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Let $F$, $S$ be bounded measurable sets in $\mathbb{R}^d$. Let $P_F : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d) $ be the orthogonal projection on the subspace of functions with compact support on $F$, and let $B_S : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$ be the orthogonal projection on the subspace of functions with Fourier transforms having compact support on $S$. In this paper, we derive improved distributional estimates on the eigenvalue sequence $1 \geq \lambda_1(F,S) \geq \lambda_2(F,S) \geq \cdots > 0$ of the \emph{spatio-spectral limiting operator} $B_S P_F B_S : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$. The significance of such estimates lies in their diverse applications in medical imaging, signal processing, geophysics and astronomy. Our proof is based on the decomposition techniques developed in \cite{MaRoSp23}. The novelty of our approach is in the use of a two-stage dyadic decomposition with respect to both the spatial and frequency domains, and the application of the results in \cite{ArieAzita23} on the eigenvalues of spatio-spectral limiting operators associated to cubical domains., Comment: 18 pages

Published biomedical information has and continues to rapidly increase. The recent advancements in Natural Language Processing (NLP), have generated considerable interest in automating the extraction, normalization, and representation of biomedical knowledge about entities such as genes and diseases. Our study analyzes germline abstracts in the construction of knowledge graphs of the of the immense work that has been done in this area for genes and diseases. This paper presents SimpleGermKG, an automatic knowledge graph construction approach that connects germline genes and diseases. For the extraction of genes and diseases, we employ BioBERT, a pre-trained BERT model on biomedical corpora. We propose an ontology-based and rule-based algorithm to standardize and disambiguate medical terms. For semantic relationships between articles, genes, and diseases, we implemented a part-whole relation approach to connect each entity with its data source and visualize them in a graph-based knowledge representation. Lastly, we discuss the knowledge graph applications, limitations, and challenges to inspire the future research of germline corpora. Our knowledge graph contains 297 genes, 130 diseases, and 46,747 triples. Graph-based visualizations are used to show the results., Comment: 10 pages

Using the Girard--Newton formulae, I give a simple proof of isotropic square function estimates for extension operators along the moment curve in generic local fields. Using Bezout's Theorem and the Implicit Function Theorem, I give an alternate, sharper proof for real or complex non-degenerate, polynomial curves., Comment: 10 pages, related to arXiv:1906.05877, arXiv:2201.09649 and arXiv:2203.13644, comments welcome :) Small improvements to the exposition have been made including clarifying the dependence on the dimension in the relevant bounds (e.g., Theorem 1; thanks to Trevor Wooley for pointing this out to me). A section at the end of the paper dicussing the connection to Superorthogonality has been added

We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely does solution counting in older partial progress on Vinogradov's mean value theorem correspond to in Fourier decoupling theory., Comment: 25 pages; revised version incorporating referee comments, to appear in Mathematika

We study the number of degree $n$ number fields with discriminant bounded by $X$. In this article, we improve an upper bound due to Schmidt on the number of such fields that was previously the best known upper bound for $6 \leq n \leq 94$., Comment: 24 pages; official version for Discrete Analysis

Direct fired supercritical CO2 (sCO2) power cycles allow for the combustion of gaseous fuels under oxyfuel conditions with inherent carbon capture. As the CO2 is captured intrinsically, the efficiency penalty of capture on the overall plant is small, meaning that power plants achieve a similar efficiency to traditional fossil fuel power plants without carbon capture and storage. However, at high pressures and in large dilutions of CO2, combustion mechanisms are poorly understood. Therefore, in this paper sensitivity and quantitative analysis of four established chemical kinetic mechanisms have been employed to determine the most important reactions and the best performing mechanisms over a range of different conditions. CH3O2 chemistry was identified as a pivotal mechanism component for modelling methane combustion above 200 atm. The University of Sheffield (UoS) sCO2 mechanism created in the present work better models the ignition delay time (IDT) of high-pressure combustion in a large dilution of CO2. Quantitative analysis showed that the UoS sCO2 mechanism was the best fit to the greatest number of IDT datasets and had the lowest average absolute error value, thus indicating a superior performance compared to the four existing chemical kinetic mechanisms, well-validated for lower pressure conditions., Comment: 26 pages, 9 figures