arXiv subjects

Geoffrey Smith

Publications and source records attributed to Geoffrey Smith.

17 recordsLinked to original sources

arXiv2024

Robust Meta-Model for Predicting the Need for Blood Transfusion in Non-traumatic ICU Patients

Objective: Blood transfusions, crucial in managing anemia and coagulopathy in ICU settings, require accurate prediction for effective resource allocation and patient risk assessment. However, existing clinical decision support systems have primarily targeted a particular patient demographic with unique medical conditions and focused on a single type of blood transfusion. This study aims to develop an advanced machine learning-based model to predict the probability of transfusion necessity over the next 24 hours for a diverse range of non-traumatic ICU patients. Methods: We conducted a retrospective cohort study on 72,072 adult non-traumatic ICU patients admitted to a high-volume US metropolitan academic hospital between 2016 and 2020. We developed a meta-learner and various machine learning models to serve as predictors, training them annually with four-year data and evaluating on the fifth, unseen year, iteratively over five years. Results: The experimental results revealed that the meta-model surpasses the other models in different development scenarios. It achieved notable performance metrics, including an Area Under the Receiver Operating Characteristic (AUROC) curve of 0.97, an accuracy rate of 0.93, and an F1-score of 0.89 in the best scenario. Conclusion: This study pioneers the use of machine learning models for predicting blood transfusion needs in a diverse cohort of critically ill patients. The findings of this evaluation confirm that our model not only predicts transfusion requirements effectively but also identifies key biomarkers for making transfusion decisions.

cs.LG↗

arXiv2023

Hierarchical Classification System for Breast Cancer Specimen Report (HCSBC) -- an end-to-end model for characterizing severity and diagnosis

Automated classification of cancer pathology reports can extract information from unstructured reports and categorize each report into structured diagnosis and severity categories. Thus, such system can reduce the burden for populating tumor registries, help registration for clinical trial as well as developing large dataset for deep learning model development using true pathologic ground truth. However, the content of breast pathology reports can be difficult for categorize due to the high linguistic variability in content and wide variety of potential diagnoses >50. Existing NLP models are primarily focused on developing classifier for primary breast cancer types (e.g. IDC, DCIS, ILC) and tumor characteristics, and ignore the rare diagnosis of cancer subtypes. We then developed a hierarchical hybrid transformer-based pipeline (59 labels) - Hierarchical Classification System for Breast Cancer Specimen Report (HCSBC), which utilizes the potential of the transformer context-preserving NLP technique and compared our model to several state of the art ML and DL models. We trained the model on the EUH data and evaluated our model's performance on two external datasets - MGH and Mayo Clinic. We publicly release the code and a live application under Huggingface spaces repository

cs.CV↗

arXiv2023

Stability of normal bundles of Brill-Noether curves

We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function of $g$ and $r$. We further prove that the normal bundle is in fact stable if $g\geq 2$ and either $g$ or $d$ satisfy slightly stronger bounds. In particular, for each $r$ and $g\geq 1$ (respectively, $g\geq2$), there are at most finitely many $(d,g)$ for which the normal bundle of the general Brill-Noether curve is not semistable (respectively, stable).

math.AG↗

arXiv2022

Lines highly tangent to a hypersurface

We study spaces of lines that meet a smooth hypersurface X in P^n to high order. As an application, we give a polynomial upper bound on the number of planes contained in a smooth degree d hypersurface in P^5 and provide a proof of a result of Landsberg without using moving frames.

math.AG↗

arXiv2022

Effective cycles on universal hypersurfaces

We study the effective cones of cycles on universal hypersurfaces on a projective variety $X$, particularly focusing on the case of universal hypersurfaces in $\mathbb{P}^n$. We determine the effective cones of cycles on the universal conic over $\mathbb{P}^2$. We also determine every effective cone of cycles of dimension at most 6 or equal to 10 on any universal plane curve.

math.AG↗

arXiv2022

Stability and cohomology of kernel bundles on projective space

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an asymptotic cohomology vanishing theorem. We characterize the stability of general Steiner bundles on projective space. We also give a criterion for a Steiner bundle to be ample.

math.AG↗

arXiv2022

The EMory BrEast imaging Dataset (EMBED): A Racially Diverse, Granular Dataset of 3.5M Screening and Diagnostic Mammograms

Developing and validating artificial intelligence models in medical imaging requires datasets that are large, granular, and diverse. To date, the majority of publicly available breast imaging datasets lack in one or more of these areas. Models trained on these data may therefore underperform on patient populations or pathologies that have not previously been encountered. The EMory BrEast imaging Dataset (EMBED) addresses these gaps by providing 3650,000 2D and DBT screening and diagnostic mammograms for 116,000 women divided equally between White and African American patients. The dataset also contains 40,000 annotated lesions linked to structured imaging descriptors and 61 ground truth pathologic outcomes grouped into six severity classes. Our goal is to share this dataset with research partners to aid in development and validation of breast AI models that will serve all patients fairly and help decrease bias in medical AI.

eess.IV↗

arXiv2021

Rational linear subspaces of hypersurfaces over finite fields

Let $X \subset \mathbb{P}^n$ be a hypersurface of degree $d$ defined over a finite field of characteristic $p > 0$. We prove that if $n \ge r + \binom{d+r}{r+1}$, then $X$ contains a rational $r$-plane. We prove better bounds when $X$ is smooth and $p$ is sufficiently large. We also present experimental data regarding the existence of rational lines on cubic threefolds over $\mathbb{F}_7$, $\mathbb{F}_8$, and $\mathbb{F}_9$. In particular, we construct an example of a smooth cubic threefold over $\mathbb{F}_7$ with exactly $8$ rational lines. It remains an open question whether smooth cubic threefolds over $\mathbb{F}_7$, $\mathbb{F}_8$, and $\mathbb{F}_9$ always contain a rational line.

