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Mark Green

Publications and source records attributed to Mark Green.

At least 19 recordsLinked to original sources
arXiv2026

Comparing how Large Language Models perform against keyword-based searches for social science research data discovery

This paper evaluates the performance of a large language model (LLM) based semantic search tool relative to a traditional keyword-based search for data discovery. Using real-world search behaviour, we compare outputs from a bespoke semantic search system applied to UKRI data services with the Consumer Data Research Centre (CDRC) keyword search. Analysis is based on 131 of the most frequently used search terms extracted from CDRC search logs between December 2023 and October 2024. We assess differences in the volume, overlap, ranking, and relevance of returned datasets using descriptive statistics, qualitative inspection, and quantitative similarity measures, including exact dataset overlap, Jaccard similarity, and cosine similarity derived from BERT embeddings. Results show that the semantic search consistently returns a larger number of results than the keyword search and performs particularly well for place based, misspelled, obscure, or complex queries. While the semantic search does not capture all keyword based results, the datasets returned are overwhelmingly semantically similar, with high cosine similarity scores despite lower exact overlap. Rankings of the most relevant results differ substantially between tools, reflecting contrasting prioritisation strategies. Case studies demonstrate that the LLM based tool is robust to spelling errors, interprets geographic and contextual relevance effectively, and supports natural-language queries that keyword search fails to resolve. Overall, the findings suggest that LLM driven semantic search offers a substantial improvement for data discovery, complementing rather than fully replacing traditional keyword-based approaches.

cs.IR↗
arXiv2025

Period maps at infinity

Let $\overline{B}$ be a smooth projective varieity, and $Z \subset \overline{B}$ a simple normal crossing divisor. Assume that $B = \overline{B} - Z$ admits a variation of pure, polarized Hodge structure. The divisor $Z$ is naturally stratified, and Schmid's nilpotent orbit theorem defines a family/variation of nilpotent orbits along each strata. We study the rich geometric structure encoded by this family, its relationship to the induced (quotient) variation of pure Hodge structure on the strata, and establish a relationship between the extension data in the nilpotent orbits and the normal bundles of the smooth irreducible components of $Z$.

math.AG↗
arXiv2025

Lagrangian interpretation of Abel-Jacobi mappings associated to Fano threefolds

Using the general framework due to Donagi-Markman \cite{DM} and Markushevich \cite{M} we shall derive an expression for the differential of Abel-Jacobi mappings on Fano threefolds. This formula involves information normal to the Lagrangian submanifolds constructed in \cite{DM} and \cite{M}. It may be applied to give new proofs of a number of classical results about these varieties.

math.AG↗
arXiv2025

A framework for 3D interaction techniques

This paper presents a software architecture for 3D interaction techniques (ITs) and an object oriented, toolkit-independent framework that implements such architecture. ITs are composed of basic filters connected in a dataflow, where virtual input devices and objects in the scene are sources of information. An execution model defines the general flow of information between filters. This framework has been designed to be extensible: new information types, new input devices, new execution models, or new interaction techniques can easily be added. Application specific code and application specific ITs are seamlessly integrated into this architecture.

cs.HC↗
arXiv2025

A wireless, inexpensive optical tracker for the CAVE

CAVE displays offer many advantages over other virtual reality (VR) displays, including a large, unencumbering viewing space. Unfortunately, the typical tracking subsystems used with CAVE displays tether the user and lessen this advantage. We have designed a simple, low-cost feet tracker that is wireless, leaving the user free to move. The tracker can be assembled for less than $200 US, and achieves an accuracy of 10 cm at a 20 Hz sampling rate. We have tested the prototype with two applications: a visualization supporting close visual inspection, and a walkthrough of the campus. Although the tracking was convincing, it was clear that the tracker's limitations make it less than ideal for applications requiring precise visual inspection. However, the freedom of motion allowed by the tracker was a compelling supplement to our campus walkthrough, allowing users to stroll and look around corners.

