More Like this

1. A Toda Bracket Convergence Theorem for Multiplicative Spectral Sequences

   https://doi.org/10.1007/s42543-025-00099-x  

   Belmont, Eva; Kong, Hana_Jia (June 2025, Peking Mathematical Journal)

   Abstract Moss’ theorem, which relates Massey products in the$$E_r$$ $E_r$-page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric monoidal stable simplicial model category, we prove a general version of Moss’ theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. This involves the study of Massey products and Toda brackets in a non-strictly associative context. The theorem has broad applications, e.g., to the computation of the motivic slice spectral sequence and other colocalization towers. 

   more » « less
2. Generalized Bockstein maps and Massey products

   https://doi.org/10.1017/fms.2022.103  

   Lam, Yeuk Hay; Liu, Yuan; Sharifi, Romyar; Wake, Preston; Wang, Jiuya (January 2023, Forum of Mathematics, Sigma)

   Abstract Given a profinite group G of finite p -cohomological dimension and a pro- p quotient H of G by a closed normal subgroup N , we study the filtration on the Iwasawa cohomology of N by powers of the augmentation ideal in the group algebra of H . We show that the graded pieces are related to the cohomology of G via analogues of Bockstein maps for the powers of the augmentation ideal. For certain groups H , we relate the values of these generalized Bockstein maps to Massey products relative to a restricted class of defining systems depending on H . We apply our study to prove lower bounds on the p -ranks of class groups of certain nonabelian extensions of $$\mathbb {Q}$$ and to give a new proof of the vanishing of Massey triple products in Galois cohomology. 

   more » « less
3. Measuring Skin Color: Consistency, Comparability, and Meaningfulness of Rating Scale Scores and Handheld Device Readings

   https://doi.org/10.1093/jssam/smab046  

   Gordon, Rachel A. (April 2022, Journal of Survey Statistics and Methodology)

   As US society continues to diversify and calls for better measurements of racialized appearance increase, survey researchers need guidance about effective strategies for assessing skin color in field research. This study examined the consistency, comparability, and meaningfulness of the two most widely used skin tone rating scales (Massey–Martin and PERLA) and two portable and inexpensive handheld devices for skin color measurement (Nix colorimeter and Labby spectrophotometer). We collected data in person using these four instruments from forty-six college students selected to reflect a wide range of skin tones across four racial-ethnic groups (Asian, Black, Latinx, White). These college students, five study staff, and 459 adults from an online sample also rated forty stock photos, again selected for skin tone diversity. Our results—based on data collected under controlled conditions—demonstrate high consistency across raters and readings. The Massey–Martin and PERLA scale scores were highly linearly related to each other, although PERLA better differentiated among people with the lightest skin tones. The Nix and Labby darkness-to-lightness (L*) readings were likewise linearly related to each other and to the Massey–Martin and PERLA scores, in addition to showing expected variation within and between race ethnicities. In addition, darker Massey–Martin and PERLA ratings correlated with online raters’ expectations that a photographed person experienced greater discrimination. In contrast, the redness (a*) and yellowness (b*) undertones were highest in the mid-range of the rating scale scores and demonstrated greater overlap across race-ethnicities. Overall, each instrument showed sufficient consistency, comparability, and meaningfulness for use in field surveys when implemented soundly (e.g., not requiring memorization). However, PERLA might be preferred to Massey–Martin in studies representing individuals with the lightest skin tones, and handheld devices may be preferred to rating scales to reduce measurement error when studies could gather only a single rating. 

   more » « less
4. The synergy of passive and active learning modes in adaptive perceptual learning

   Mettler, E. (January 2019, Proceedings of the 41st Annual Conference of the Cognitive Science Society)

   Adaptive learning systems that generate spacing intervals based on learner performance enhance learning efficiency and retention (Mettler, Massey & Kellman, 2016). Recent research in factual learning suggests that initial blocks of passive trials, where learners observe correct answers without overtly responding, produce greater learning than passive or active trials alone (Mettler, Massey, Burke, Garrigan & Kellman, 2018). Here we tested whether this passive + active advantage generalizes beyond factual learning to perceptual learning. Participants studied and classified images of butterfly genera using either: 1) Passive Only presentations, 2) Passive Initial Blocks followed by active, adaptive scheduling, 3) Passive Initial Category Exemplar followed by active, adaptive scheduling, or 4) Active Only learning. We found an advantage for combinations of active and passive presentations over Passive Only or Active Only presentations. Passive trials presented in initial blocks showed the best performance, paralleling earlier findings in factual learning. Combining active and passive learning produces greater learning gains than either alone, and these effects occur for diverse forms of learning, including perceptual learning. 

   more » « less
5. Adaptive vs. fixed spacing of learning items: Evidence from studies of learning and transfer in chemistry education

   Mettler, E.; El-Ashmawy, A. K.; Massey, C. M.; & Kellman, P. J. (July 2020, Proceedings of the Annual Conference of the Cognitive Science Society)

   Denison, S.; Mack, M.; Xu, Y.; Armstrong, B. C. (Ed.)

   Spacing presentations of learning items across time improves memory relative to massed schedules of practice – the well-known spacing effect. Spaced practice can be further enhanced by adaptively scheduling the presentation of learning items to deliver customized spacing intervals for individual items and learners. ARTS - Adaptive Response-time-based Sequencing (Mettler, Massey, & Kellman 2016) determines spacing dynamically in relation to each learner’s ongoing speed and accuracy in interactive learning trials. We demonstrate the effectiveness of ARTS when applied to chemistry nomenclature in community college chemistry courses by comparing adaptive schedules to fixed schedules consisting of continuously expanding spacing intervals. Adaptive spacing enhanced the efficiency and durability of learning, with learning gains persisting after a two-week delay and generalizing to a standardized assessment of chemistry knowledge after 2-3 months. Two additional experiments confirmed and extended these results in both laboratory and community college settings. 

   more » « less