math.AG↗

arXiv2021

Exceptional loci in Lefschetz theory

Let $\phi:X\rightarrow \mathbb{P}^n$ be a morphism of varieties. Given a hyperplane $H$ in $\mathbb{P}^n$, there is a Gysin map from the compactly supported cohomology of $\phi^{-1}(H)$ to that of $X$. We give conditions on the degree of the cohomology under which this map is an isomorphism for all but a low-dimensional set of hyperplanes, generalizing results due to Skorobogatov, Benoist, and Poonen-Slavov. Our argument is based on Beilinson's theory of singular supports for \'etale sheaves.

math.AG↗

arXiv2021

Very free rational curves in Fano varieties

Let $X$ be a projective variety and let $C$ be a rational normal curve on $X$. We compute the normal bundle of $C$ in a general complete intersection of hypersurfaces of sufficiently large degree in $X$. As a result, we establish the separable rational connectedness of a large class of varieties, including general Fano complete intersections of hypersurfaces of degree at least three in flag varieties, in arbitrary characteristic. In addition, we give a new way of computing the normal bundle of certain rational curves in products of varieties in terms of their restricted tangent bundles and normal bundles on each factor.

math.AG↗

arXiv2020

Vector bundles on trees of smooth rational curves

Given a vector bundle $E$ on a tree of smooth rational curves $C$, we give necessary and sufficient conditions for a vector bundle $E'$ on $\mathbb{P}^1$ to specialize to $E$ on $C$, generalizing the rank 2 case, due to Coskun.

math.AG↗

arXiv2020

Covering gonalities of complete intersections in positive characteristic

We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a smooth multidegree $(d_1,\ldots,d_k)$ complete intersection in $\mathbb{P}^N$ has separable covering gonality at least $d-N+1$, where $d=d_1+\cdots+d_k$. We also show that the very general such variety has covering gonality at least $\frac{d-N+2}{2}$.

math.AG↗

arXiv2019

Tilt stability and the degree of irrationality of surfaces on threefolds

Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt semistable objects conjectured by Bayer-Macr\`i-Stellari, then the minimum degree of a dominant rational map $S\dashrightarrow\mathbb{P}^2$ is either relatively large or determined by a net of curves of low degree on $S$. As one application, we prove that the complete intersection of three very general quadrics in $\mathbb{P}^5$ has degree of irrationality 4.

math.AG↗

arXiv2019

Low degree points on curves

In this paper we investigate an arithmetic analogue of the gonality of a smooth projective curve $C$ over a number field $k$: the minimal $e$ such there are infinitely many points $P \in C(\bar{k})$ with $[k(P):k] \leq e$. Developing techniques that make use of an auxiliary smooth surface containing the curve, we show that this invariant can take any value subject to constraints imposed by the gonality. Building on work of Debarre--Klassen, we show that this invariant is equal to the gonality for all sufficiently ample curves on a surface $S$ with trivial irregularity.

math.NT↗

arXiv2017

Constants in Titchmarsh divisor problems for elliptic curves

Inspired by the analogy between the group of units $\mathbb{F}_p^{\times}$ of the finite field with $p$ elements and the group of points $E(\mathbb{F}_p)$ of an elliptic curve $E/\mathbb{F}_p$, E. Kowalski, A. Akbary & D. Ghioca, and T. Freiberg & P. Kurlberg investigated the asymptotic behaviour of elliptic curve sums analogous to the Titchmarsh divisor sum $\sum_{p \leq x} \tau(p + a) \sim C x$. In this paper, we present a comprehensive study of the constants $C(E)$ emerging in the asymptotic study of these elliptic curve divisor sums. Specifically, by analyzing the division fields of an elliptic curve $E/\mathbb{Q}$, we prove upper bounds for the constants $C(E)$ and, in the generic case of a Serre curve, we prove explicit closed formulae for $C(E)$ amenable to concrete computations. Moreover, we compute the moments of the constants $C(E)$ over two-parameter families of elliptic curves $E/\mathbb{Q}$. Our methods and results complement recent studies of average constants occurring in other conjectures about reductions of elliptic curves by addressing not only the average behaviour, but also the individual behaviour of these constants, and by providing explicit tools towards the computational verifications of the expected asymptotics.

math.NT↗

arXiv2014

Congruence properties of Taylor coefficients of modular forms

In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We examine similar congruence properties, but for the coefficients of a modified Taylor expansion about a CM point $τ$. These coefficients can be shown to be the product of a power of a constant transcendental factor and an algebraic integer. In our work, we give conditions on $τ$ and a prime number $p$ that, if satisfied, imply that $p^m$ divides the algebraic part of all the Taylor coefficients of $f$ of sufficiently high degree. We also give effective bounds on the largest $n$ such that $p^m$ does not divide the algebraic part of the $n^{\text{th}}$ Taylor coefficient of $f$ at $τ$ that are sharp under certain additional hypotheses.

math.NT↗

arXiv1999

Resource Discovery in Trilogy

Trilogy is a collaborative project whose key aim is the development of an integrated virtual laboratory to support research training within each institution and collaborative projects between the partners. In this paper, the architecture and underpinning platform of the system is described with particular emphasis being placed on the structure and the integration of the distributed database. A key element is the ontology that provides the multi-agent system with a conceptualisation specification of the domain; this ontology is explained, accompanied by a discussion how such a system is integrated and used within the virtual laboratory. Although in this paper, Telecommunications and in particular Broadband networks are used as exemplars, the underlying system principles are applicable to any domain where a combination of experimental and literature-based resources are required.

cs.DL↗