Search for: All records

This paper aims to introduce a new paradigm for mathematics literacy. By integrating computational thinking and coding into curricular units from The Algebra Project, we engaged middle school students in creativity, imagination, and self-expression in the mathematics classroom. We refined instruments to measure the development of student voice, agency, and belongingness. In the context of the mathematics classroom, there is potential for an earned insurgency to arise when these attributes of mathematical identity are amplified, leading students to engage in a learning community that rejects the repressive logic of the current racialized, classed, and otherwise oppressive mathematics education 

This chapter provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several applications of these operators in imaging science, geophysics, harmonic maps, and deep (machine) learning. Various notions of solutions to linear fractional elliptic equations are provided and numerical schemes for fractional Laplacian and fractional time derivative are discussed. Special emphasis is given to exterior optimal control problems with a linear elliptic equation as constraints. In addition, optimal control problems with interior control and state constraints are considered. We also provide a discussion on fractional deep neural networks, which is shown to be a minimization problem with fractional in time ordinary differential equation as constraint. The paper concludes with a discussion on several open problems. 

Coral bleaching events are increasing with such frequency and intensity that many of the world’s reef-building corals are in peril. Some corals appear to be more resilient after bleaching but the mechanisms underlying their ability to recover from bleaching and persist are not fully understood. We used shotgun proteomics to compare the proteomes of the outer layer (OL) tissue and inner core (IC) tissue and skeleton compartments of experimentally bleached and control (i.e., non-bleached) colonies of Montipora capitata, a perforate Hawaiian species noted for its resilience after bleaching. We identified 2,361 proteins in the OL and IC compartments for both bleached and non-bleached individuals. In the OL of bleached corals, 63 proteins were significantly more abundant and 28 were significantly less abundant compared to the OL of nonbleached corals. In the IC of bleached corals, 22 proteins were significantly more abundant and 17 were significantly less abundant compared to the IC of non-bleached corals. Gene ontology (GO) and pathway analyses revealed metabolic processes that were occurring in bleached corals but not in non-bleached corals. The OL of bleached corals used the glyoxylate cycle to derive carbon from internal storage compounds such as lipids, had a high protein turnover rate, and shifted reliance on nitrogen from ammonia to nitrogen produced from the breakdown of urea and betaine. The IC of bleached corals compartmentalized the shunting of glucose to the pentose phosphate pathway. Bleached corals increased abundances of several antioxidant proteins in both the OL and IC compartments compared to non-bleached corals. These results highlight contrasting strategies for responding to bleaching stress in different compartments of bleached M. capitata and shed light on some potential mechanisms behind bleaching resilience. 

The microbiomes of tropical corals are actively studied using 16S rRNA gene amplicons to understand microbial roles in coral health, metabolism, and disease resistance. However, primers targeting bacterial and archaeal 16S rRNA genes may also amplify organelle rRNA genes from the coral, associated microbial eukaryotes, and encrusting organisms. In this manuscript, we demonstrate that standard workflows for annotating microbial taxonomy severely under-annotate mitochondrial sequences in 1272 coral microbiomes from the Earth Microbiome Project. This issue prevents annotation of >95% of reads in some samples and persists when using either Greengenes or SILVA taxonomies. Worse, mitochondrial under-annotation varies between species and across anatomy, biasing comparisons of α- and β-diversity. By supplementing existing taxonomies with diverse mitochondrial rRNA sequences, we resolve ~97% of unique unclassified sequences as mitochondrial, without increasing misannotation in mock communities. We recommend using these extended taxonomies for coral microbiome analysis and encourage vigilance regarding similar issues in other hosts.