Teaching Mathematics for Social Justice: Conversations with Educators – A Symposium

Using Marilyn Frankenstein’s germinal 1983 article “Critical Mathematics Education: An Application of Paulo Freire’s Epistemology” and Ole Skovsmose’s 1985 germinal article “Mathematics Education Versus Critical Education” as credible “start points”, critical mathematics or more broadly, social justice mathematics, is marking three decades of empowering yet uncertain possibilities. Nonetheless, there are two recurring questions: What is it? and What does it “look like”? Drawing on the collective stories (and wisdom) of critical mathematics educators, this symposium aims to offer some open, non-definitive answers to these two questions

Analysis of dropout learning regarded as ensemble learning

Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers, huge number of units, and connections. Therefore, overfitting is a serious problem. To avoid this problem, dropout learning is proposed. Dropout learning neglects some inputs and hidden units in the learning process with a probability, p, and then, the neglected inputs and hidden units are combined with the learned network to express the final output. We find that the process of combining the neglected hidden units with the learned network can be regarded as ensemble learning, so we analyze dropout learning from this point of view.Comment: 9 pages, 8 figures, submitted to Conferenc

A sensitive and specific neural signature for picture-induced negative affect

Neuroimaging has identified many correlates of emotion but has not yet yielded brain representations predictive of the intensity of emotional experiences in individuals. We used machine learning to identify a sensitive and specific signature of emotional responses to aversive images. This signature predicted the intensity of negative emotion in individual participants in cross validation (n =121) and test (n = 61) samples (high–low emotion = 93.5% accuracy). It was unresponsive to physical pain (emotion–pain = 92% discriminative accuracy), demonstrating that it is not a representation of generalized arousal or salience. The signature was comprised of mesoscale patterns spanning multiple cortical and subcortical systems, with no single system necessary or sufficient for predicting experience. Furthermore, it was not reducible to activity in traditional “emotion-related” regions (e.g., amygdala, insula) or resting-state networks (e.g., “salience,” “default mode”). Overall, this work identifies differentiable neural components of negative emotion and pain, providing a basis for new, brain-based taxonomies of affective processes

Age-Related Changes in Perirhinal Cortex Sensitivity to Configuration and Part Familiarity and Connectivity to Visual Cortex

The perirhinal cortex (PRC) is a medial temporal lobe (MTL) structure known to be involved in assessing whether an object is familiar (i.e., meaningful) or novel. Recent evidence shows that the PRC is sensitive to the familiarity of both whole object configurations and their parts, and suggests the PRC may modulate part familiarity responses in V2. Here, using functional magnetic resonance imaging (fMRI), we investigated age-related decline in the PRC’s sensitivity to part/configuration familiarity and assessed its functional connectivity to visual cortex in young and older adults. Participants categorized peripherally presented silhouettes as familiar (“real-world”) or novel. Part/configuration familiarity was manipulated via three silhouette configurations: Familiar (parts/configurations familiar), Control Novel (parts/configurations novel), and Part-Rearranged Novel (parts familiar, configurations novel). “Real-world” judgments were less accurate than “novel” judgments, although accuracy did not differ between age groups. The fMRI data revealed differential neural activity, however: In young adults, a linear pattern of activation was observed in left hemisphere (LH) PRC, with Familiar > Control Novel > Part-Rearranged Novel. Older adults did not show this pattern, indicating age-related decline in the PRC’s sensitivity to part/configuration familiarity. A functional connectivity analysis revealed a significant coupling between the PRC and V2 in the LH in young adults only. Older adults showed a linear pattern of activation in the temporopolar cortex (TPC), but no evidence of TPC-V2 connectivity. This is the first study to demonstrate age-related decline in the PRC’s representations of part/configuration familiarity and its covariance with visual cortex

An amorphous oxide semiconductor thin-film transistor route to oxide electronics

Amorphous oxide semiconductor (AOS) thin-film transistors (TFTs) invented only one decade ago are now being commercialized for active-matrix liquid crystal display (AMLCD) backplane applications. They also appear to be well positioned for other flat-panel display applications such as active-matrix organic light-emitting diode (AMOLED) applications, electrophoretic displays, and transparent displays. The objectives of this contribution are to overview AOS materials design; assess indium gallium zinc oxide (IGZO) TFTs for AMLCD and AMOLED applications; identify several technical topics meriting future scrutiny before they can be confidently relied upon as providing a solid scientific foundation for underpinning AOS TFT technology; and briefly speculate on the future of AOS TFTs for display and non-display applications

Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow

The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity