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1. Quantum Unique Ergodicity for Cayley Graphs of Quasirandom Groups

   https://doi.org/10.1007/s00220-023-04801-x  

   Magee, Michael; Thomas, Joe; Zhao, Yufei (September 2023, Communications in Mathematical Physics)

   Abstract A finite groupGis calledC-quasirandom (by Gowers) if all non-trivial irreducible complex representations ofGhave dimension at leastC. For any unit$$\ell ^{2}$$ ${\ell }^2$function on a finite group we associate thequantum probability measureon the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on suitably selected subsets of the group that are not too small. 

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2. Adaptive Group Testing with Mismatched Models

   https://doi.org/10.1109/ICASSP43922.2022.9747665  

   Fan, Mingzhou; Yoon, Byung-Jun; Alexander, Francis J.; Dougherty, Edward R.; Qian, Xiaoning (May 2022, ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can be more efficient. In this work, we consider noisy adaptive group testing design with specific test sensitivity and specificity that select the optimal group given previous test results based on pre-selected utility function. As in prior studies on group testing, we model this problem as a sequential Bayesian Optimal Experimental Design (BOED) to adaptively design the groups for each test. We analyze the required number of group tests when using the updated posterior on the infection status and the corresponding Mutual Information (MI) as our utility function for selecting new groups. More importantly, we study how the potential bias on the ground-truth noise of group tests may affect the group testing sample complexity. 

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3. Multi-Attribute Graph Estimation With Sparse-Group Non-Convex Penalties

   https://doi.org/10.1109/ACCESS.2025.3566959  

   Tugnait, Jitendra K (January 2025, IEEE Access)

   We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper we provide a unified theoretical analysis of multi-attribute graph learning using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and sparse-group non-convex (log-sum and smoothly clipped absolute deviation (SCAD) penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) approach coupled with local linear approximation to non-convex penalties is presented for optimization of the objective function. For non-convex penalties, theoretical analysis establishing local consistency in support recovery, local convexity and precision matrix estimation in high-dimensional settings is provided under two sets of sufficient conditions: with and without some irrepresentability conditions. We illustrate our approaches using both synthetic and real-data numerical examples. In the synthetic data examples the sparse-group log-sum penalized objective function significantly outperformed the lasso penalized as well as SCAD penalized objective functions with F1 -score and Hamming distance as performance metrics. 

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4. Injectivity of the Heisenberg X-ray transform

   https://doi.org/10.1016/j.jfa.2020.108886  

   Flynn, Steven (March 2021, Journal of Functional Analysis)

   We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier transform, we prove an operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg group is determined by its line integrals over sub-Riemannian geodesics. We also consider the family of taming metrics $$g_\epsilon$$ approximating the sub-Riemannian metric, and show that the associated X-ray transform is injective for all $$\epsilon > 0$$. This result gives a concrete example of an injective X-ray transform in a geometry with an abundance of conjugate points. 

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5. Supranutritional Maternal Organic Selenium Supplementation during Different Trimesters of Pregnancy Affects the Muscle Gene Transcriptome of Newborn Beef Calves in a Time-Dependent Manner

   https://doi.org/10.3390/genes12121884  

   Diniz, Wellison J.; Bobe, Gerd; Klopfenstein, Joseph J.; Gultekin, Yunus; Davis, T. Zane; Ward, Alison K.; Hall, Jean A. (December 2021, Genes)

   Selenium (Se) is an essential micronutrient for growth and immune function in beef cattle. We previously showed that supranutritional maternal organic Se supplementation during late pregnancy improves immune function in their newborn calves; however, the effects of maternal organic Se-supplementation on fetal programming during different pregnancy stages have yet to be elucidated. Herein, we investigated the effects of supranutritional maternal organic Se-supplementation in different pregnancy trimesters on their beef calf’s genome-wide transcriptome profiles. Within 12 to 48 h of birth, whole blood and Longissimus dorsi (LD) muscle biopsies were collected from calves born to 40 crossbred Angus cows that received, except for the control group (CTR), Se-yeast boluses (105 mg of Se/wk) during the first (TR1), second (TR2), or third (TR3) trimester of gestation. Whole-blood Se concentrations of newborn calves increased from CTR, TR1, TR2 to TR3, whereas muscle Se concentrations of newborn calves were only increased in TR3 group. We identified 3048 unique differentially expressed genes (DEGs) across all group comparisons (FDR ≤ 0.05 and |log2FC| ≥ 1.5). Furthermore, we predicted 237 unique transcription factors that putatively regulate the DEGs. Independent of supplementation trimester, supranutritional maternal organic Se supplementation downregulated genes involved in adaptive immunity in all trimesters. Dependent on supplementation trimester, genes involved in muscle development were upregulated by TR3 Se supplementation and downregulated by TR1 Se-supplementation, and genes involved in collagen formation were downregulated by TR2 Se-supplementation. Supranutritional maternal organic Se supplementation in the last trimester of pregnancy resulted in upregulation of myosin and actin filament associated genes, potentially allowing for optimal muscle function and contraction. Our findings suggest a beneficial effect of supranutritional maternal organic Se supplementation during late gestation on Se-status and muscle development and function of newborn calves. 

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