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1. Critical Groups of Arithmetical Structures on Star Graphs and Complete Graphs

   https://doi.org/10.37236/11729  

   Archer, Kassie; Diaz-Lopez, Alexander; Glass, Darren Broderick; Louwsma, Joel (January 2024, The Electronic Journal of Combinatorics)

   An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group. We show how to determine the critical group of an arithmetical structure on a star graph or complete graph in terms of the entries of the arithmetical structure. We use this to investigate which finite abelian groups can occur as critical groups of arithmetical structures on these graphs. 

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2. The Stabilized Automorphism Group of a Subshift

   https://doi.org/10.1093/imrn/rnab204  

   Hartman, Yair; Kra, Bryna; Schmieding, Scott (August 2021, International Mathematics Research Notices)

   Abstract For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group, study its algebraic properties, and use them to distinguish many of the stabilized automorphism groups. We also show that for a full shift, the subgroup of the stabilized automorphism group generated by elements of finite order is simple and that the stabilized automorphism group is an extension of a free abelian group of finite rank by this simple group. 

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3. Computational investigation of structural, electronic, and spectroscopic properties of Ni and Zn metalloporphyrins with varying anchoring groups

   https://doi.org/10.1063/5.0191858  

   Bashir, Beenish; Alotaibi, Maha_M; Clayborne, Andre_Z (April 2024, The Journal of Chemical Physics)

   Porphyrins are prime candidates for a host of molecular electronics applications. Understanding the electronic structure and the role of anchoring groups on porphyrins is a prerequisite for researchers to comprehend their role in molecular devices at the molecular junction interface. Here, we use the density functional theory approach to investigate the influence of anchoring groups on Ni and Zn diphenylporphyrin molecules. The changes in geometry, electronic structure, and electronic descriptors were evaluated. There are minimal changes observed in geometry when changing the metal from Ni to Zn and the anchoring group. However, we find that the distribution of electron density changes when changing the anchoring group in the highest occupied and lowest unoccupied molecular orbitals. This has a direct effect on electronic descriptors such as global hardness, softness, and electrophilicity. Additionally, the optical spectra of both Ni and Zn diphenylporphyrin molecules exhibit either blue or red shifts when changing the anchoring group. These results indicate the importance of the anchoring group on the electronic structure and optical properties of porphyrin molecules. 

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4. Structure learning principles of stereotype change

   https://doi.org/10.3758/s13423-023-02252-y  

   Gershman, Samuel J.; Cikara, Mina (January 2023, Psychonomic Bulletin & Review)

   Why, when, and how do stereotypes change? This paper develops a computational account based on the principles of structure learning: stereotypes are governed by probabilistic beliefs about the assignment of individuals to groups. Two aspects of this account are particularly important. First, groups are flexibly constructed based on the distribution of traits across individuals; groups are not fixed, nor are they assumed to map on to categories we have to provide to the model. This allows the model to explain the phenomena of group discovery and subtyping, whereby deviant individuals are segregated from a group, thus protecting the group’s stereotype. Second, groups are hierarchically structured, such that groups can be nested. This allows the model to explain the phenomenon of subgrouping, whereby a collection of deviant individuals is organized into a refinement of the superordinate group. The structure learning account also sheds light on several factors that determine stereotype change, including perceived group variability, individual typicality, cognitive load, and sample size. 

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5. 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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