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Microtubules (MTs) are dynamic components of the cytoskeleton and play essential roles in morphogenesis and maintenance of tissue and cell integrity. Despite recent advances in understanding MT ultrastructure, organization, and growth control, how cells regulate MT organization at the cell cortex remains poorly understood. The EFA-6/EFA6 proteins are recently identified membrane-associated proteins that inhibit cortical MT dynamics. Here, combining visualization of endogenously tagged C. elegans EFA-6 with genetic screening, we uncovered tubulin-dependent regulation of EFA-6 patterning. In the mature epidermal epithelium, EFA-6 forms punctate foci in specific regions of the apical cortex, dependent on its intrinsically disordered region (IDR). We further show the EFA-6 IDR is sufficient to form biomolecular condensates in vitro. In screens for mutants with altered GFP::EFA-6 localization, we identified a novel gain-of-function (gf) mutation in an α-tubulin tba-1 that induces ectopic EFA-6 foci in multiple cell types. tba-1(gf) animals exhibit temperature-sensitive embryonic lethality, which is partially suppressed by efa-6(lf), indicating the interaction between tubulins and EFA-6 is important for normal development. TBA-1(gf) shows reduced incorporation into filamentous MTs but has otherwise mild effects on cellular MT organization. The ability of TBA-1(gf) to trigger ectopic EFA-6 foci formation requires β-tubulin TBB-2 and the chaperon EVL-20/Arl2. The tba-1(gf)-induced EFA-6 foci display slower turnover, contain the MT-associated protein TAC-1/TACC, and require the EFA-6 MTED. Our results reveal a novel crosstalk between cellular tubulins and cortical MT regulators in vivo.

Elementary students' early development of embedding and disembedding is complex and paves the way for later STEM learning. The purpose of this study was to clarify the factors that support students' embedding (i.e., overlapping shapes to form a new shape) and disembedding (i.e., identifying discrete shapes within another shape) through the use of filled shapes as opposed to shape frames. We recruited 26 Grade 1 students (~6-7 years old) and 23 Grade 3 students (~8-9 years old), asked them to work on two layered puzzle designs from the Color Code puzzle game, and interviewed them about their thinking processes. The first graders had higher success rates at fixing and embedding the tiles correctly, and students at both grade levels improved on the three-tile design when encountering it a second time about two months later. The four-tile design was more difficult, but students improved if they could identify a correct sub-structure of the design. Successful students used a combination of pictorial shape strategies and schematic location strategies, systematically testing tiles and checking how they could be embedded. The results suggest that helping students focus on sub-structures can promote their effective embedding.

Elementary students demonstrate conflicts when measuring with rulers as well as measuring with discrete units. Their conflicts often lie in their focus on counting tick marks or focusing on the endpoint of objects on rulers or ignoring spaces with discrete units. In this study, we also investigated another area of conflict: students' conceptions on where measurements should start on a ruler. Across two time points, 32 first graders and 37 third graders responded to a series of measurement tasks in the form of incorrect worked examples meant to expose students to these common conflicts of where the measurement starts and how to determine the overall length. Although students often said the objects should start at one, they were more likely to indicate that the object should be aligned with zero the closer the object was positioned to zero. However, many students said starting at the edge of the ruler (before zero) was okay, effectively equating the edge with either zero or one. Interestingly, on two related worked examples, their continuous and discrete measurements were not associated with each other. The incorrect worked examples helped illustrate important areas for further instruction, especially around their conceptions of rulers' edges and the impact of spaces with discrete units.

The conserved MAP3K Dual-Leucine-Zipper Kinase (DLK) and Leucine-Zipper-bearing Kinase (LZK) can activate JNK via MKK4 or MKK7. These two MAP3Ks share similar biochemical activities and undergo auto-activation upon increased expression. Depending on cell-type and nature of insults DLK and LZK can induce pro-regenerative, pro-apoptotic or pro-degenerative responses, although the mechanistic basis of their action is not well understood. Here, we investigated these two MAP3Ks in cerebellar Purkinje cells using loss- and gain-of function mouse models. While loss of each or both kinases does not cause discernible defects in Purkinje cells, activating DLK causes rapid death and activating LZK leads to slow degeneration. Each kinase induces JNK activation and caspase-mediated apoptosis independent of each other. Significantly, deleting CELF2, which regulates alternative splicing of Map2k7, strongly attenuates Purkinje cell degeneration induced by LZK, but not DLK. Thus, controlling the activity levels of DLK and LZK is critical for neuronal survival and health.

