Indexed induction and coinduction, fibrationally.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

Pupillary Responses Obey Emmert’s Law and Co-vary with Autistic Traits

We measured the pupil response to a light stimulus subject to a size illusion and found that stimuli perceived as larger evoke a stronger pupillary response. The size illusion depends on combining retinal signals with contextual 3D information; contextual processing is thought to vary across individuals, being weaker in individuals with stronger autistic traits. Consistent with this theory, autistic traits correlated negatively with the magnitude of pupil modulations in our sample of neurotypical adults; however, psychophysical measurements of the illusion did not correlate with autistic traits, or with the pupil modulations. This shows that pupillometry provides an accurate objective index of complex perceptual processes, particularly useful for quantifying interindividual differences, and potentially more informative than standard psychophysical measures

Subitizing but not estimation of numerosity requires attentional resources

The numerosity of small numbers of objects, up to about four, can be rapidly appraised without error, a phenomenon known as subitizing. Larger numbers can either be counted, accurately but slowly, or estimated, rapidly but with errors. There has been some debate as to whether subitizing uses the same or different mechanisms than those of higher numerical ranges and whether it requires attentional resources. We measure subjects' accuracy and precision in making rapid judgments of numerosity for target numbers spanning the subitizing and estimation ranges while manipulating the attentional load, both with a spatial dual task and the "attentional blink" dual-task paradigm. The results of both attentional manipulations were similar. In the high-load attentional condition, Weber fractions were similar in the subitizing (2-4) and estimation (5-7) ranges (10-15%). In the low-load and single-task condition, Weber fractions substantially improved in the subitizing range, becoming nearly error-free, while the estimation range was relatively unaffected. The results show that the mechanisms operating over the subitizing and estimation ranges are not identical. We suggest that pre-attentive estimation mechanisms works at all ranges, but in the subitizing range, attentive mechanisms also come into play

Objective pupillometry shows that perceptual styles covary with autistic-like personality traits

We measured the modulation of pupil-size (in constant lighting) elicited by observing transparent surfaces of black and white moving dots, perceived as a cylinder rotating about its vertical axis. The direction of rotation was swapped periodically by flipping stereo-depth of the two surfaces. Pupil size modulated in synchrony with the changes in front-surface color (dilating when black). The magnitude of pupillary modulation was larger for human participants with higher Autism-Spectrum Quotient (AQ), consistent with a local perceptual style, with attention focused on the front surface. The modulation with surface color, and its correlation with AQ, was equally strong when participants passively viewed the stimulus. No other indicator, including involuntary pursuit eye-movements, covaried with AQ. These results reinforce our previous report with a similar bistable stimulus (Turi, Burr, & Binda, 2018), and go on to show that bistable illusory motion is not necessary for the effect, or its dependence on AQ

Pupillary Responses Obey Emmert’s Law and Co-vary with Autistic Traits

We measured the pupil response to a light stimulus subject to a size illusion and found that stimuli perceived as larger evoke a stronger pupillary response. The size illusion depends on combining retinal signals with contextual 3D information; contextual processing is thought to vary across individuals, being weaker in individuals with stronger autistic traits. Consistent with this theory, autistic traits correlated negatively with the magnitude of pupil modulations in our sample of neurotypical adults; however, psychophysical measurements of the illusion did not correlate with autistic traits, or with the pupil modulations. This shows that pupillometry provides an accurate objective index of complex perceptual processes, particularly useful for quantifying interindividual differences, and potentially more informative than standard psychophysical measures

The effects of cross-sensory attentional demand on subitizing and on mapping number onto space

Various aspects of numerosity judgments, especially subitizing and the mapping of number onto space, depend strongly on attentional resources. Here we use a dual-task paradigm to investigate the effects of cross-sensory attentional demands on visual subitizing and spatial mapping. The results show that subitizing is strongly dependent on attentional resources, far more so than is estimation of higher numerosities. But unlike many other sensory tasks, visual subitizing is equally affected by concurrent attentionally demanding auditory and tactile tasks as it is by visual tasks, suggesting that subitizing may be amodal. Mapping number onto space was also strongly affected by attention, but only when the dual-task was in the visual modality. The non-linearities in numberline mapping under attentional load are well explained by a Bayesian model of central tendency. © 2012 Elsevier Ltd

Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude

Abstract How numerical quantity is processed is a central issue for cognition. On the one hand the “number sense theory” claims that numerosity is perceived directly, and may represent an early precursor for acquisition of mathematical skills. On the other, the “theory of magnitude” notes that numerosity correlates with many continuous properties such as size and density, and may therefore not exist as an independent feature, but be part of a more general system of magnitude. In this study we examined interactions in sensitivity between numerosity and size perception. In a group of children, we measured psychophysically two sensory parameters: perceptual adaptation and discrimination thresholds for both size and numerosity. Neither discrimination thresholds nor adaptation strength for numerosity and size correlated across participants. This clear lack of correlation (confirmed by Bayesian analyses) suggests that numerosity and size interference effects are unlikely to reflect a shared sensory representation. We suggest these small interference effects may rather result from top-down phenomena occurring at late decisional levels rather than a primary “sense of magnitude”

CO2 capture from natural gas combined cycles by CO2 selective membranes

This paper performs a techno-economic analysis of natural gas-fired combined cycle (NGCC) power plants integrated with CO2 selective membranes for post-combustion CO2 capture. The configuration assessed is based on a two-membrane system: a CO2 capture membrane that separates the CO2 for final sequestration and a CO2 recycle membrane that selectively recycles CO2 to the gas turbine compressor inlet in order to increase the CO2 concentration in the gas turbine flue gas. Three different membrane technologies with different permeability and selectivity have been investigated. The mass and energy balances are calculated by integrating a power plant model, a membrane model and a CO2 purification unit model. An economic model is then used to estimate the cost of electricity and of CO2 avoided. A sensitivity analysis on the main process parameters and economic assumptions is also performed. It was found that a combination of a high permeability membrane with moderate selectivity as a recycle membrane and a very high selectivity membrane with high permeability used for the capture membrane resulted in the lowest CO2 avoided cost of 75 US$/tCO2. This plant features a feed pressure of 1.5 bar and a permeate pressure of 0.2 bar for the capture membrane. This result suggests that membrane systems can be competitive for CO2 capture from NGCC power plants when compared with MEA absorption. However, to achieve significant advantages with respect to benchmark MEA capture, better membrane permeability and lower costs are needed with respect to the state of the art technology. In addition, due to the selective recycle, the gas turbine operates with a working fluid highly enriched with CO2. This requires redesigning gas turbine components, which may represent a major challenge for commercial deployment