cs.HC↗
arXiv2024

Infinitesimal invariants of mixed Hodge structures

We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and in more detail in the case when $X$ is a cubic threefold. In this last setting, we obtain a generic global Torelli theorem for pairs.

math.AG↗
arXiv2022

Shafarevich mappings and period mappings

We shall show that a smooth, quasi-projective variety $X$ has a holomorphically convex universal covering $\wt X$ when (i) $\pi_1(X)$ is residually nilpotent and (ii) there is an admissable variation of \mhs\ over $X$ whose monodromy representation has a finite kernel, and where in each case a corresponding period mapping is assumed to be proper.

math.AG↗
arXiv2021

Evaluating the performance of personal, social, health-related, biomarker and genetic data for predicting an individuals future health using machine learning: A longitudinal analysis

As we gain access to a greater depth and range of health-related information about individuals, three questions arise: (1) Can we build better models to predict individual-level risk of ill health? (2) How much data do we need to effectively predict ill health? (3) Are new methods required to process the added complexity that new forms of data bring? The aim of the study is to apply a machine learning approach to identify the relative contribution of personal, social, health-related, biomarker and genetic data as predictors of future health in individuals. Using longitudinal data from 6830 individuals in the UK from Understanding Society (2010-12 to 2015-17), the study compares the predictive performance of five types of measures: personal (e.g. age, sex), social (e.g. occupation, education), health-related (e.g. body weight, grip strength), biomarker (e.g. cholesterol, hormones) and genetic single nucleotide polymorphisms (SNPs). The predicted outcome variable was limiting long-term illness one and five years from baseline. Two machine learning approaches were used to build predictive models: deep learning via neural networks and XGBoost (gradient boosting decision trees). Model fit was compared to traditional logistic regression models. Results found that health-related measures had the strongest prediction of future health status, with genetic data performing poorly. Machine learning models only offered marginal improvements in model accuracy when compared to logistic regression models, but also performed well on other metrics e.g. neural networks were best on AUC and XGBoost on precision. The study suggests that increasing complexity of data and methods does not necessarily translate to improved understanding of the determinants of health or performance of predictive models of ill health.

stat.ML↗
arXiv2020

Analog of Satake-Baily-Borel for period maps

We propose an analog of the Satake--Baily--Borel compactification and Borel's extension theorem for arbitrary period maps. The proposed analog is constructed as a proper topological completion of the period map. It is conjectured that the construction is projective algebraic, and the conjecture is reduced to a certain extension problem.

math.AG↗
arXiv2020

A deep learning approach to identify unhealthy advertisements in street view images

While outdoor advertisements are common features within towns and cities, they may reinforce social inequalities in health. Vulnerable populations in deprived areas may have greater exposure to fast food, gambling and alcohol advertisements encouraging their consumption. Understanding who is exposed and evaluating potential policy restrictions requires a substantial manual data collection effort. To address this problem we develop a deep learning workflow to automatically extract and classify unhealthy advertisements from street-level images. We introduce the Liverpool 360 Street View (LIV360SV) dataset for evaluating our workflow. The dataset contains 25,349, 360 degree, street-level images collected via cycling with a GoPro Fusion camera, recorded Jan 14th - 18th 2020. 10,106 advertisements were identified and classified as food (1335), alcohol (217), gambling (149) and other (8405) (e.g., cars and broadband). We find evidence of social inequalities with a larger proportion of food advertisements located within deprived areas and those frequented by students. Our project presents a novel implementation for the incidental classification of street view images for identifying unhealthy advertisements, providing a means through which to identify areas that can benefit from tougher advertisement restriction policies for tackling social inequalities.