A challenge for prospective teachers (PTs) is to determine what students know about a topic through asking appropriate questions and being thoughtful about the wording of these questions so as to capture and reframe students' spontaneous mathematical thinking and eventually unriddle the fuzzy boundary of students' complex thinking. This study examined four PTs' efforts to elicit kindergarteners' subtraction strategies and make conclusions about their subtraction understanding. Drawing on PTs' plans for interviewing kindergarteners on subtraction problems, interview transcripts, and reflection papers, the results suggest that PTs provided effective scaffolds, adding context to numerical problems or explaining mathematical terms and symbols as needed. However, they avoided asking problems with subtrahends greater than five, numbers above ten, and missing starts or missing subtrahends, limiting their ability to draw targeted conclusions about the students' strengths and needs. Using effective questions allowed one PT who posed a limited variety of problems to make stronger conclusions about her student's subtraction understanding, while asking a broader variety of problems helped another PT who used limited questions make conclusions about her student's subtraction understanding. Based on these results, mathematics teacher educators could leverage their PTs' strengths to either encourage multiple interviews, each targeting different problem types, or one interview with a broader variety of problem types. The results of this study further highlight the need for PTs to move beyond just asking students to explain their strategies and have them justify or represent their strategies as well.

We present exponential wave integrator Fourier pseudospectral (EWI‐FP) methods and establish their error estimates of the fully discrete schemes for the Dirac equation in the massless and nonrelativistic regime. This regime involves a small dimensionless parameter where 0<ε≤1$$ 0<\varepsilon \le 1 $$, and ε$$ \varepsilon $$ is inversely proportional to the speed of light. The solution exhibits highly oscillatory behavior in time and rapid wave propagation in space in this regime. Specifically, the time oscillations have a wavelength of O(ε)$$ O\left(\varepsilon \right) $$, while the spatial oscillations have a wavelength of O(1)$$ O(1) $$, with a wave speed of O(ε−1)$$ O\left({\varepsilon}^{-1}\right) $$. We employ (symmetric) exponential wave integrators for temporal derivatives and Fourier spectral discretization for spatial derivatives. We rigorously derive the error bounds which explicitly depend on the mesh size h$$ h $$, the time step τ$$ \tau $$ and the small dimensionless parameter ε$$ \varepsilon $$. The error estimates for the EWI‐FP methods demonstrate that their meshing strategy requirement (ε$$ \varepsilon $$‐scalability) necessitates setting h=O(1)$$ h=O(1) $$ and τ=O(ε)$$ \tau =O\left(\varepsilon \right) $$ when 0<ε≪1$$ 0<\varepsilon \ll 1 $$. Finally, some numerical examples are provided to validate the error bounds. [ABSTRACT FROM AUTHOR]

Let (X , ≤) be a locally finite pre-ordered set and R be a commutative ring with unity. In this paper we apply the theory of zero product determined algebras to show that each linear map on the incidence algebra I (X , R) which is derivable at zero is a generalized derivation and every local derivation on I (X , R) is a derivation. [ABSTRACT FROM AUTHOR]

A laboratory class was developed and evaluated to illustrate the synthesis of metal nanoclusters (NCs) and to explain their photoluminescence properties for the case of silver. The described experiment employs a synthetic protocol that consists of two sequential phases in a single reaction pot: the reduction of silver ions into plasmonic silver nanoparticles (NPs) (bottom-up), followed by etching the formed silver NPs into ultrasmall atomically precise fluorescent silver NCs (top-down), Ag[subscript 29] (DHLA)[subscript 12] (DHLA: dihydrolipoic acid). UV-vis absorption and fluorescence spectroscopy were employed as a function of reaction time to confirm the development of the plasmonic character of silver NPs (reaction intermediate) and, later on, the onset of fluorescence emission of the silver NCs (final product). Collectively, this experiment was found to be simple to carry out, safe, reproducible, and cost-effective, and it achieved the intended learning outcomes. Participating students found this laboratory class suitable to be implemented into an upper-division undergraduate or graduate curriculum.

The conversion of α-HMX to β-HMX was studied by the hydrothermal method, that is, when the solvent is deionized water, α-HMX can be converted to β-HMX. It was confirmed to be β-HMX after being characterized by mid-infrared spectroscopy, and its crystal form was further observed by high-power optical microscope, which was consistent with the infrared characterization results. The method is simple to operate, green and safe, reduces the production cost, and also solves the problem of traditional transcrystallization waste liquid treatment. [ABSTRACT FROM AUTHOR]