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1. Bitangents to symmetric quartics

   Bethea, Candace; Brazelton, Thomas (October 2024, arXiv pre-print repository)

   NA (Ed.)

   Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms. The classification of (necessarily finite) groups appearing as automorphism groups of non-singular curves of genus three dates back to the last decade of the 19th century. As these groups act on the quartic via projective linear transformations, they induce symmetries on the 28 bitangents. Given such an automorphism group G=Aut(C), we prove the G-orbits of the bitangents are independent of the choice of C, and we compute them for all twelve types of smooth symmetric planar quartic curves. We further observe that techniques deriving from equivariant homotopy theory directly reveal patterns which are not obvious from a classical moduli perspective. 

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2. Bitangents to symmetric quartics

   https://doi.org/10.1016/j.jalgebra.2025.12.010  

   Bethea, Candace; Brazelton, Thomas (May 2026, Journal of Algebra)

   Not AvailableRecall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms. The classification of (necessarily finite) groups appearing as automorphism groups of non-singular curves of genus three dates back to the last decade of the 19th century. As these groups act on the quartic via projective linear transformations, they induce symmetries on the 28 bitangents. Given such an automorphism group G = Aut(C), we leverage tools from equivariant homotopy theory to prove that the Gorbits of the bitangents are independent of the choice of C, and we compute them for all twelve types of smooth symmetric planar quartic curves. We further observe that techniques deriving from equivariant homotopy theory directly reveal patterns which are not obvious from a classical moduli perspective. 

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3. Site-specific 2D IR spectroscopy: a general approach for the characterization of protein dynamics with high spatial and temporal resolution

   https://doi.org/10.1039/C8CP06146G  

   Ramos, Sashary; Horness, Rachel E.; Collins, Jessica A.; Haak, David; Thielges, Megan C. (January 2019, Physical Chemistry Chemical Physics)

   The conformational heterogeneity and dynamics of protein side chains contribute to function, but investigating exactly how is hindered by experimental challenges arising from the fast timescales involved and the spatial heterogeneity of protein structures. The potential of two-dimensional infrared (2D IR) spectroscopy for measuring conformational heterogeneity and dynamics with unprecedented spatial and temporal resolution has motivated extensive effort to develop amino acids with functional groups that have frequency-resolved absorptions to serve as probes of their protein microenvironments. We demonstrate the full advantage of the approach by selective incorporation of the probe p -cyanophenylalanine at six distinct sites in a Src homology 3 domain and the application of 2D IR spectroscopy to site-specifically characterize heterogeneity and dynamics and their contribution to cognate ligand binding. The approach revealed a wide range of microenvironments and distinct responses to ligand binding, including at the three adjacent, conserved aromatic residues that form the recognition surface of the protein. Molecular dynamics simulations performed for all the labeled proteins provide insight into the underlying heterogeneity and dynamics. Similar application of 2D IR spectroscopy and site-selective probe incorporation will allow for the characterization of heterogeneity and dynamics of other proteins, how heterogeneity and dynamics are affected by solvation and local structure, and how they might contribute to biological function. 

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4. Protein Dynamics by Two-Dimensional Infrared Spectroscopy

   https://doi.org/10.1146/annurev-anchem-091520-091009  

   Tumbic, Goran W.; Hossan, Md Yeathad; Thielges, Megan C. (July 2021, Annual Review of Analytical Chemistry)

   Proteins function as ensembles of interconverting structures. The motions span from picosecond bond rotations to millisecond and longer subunit displacements. Characterization of functional dynamics on all spatial and temporal scales remains challenging experimentally. Two-dimensional infrared spectroscopy (2D IR) is maturing as a powerful approach for investigating proteins and their dynamics. We outline the advantages of IR spectroscopy, describe 2D IR and the information it provides, and introduce vibrational groups for protein analysis. We highlight example studies that illustrate the power and versatility of 2D IR for characterizing protein dynamics and conclude with a brief discussion of the outlook for biomolecular 2D IR. 

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5. A Communication-Avoiding 3D LU Factorization Algorithm for Sparse Matrices

   Sao, Piyush; Li, Xiaoye; Vuduc, Richard (May 2018, Proceedings - IEEE International Parallel and Distributed Processing Symposium)

   We propose a new algorithm to improve the strong scalability of right-looking sparse LU factorization on distributed memory systems. Our 3D sparse LU algorithm uses a three-dimensional PI process grid, aggressively exploits elimination tree parallelism and trades off increased memory for reduced per-process communication. We also analyze the asymptotic improvements for planar graphs (e.g., from 2D grid or mesh domains) and certain non-planar graphs (specifically for 3D grids and meshes). For planar graphs with n vertices, our algorithm reduces communication volume asymptotically in n by a factor of O(sqrt(logn)) and latency by a factor of O(logn). For non-planar cases, our algorithm can reduce the per-process communication volume by 3× and latency by O(n^1/3) times. In all cases, the memory needed to achieve these gains is a constant factor. We implemented our algorithm by extending the 2D data structure used in SuperLU_DIST. Our new 3D code achieves speedups up to 27× for planar graphs and up to 3.3× for non-planar graphs over the baseline 2D SuperLU_DIST when run on 24,000 cores of a Cray XC30. 

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