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1. On extremizing sequences for adjoint Fourier restriction to the sphere

   https://doi.org/10.1016/j.aim.2024.109854  

   Flock, Taryn C; Stovall, Betsy (September 2024, Advances in Mathematics)

   In this article, we develop a linear profile decomposition for the $$L^p \to L^q$$ adjoint Fourier restriction operator associated to the sphere, valid for exponent pairs $p\max\{p,\tfrac{d+2}d p'\}$$, or if $$q=\tfrac{d+2}d p'$$ and the operator norm exceeds a certain constant times the operator norm of the parabolic extension operator. 

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2. Bi-Sobolev Extensions

   https://doi.org/10.1007/s12220-023-01363-1  

   Koski, Aleksis; Onninen, Jani (July 2023, The Journal of Geometric Analysis)

   Abstract We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling–Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling–Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos. 

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3. Robust Inverse Regression for Multivariate Elliptical Functional Data

   https://doi.org/10.5705/ss.202023.0341  

   Solea, Eftychia; Christou, Eliana; Song, Jun (May 2024, Statistica Sinica)

   Functional data have received significant attention as they frequently appear in modern applications, such as functional magnetic resonance imaging (fMRI) and natural language processing. The infinite-dimensional nature of functional data makes it necessary to use dimension reduction techniques. Most existing techniques, however, rely on the covariance operator, which can be affected by heavy-tailed data and unusual observations. Therefore, in this paper, we consider a robust sliced inverse regression for multivariate elliptical functional data. For that reason, we introduce a new statistical linear operator, called the conditional spatial sign Kendall’s tau covariance operator, which can be seen as an extension of the multivariate Kendall’s tau to both the conditional and functional settings. The new operator is robust to heavy-tailed data and outliers, and hence can provide a robust estimate of the sufficient predictors. We also derive the convergence rates of the proposed estimators for both completely and partially observed data. Finally, we demonstrate the finite sample performance of our estimator using simulation examples and a real dataset based on fMRI. 

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4. Vertex operator superalgebras and the 16-fold way

   https://doi.org/10.1090/tran/8454  

   Dong, Chongying; Ng, Siu-Hung; Ren, Li (July 2021, Transactions of the American Mathematical Society)

   Let V V be a vertex operator superalgebra with the natural order 2 automorphism σ \sigma . Under suitable conditions on V V , the σ \sigma -fixed subspace V 0 ¯ V_{\bar 0} is a vertex operator algebra and the V 0 ¯ V_{\bar 0} -module category C V 0 ¯ \mathcal {C}_{V_{\bar 0}} is a modular tensor category. In this paper, we prove that C V 0 ¯ \mathcal {C}_{V_{\bar 0}} is a fermionic modular tensor category and the Müger centralizer C V 0 ¯ 0 \mathcal {C}_{V_{\bar 0}}^0 of the fermion in C V 0 ¯ \mathcal {C}_{V_{\bar 0}} is generated by the irreducible V 0 ¯ V_{\bar 0} -submodules of the V V -modules. In particular, C V 0 ¯ 0 \mathcal {C}_{V_{\bar 0}}^0 is a super-modular tensor category and C V 0 ¯ \mathcal {C}_{V_{\bar 0}} is a minimal modular extension of C V 0 ¯ 0 \mathcal {C}_{V_{\bar 0}}^0 . We provide a construction of a vertex operator superalgebra V l V^l for each positive integer l l such that C ( V l ) 0 ¯ \mathcal {C}_{{(V^l)_{\bar 0}}} is a minimal modular extension of C V 0 ¯ 0 \mathcal {C}_{V_{\bar 0}}^0 . We prove that these modular tensor categories C ( V l ) 0 ¯ \mathcal {C}_{{(V^l)_{\bar 0}}} are uniquely determined, up to equivalence, by the congruence class of l l modulo 16. 

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5. Fuzzy Integration of Data Lake Tables. In EDBT 2026.

   https://doi.org/10.48786/edbt.2026.08  

   Khatiwada, Aamod; Shraga, Roee; Miller, Renée J (January 2026, OpenProceedings.org)

   EDBT (Ed.)

   Data integration is an important step in any data science pipeline where the objective is to unify the information available in differ- ent datasets for comprehensive analysis. Full Disjunction, which is an associative extension of the outer join operator, has been shown to be an effective operator for integrating datasets. It fully preserves and combines the available information. Existing Full Disjunction algorithms only consider the equi-join scenario where only tuples having the same value on joining columns are integrated. This, however, does not realistically represent many realistic scenarios where datasets come from diverse sources with inconsistent values (e.g., synonyms, abbreviations, etc.) and with limited metadata. So, joining just on equal values severely limits the ability of Full Disjunction to fully combine datasets. Thus, in this work, we propose an extension of Full Disjunction to also account for “fuzzy” matches among tuples. We present a novel data-driven approach to enable the joining of approximate or fuzzy matches within Full Disjunction. Experimentally, we show that fuzzy Full Disjunction does not add significant time over- head over a state-of-the-art Full Disjunction implementation and also that it enhances the accuracy of a downstream data quality task. 

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