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1. Stability of the centers of group algebras of $$GL_n(q)$$

   https://doi.org/https://doi.org/10.1016/j.aim.2019.04.026  

   Wan, Jinkui; Wang, Weiqiang (April 2019, Advances in mathematics)

   The center $$Z_n(q)$$ of the integral group algebra of the general linear group $$GL_n(q)$$ over a finite field admits a filtration with respect to the reflection length. We show that the structure constants of the associated graded algebras $$\mathscr{G}_n(q)$$ are independent of $$n$$, and this stability leads to a universal stable center with positive integer structure constants which governs the algebras $$\mathscr{G}_n(q)$$ for all $$n$$. Various structure constants of the stable center are computed and several conjectures are formulated. Analogous stability properties for symmetric groups and wreath products were established earlier by Farahat-Higman and the second author. 

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2. A Review of 3D-Printing of Microneedles

   https://doi.org/10.3390/pharmaceutics14122693  

   Olowe, Michael; Parupelli, Santosh Kumar; Desai, Salil (December 2022, Pharmaceutics)

   Microneedles are micron-sized devices that are used for the transdermal administration of a wide range of active pharmaceutics substances with minimally invasive pain. In the past decade, various additive manufacturing technologies have been used for the fabrication of microneedles; however, they have limitations due to material compatibility and bioavailability and are time-consuming and expensive processes. Additive manufacturing (AM), which is popularly known as 3D-printing, is an innovative technology that builds three-dimensional solid objects (3D). This article provides a comprehensive review of the different 3D-printing technologies that have the potential to revolutionize the manufacturing of microneedles. The application of 3D-printed microneedles in various fields, such as drug delivery, vaccine delivery, cosmetics, therapy, tissue engineering, and diagnostics, are presented. This review also enumerates the challenges that are posed by the 3D-printing technologies, including the manufacturing cost, which limits its viability for large-scale production, the compatibility of the microneedle-based materials with human cells, and concerns around the efficient administration of large dosages of loaded microneedles. Furthermore, the optimization of microneedle design parameters and features for the best printing outcomes is of paramount interest. The Food and Drug Administration (FDA) regulatory guidelines relating to the safe use of microneedle devices are outlined. Finally, this review delineates the implementation of futuristic technologies, such as artificial intelligence algorithms, for 3D-printed microneedles and 4D-printing capabilities. 

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3. Automated analysis of the visual properties of superconducting detectors

   https://doi.org/10.1088/1748-0221/20/06/P06011  

   Ferguson, KR; Bender, AN; Whitehorn, N; Barry, PS; Cecil, TW; Dibert, KR; Martsen, ES (June 2025, Journal of Instrumentation)

   Abstract The testing and quality assurance of cryogenic superconducting detectors is a time- and labor-intensive process. As experiments deploy increasingly larger arrays of detectors, new methods are needed for performing this testing quickly. Here, we propose a process for flagging under-performing detector wafers before they are ever tested cryogenically. Detectors are imaged under an optical microscope, and computer vision techniques are used to analyze the images, searching for visual defects and other predictors of poor performance. Pipeline performance is verified via a suite of images with simulated defects, yielding a detection accuracy of 98.6%. Lastly, results from running the pipeline on prototype microwave kinetic inductance detectors from the planned SPT-3G+ experiment are presented. 

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4. A Study of Tolerance of Ambiguity of Undergraduate Students at an HBCU

   Khan, M. J.; Aji, C. A. (January 2021, ASEE CoNECD)

   null (Ed.)

   Real world problems are rarely well-defined and are usually with incomplete information, in other words epitomes of ambiguity. In contrast, undergraduate students are rarely exposed to the class of problems that they will encounter in their professions. The correlation between students’ tolerance of ambiguity as signified by their cognitive models of the world, and academic success has received limited attention. A cross sectional and longitudinal study at an HBCU is being conducted to establish baselines for the mental models of students and their tolerance to ambiguity. Analysis of cross-sectional data collected at an HBCU indicates little change in tolerance of ambiguity of undergraduate students with time spent in college. This research is supported by NSF Grant# . 

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5. Size of nodal domains of the eigenvectors of a graph

   https://doi.org/10.1002/rsa.20925  

   Huang, Han; Rudelson, Mark (April 2020, Random Structures & Algorithms)

   Consider an eigenvector of the adjacency matrix of aG(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other. 

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