$). At M*$<10^{9.5} M_\odot$, our median H$\beta$--to--FUV ratio is lower than that of local galaxies at the same M*, implying a redshift evolution. Bursty SFH on a timescale of a few tens of megayears on galactic scales provides a plausible explanation of our results, and the importance of the burstiness increases as M* decreases. Due to sample selection effects, our H$\beta$--to--FUV ratio may be an upper limit of the true value of a complete sample, which strengthens our conclusions. Other models, e.g., non-universal initial mass function or stochastic star formation on star cluster scales, are unable to plausibly explain our results.Comment: 13 pages, 8 figures. ApJ accepted. The main conclusions are not changed. Major modifications include: (1) to be consistent with the literature, now reporting H\beta--to--FUV ratio (rather than FUV--to--H\beta\ in the first version); (2) detailed discussions on dust extinction correction; (3) new SF bustiness calculation; and (4) enriched discussions in Introductio

CANDELS: The correlation between galaxy morphology and star formation activity at z~2

We discuss the state of the assembly of the Hubble Sequence in the mix of bright galaxies at redshift 1.4< z \le 2.5 with a large sample of 1,671 galaxies down to H_{AB}~26, selected from the HST/ACS and WFC3 images of the GOODS--South field obtained as part of the GOODS and CANDELS observations. We investigate the relationship between the star formation properties and morphology using various parametric diagnostics, such as the Sersic light profile, Gini (G), M_{20}, Concentration (C), Asymmetry (A) and multiplicity parameters. Our sample clearly separates into massive, red and passive galaxies versus less massive, blue and star forming ones, and this dichotomy correlates very well with the galaxies' morphological properties. Star--forming galaxies show a broad variety of morphological features, including clumpy structures and bulges mixed with faint low surface brightness features, generally characterized by disky-type light profiles. Passively evolving galaxies, on the other hand, very often have compact light distribution and morphology typical of today's spheroidal systems. We also find that artificially redshifted local galaxies have a similar distribution with z~2galaxies in a G-M_{20} plane. Visual inspection between the rest-frame optical and UV images show that there is a generally weak morphological k-correction for galaxies at z~2, but the comparison with non-parametric measures show that galaxies in the rest-frame UV are somewhat clumpier than rest-frame optical. Similar general trends are observed in the local universe among massive galaxies, suggesting that the backbone of the Hubble sequence was already in place at z~2.Comment: 22 pages, 19 figures, ApJ accepted (added 3 references

CANDELS Sheds Light on the Environmental Quenching of Low-mass Galaxies

We investigate the environmental quenching of galaxies, especially those with stellar masses (M*)$<10^{9.5} M_\odot$, beyond the local universe. Essentially all local low-mass quenched galaxies (QGs) are believed to live close to massive central galaxies, which is a demonstration of environmental quenching. We use CANDELS data to test {\it whether or not} such a dwarf QG--massive central galaxy connection exists beyond the local universe. To this purpose, we only need a statistically representative, rather than a complete, sample of low-mass galaxies, which enables our study to $z\gtrsim1.5$. For each low-mass galaxy, we measure the projected distance ($d_{proj}$) to its nearest massive neighbor (M*$>10^{10.5} M_\odot$) within a redshift range. At a given redshift and M*, the environmental quenching effect is considered to be observed if the $d_{proj}$ distribution of QGs ($d_{proj}^Q$) is significantly skewed toward lower values than that of star-forming galaxies ($d_{proj}^{SF}$). For galaxies with $10^{8} M_\odot < M* < 10^{10} M_\odot$, such a difference between $d_{proj}^Q$ and $d_{proj}^{SF}$ is detected up to $z\sim1$. Also, about 10\% of the quenched galaxies in our sample are located between two and four virial radii ($R_{Vir}$) of the massive halos. The median projected distance from low-mass QGs to their massive neighbors, $d_{proj}^Q / R_{Vir}$, decreases with satellite M* at $M* \lesssim 10^{9.5} M_\odot$, but increases with satellite M* at $M* \gtrsim 10^{9.5} M_\odot$. This trend suggests a smooth, if any, transition of the quenching timescale around $M* \sim 10^{9.5} M_\odot$ at $0.5<z<1.0$.Comment: 8 pages, 5 figures. ApJL accepted. Typos correcte