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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

I prove new subcritical bounds for the $\ell^p$-improving problem along restricted subsets of a degenerate curve. The key input is a new paucity estimate for associated inhomogeneous equations which is proven using an elimination method due to Wooley and Parsell--Wooley., Comment: 12 pages. Comments welcome!

In this paper, we revisit the square function estimates for extension operators over curves with torsion and prove results for planar curves of the form $(T,\phi(T))$ where $\phi(T)$ is a polynomial of degree at least 2. This includes new results for degenerate, finite type curves endowed with the Euclidean arclength measure such as those given by monomials $\phi(T) = T^k$ for $k \geq 3$. Our results are uniform over all local fields of characteristic 0., Comment: 18 pages, no figures, comments welcome!

We show that the system of equations \begin{align*} \sum_{i=1}^s (x_i^j-y_i^j) = a_j \qquad (1 \le j \le k) \end{align*} has appreciably fewer solutions in the subcritical range $s < k(k+1)/2$ than its homogeneous counterpart, provided that $a_\ell \neq 0$ for some $\ell \le k-1$. Our methods use Vinogradov's mean value theorem in combination with a shifting argument.

We apply Christ's method of refinements to the $\ell^p$-improving problem for discrete averages $\mathcal{A}_N$ along polynomial curves in $\mathbb{Z}^d$. Combined with certain elementary estimates for the number of solutions to certain special systems of diophantine equations, we obtain some restricted weak-type $p \to p'$ estimates for the averages $\mathcal{A}_N$ in the subcritical regime. The dependence on $N$ of the constants here obtained is sharp, except maybe for an $\epsilon$-loss., Comment: 19 pages, 3 figures

Accurate risk stratification is key to reducing cancer morbidity through targeted screening and preventative interventions. Numerous breast cancer risk prediction models have been developed, but they often give predictions with conflicting clinical implications. Integrating information from different models may improve the accuracy of risk predictions, which would be valuable for both clinicians and patients. BRCAPRO and BCRAT are two widely used models based on largely complementary sets of risk factors. BRCAPRO is a Bayesian model that uses detailed family history information to estimate the probability of carrying a BRCA1/2 mutation, as well as future risk of breast and ovarian cancer, based on mutation prevalence and penetrance (age-specific probability of developing cancer given genotype). BCRAT uses a relative hazard model based on first-degree family history and non-genetic risk factors. We consider two approaches for combining BRCAPRO and BCRAT: 1) modifying the penetrance functions in BRCAPRO using relative hazard estimates from BCRAT, and 2) training an ensemble model that takes as input BRCAPRO and BCRAT predictions. We show that the combination models achieve performance gains over BRCAPRO and BCRAT in simulations and data from the Cancer Genetics Network.

In this work, we consider the exponentially growing subarea of genetics in cancer. The need to synthesize and centralize this evidence for dissemination has motivated a team of physicians to manually construct and maintain a knowledge base that distills key results reported in the literature. This is a laborious process that entails reading through full-text articles to understand the study design, assess study quality, and extract the reported cancer risk estimates associated with particular hereditary cancer genes (i.e., penetrance). In this work, we propose models to automatically surface key elements from full-text cancer genetics articles, with the ultimate aim of expediting the manual workflow currently in place. We propose two challenging tasks that are critical for characterizing the findings reported cancer genetics studies: (i) Extracting snippets of text that describe \emph{ascertainment mechanisms}, which in turn inform whether the population studied may introduce bias owing to deviations from the target population; (ii) Extracting reported risk estimates (e.g., odds or hazard ratios) associated with specific germline mutations. The latter task may be viewed as a joint entity tagging and relation extraction problem. To train models for these tasks, we induce distant supervision over tokens and snippets in full-text articles using the manually constructed knowledge base. We propose and evaluate several model variants, including a transformer-based joint entity and relation extraction model to extract } pairs. We observe strong empirical performance, highlighting the practical potential for such models to aid KB construction in this space. We ablate components of our model, observing, e.g., that a joint model for fares substantially better than a pipelined approach., Comment: In proceedings of the Conference on Automated Knowledge Base Construction (AKBC), 2020

We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmetic version of the Tomas--Stein method and Magyar's decomposition of Birch's hypersurfaces. For our result about varieties of higher codimension, we use the even moment method and works of Birch and Schmidt., Comment: 16 pages