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1. Experimental characterization of Plastic Optical Fibers for Under- and Over-Filled Injections

   Abdelmoniem, Ali; Feng, Frank; Huang, Eric; Carro, Pedro Luis; Losada, María Ángeles; López, Alicia; Gascón, Javier Mateo; Ribas, Dayana; Ortega, Alfonso; Lleida, Eduardo; et al (March 2024, 2024 IEEE Southeast Conference)

   This study investigates the impact of under-filled and over-filled launching configurations on the transmission properties of Plastic Optical Fiber (POF). Experimental analyses on step and graded index fibers reveal differences in spatial and frequency properties under these launching conditions. Results show that the under-filled configuration leads to narrower radial profiles and Encircled Angular Flux (EAF) compared to the over-filled configuration. Additionally, under-filled launching produces better frequency response and larger bandwidth, particularly notable in shorter fibers. Results show that the under-filled launching significantly improves transmission properties, offering potential improvements in POF applications. 

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2. Estimating Sparse Discrete Distributions Under Privacy and Communication Constraints

   Acharya, Jayadev; Kairouz, Peter; Liu, Yuhan; Sun, Ziteng (March 2021, Proceedings of Machine Learning Research)

   We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant factor, and the sample complexity under communication constraints up to a logarithmic factor. Our upper bounds under LDP are based on the Hadamard Response, a private coin scheme that requires only one bit of communication per user. Under communication constraints we propose public coin schemes based on random hashing functions. Our tight lower bounds are based on recently proposed method of chi squared contractions. 

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3. Polynomial-Time Statistical Estimation of Species Trees Under Gene Duplication and Loss

   Legried, Brandon; Molloy, Erin K.; Warnow, Tandy; Roch, Sebastien (January 2020, International Conference on Research in Computational Molecular Biology (RECOMB 2020))

   Phylogenomics---the estimation of species trees from multi-locus datasets---is a common step in many biological studies. However, this estimation is challenged by the fact that genes can evolve under processes, including incomplete lineage sorting (ILS) and gene duplication and loss (GDL), that make their trees different from the species tree. In this paper, we address the challenge of estimating the species tree under GDL. We show that species trees are identifiable under a standard stochastic model for GDL, and that the polynomial-time algorithm ASTRAL-multi, a recent development in the ASTRAL suite of methods, is statistically consistent under this GDL model. We also provide a simulation study evaluating ASTRAL-multi for species tree estimation under GDL. All scripts and datasets used in this study are available on the Illinois Data Bank: https://doi.org/10.13012/B2IDB-2626814_V1. 

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4. Classification of solutions to an elliptic equation on $$\mathbb R^2$$ with nonlocal nonlinearity

   https://doi.org/10.3934/dcds.2025057  

   Gluck, Mathew (April 2025, Discrete and Continuous Dynamical Systems)

   A semilinear elliptic equation on $$\mathbb R^2$$ having nonlocal nonlinearity of Choquard type is considered. The entire solutions to the equation under consideration are classified under integrability assumptions that are invariant under the natural symmetries of the problem. This classification theorem can be viewed as an extension of the classification theorem of W. Chen and C. Li for the classical Liouville equation in the sense that, as the nonlocality vanishes, the classification result in the present work is consistent with that of Chen and Li. 

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5. Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons

   Zhu, Banghua and (January 2023, Proceedings of Machine Learning Research)

   Krause, Andreas and (Ed.)

   We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). We show that when the underlying true reward is linear, under both Bradley-Terry-Luce (BTL) model (pairwise comparison) and Plackett-Luce (PL) model ($$K$$-wise comparison), MLE converges under certain semi-norm for the family of linear reward. On the other hand, when training a policy based on the learned reward model, we show that MLE fails while a pessimistic MLE provides policies with good performance under certain coverage assumption. We also show that under the PL model, both the true MLE and a different MLE which splits the $$K$$-wise comparison into pairwise comparisons converge, while the true MLE is asymptotically more efficient. Our results validate the empirical success of the existing RLHF algorithms, and provide new insights for algorithm design. Our analysis can also be applied for the problem of online RLHF and inverse reinforcement learning. 

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