cs.CY↗
arXiv2019

The LLV decomposition of hyper-Kaehler cohomology

Looijenga--Lunts and Verbitsky showed that the cohomology of a compact hyper-K\"ahler manifold $X$ admits a natural action by the Lie algebra $\mathfrak{so} (4, b_2(X)-2)$, generalizing the Hard Lefschetz decomposition for compact K\"ahler manifolds. In this paper, we determine the Looijenga--Lunts--Verbitsky (LLV) decomposition for all known examples of compact hyper-K\"ahler manifolds, and propose a general conjecture on the weights occurring in the LLV decomposition, which in particular determines strong bounds on the second Betti number $b_2(X)$ of hyper-K\"ahler manifolds. Specifically, in the $K3^{[n]}$ and $\mathrm{Kum}_n$ cases, we give generating series for the formal characters of the associated LLV representations, which generalize the well-known G\"ottsche formulas for the Euler numbers, Betti numbers, and Hodge numbers for these series of hyper-K\"ahler manifolds. For the two exceptional cases of O'Grady we refine the known results on their cohomology. In particular, we note that the LLV decomposition leads to a simple proof for the Hodge numbers of hyper-K\"ahler manifolds of O'Grady 10 type. In a different direction, for all known examples of hyper-K\"ahler manifolds, we establish the so-called Nagai's conjecture on the monodromy of degenerations of hyper-K\"ahler manifolds. More consequentially, we note that Nagai's conjecture is a first step towards a more general and more natural conjecture, that we state here. Finally, we prove that this new conjecture is satisfied by the known types of hyper-K\"ahler manifolds.

math.AG↗
arXiv2018

Positivity of vector bundles and Hodge theory

It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, vanishing of higher cohomology leading to existence of global sections etc. It is also well known that bundles arising in Hodge theory tend to have positivity properties. From these considerations several issues arise: (i) In general for bundles that are semi-positive but not strictly positive; what further natural conditions lead to the existence of sections of its symmetric powers? (ii) In Hodge theory the Hodge metrics generally have singularities; what can be said about these and their curvatures, Chern forms etc.? (iii) What are some algebro-geometric applications of positivity of Hodge bundles? The purpose of these partly expository notes is fourfold. One is to summarize some of the general measures and types of positivity that have arisen in the literature. A second is to introduce and give some applications of norm positivity. This is a concept that implies the di_erent notions of metric semi-positivity that are present in many of the standard examples and one that has an algebro-geometric interpretation in these examples. A third purpose is to discuss and compare some of the types of metric singularities that arise in algebraic geometry and in Hodge theory. Finally we shall present some applications of the theory from both the classical and recent literature.

math.AG↗
arXiv2017

Period mappings and properties of the augmented Hodge line bundle

Let $P$ be the image of a period map. We discuss progress towards a conjectural Hodge theoretic completion $\overline{P}$, an analogue of the Satake-Baily-Borel compactification in the classical case. The set $\overline{P}$ is defined and given the structure of a compact Hausdorff topological space. We conjecture that it admits the structure of a compact complex analytic variety. We verify this conjecture when $\mathrm{dim} P \le 2$. In general, $\overline{P}$ admits a finite cover $\overline{S}$ (also a compact Hausdorff space, and constructed from Stein factorizations of period maps). Assuming that $\overline{S}$ is a compact complex analytic variety, we show that a lift of the augmented Hodge line bundle $\Lambda$ extends to an ample line bundle, giving $\overline{P}$ the structure of a projective normal variety. Our arguments rely on refined positivity properties of Chern forms associated to various Hodge bundles; properties that might be of independent interest.

math.AG↗
arXiv2014

Magnetic structure of the conductive triangular-lattice antiferromagnet PdCrO2

We performed neutron single crystal and synchrotron X-ray powder diffraction experiments in order to investigate the magnetic and crystal structures of the conductive layered triangular-lattice antiferromagnet PdCrO2 with a putative spin chirality, which contributes to an unconventional anomalous Hall effect. We revealed that the ground-state magnetic structure is a commensurate and nearly-coplanar 120-degrees spin structure. The 120-degrees plane in different Cr layers seem to tilt with one another, leading to a small noncoplanarity. Such a small but finite non-coplanar stacking of the 120-degrees planes gives rise to a finite scalar spin chirality, which may be responsible for the unconventional nature of the Hall effect of PdCrO2.

cond-mat.str-el↗
arXiv2009

Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results

This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds.

math.AG↗