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John Harvey

Publications and source records attributed to John Harvey.

14 recordsLinked to original sources
arXiv2026

Curvature bounds, regularity and inextendibility of spacetimes

We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This enables us to relate low-regularity inextendibility of spacetimes to unboundedness of curvature - which is at present unattainable using classical methods - thereby strengthening and complementing the results of Grant-Kunzinger-Saemann (2019) significantly.

gr-qc↗
arXiv2025

A Survey of Dimension Estimation Methods

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence the complexity of the dataset at hand. A great variety of dimension estimators have been developed to find the intrinsic dimension of the data but there is little guidance on how to reliably use these estimators. This survey reviews a wide range of dimension estimation methods, categorising them by the geometric information they exploit: tangential estimators which detect a local affine structure; parametric estimators which rely on dimension-dependent probability distributions; and estimators which use topological or metric invariants. The paper evaluates the performance of these methods, as well as investigating varying responses to curvature and noise. Key issues addressed include robustness to hyperparameter selection, sample size requirements, accuracy in high dimensions, precision, and performance on non-linear geometries. In identifying the best hyperparameters for benchmark datasets, overfitting is frequent, indicating that many estimators may not generalise well beyond the datasets on which they have been tested.

stat.ML↗
arXiv2025

Large Language Models as 'Hidden Persuaders': Fake Product Reviews are Indistinguishable to Humans and Machines

Reading and evaluating product reviews is central to how most people decide what to buy and consume online. However, the recent emergence of Large Language Models and Generative Artificial Intelligence now means writing fraudulent or fake reviews is potentially easier than ever. Through three studies we demonstrate that (1) humans are no longer able to distinguish between real and fake product reviews generated by machines, averaging only 50.8% accuracy overall - essentially the same that would be expected by chance alone; (2) that LLMs are likewise unable to distinguish between fake and real reviews and perform equivalently bad or even worse than humans; and (3) that humans and LLMs pursue different strategies for evaluating authenticity which lead to equivalently bad accuracy, but different precision, recall and F1 scores - indicating they perform worse at different aspects of judgment. The results reveal that review systems everywhere are now susceptible to mechanised fraud if they do not depend on trustworthy purchase verification to guarantee the authenticity of reviewers. Furthermore, the results provide insight into the consumer psychology of how humans judge authenticity, demonstrating there is an inherent 'scepticism bias' towards positive reviews and a special vulnerability to misjudge the authenticity of fake negative reviews. Additionally, results provide a first insight into the 'machine psychology' of judging fake reviews, revealing that the strategies LLMs take to evaluate authenticity radically differ from humans, in ways that are equally wrong in terms of accuracy, but different in their misjudgments.

cs.CL↗
arXiv2023

A Toponogov globalisation result for Lorentzian length spaces

In the synthetic geometric setting introduced by Kunzinger and S\"amann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with lower (timelike) curvature bounds. Our approach utilises a "cat's cradle" construction akin to that which appears in several proofs in the metric setting. On the road to our main result, we also provide a lemma regarding the subdivision of triangles in spaces with a local lower curvature bound and a synthetic Lorentzian version of the Lebesgue Number Lemma. Several properties of time functions and the null distance on globally hyperbolic Lorentzian length spaces are also highlighted. We conclude by presenting several applications of our results, including versions of the Bonnet--Myers Theorem and the Splitting Theorem for Lorentzian length spaces with local lower curvature bounds, as well as discussion of stability of curvature bounds under Gromov--Hausdorff convergence.

math.DG↗
arXiv2021

Estimating the reach of a manifold via its convexity defect function

The reach of a submanifold is a crucial regularity parameter for manifold learning and geometric inference from point clouds. This paper relates the reach of a submanifold to its convexity defect function. Using the stability properties of convexity defect functions, along with some new bounds and the recent submanifold estimator of Aamari and Levrard [Ann. Statist. 47 177-204 (2019)], an estimator for the reach is given. A uniform expected loss bound over a C^k model is found. Lower bounds for the minimax rate for estimating the reach over these models are also provided. The estimator almost achieves these rates in the C^3 and C^4 cases, with a gap given by a logarithmic factor.

math.ST↗
arXiv2020

Almost non-negatively curved 4-manifolds with torus symmetry

We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry.

math.DG↗
arXiv2019

Machine Learning in High Energy Physics Community White Paper

Machine learning has been applied to several problems in particle physics research, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising future research and development areas for machine learning in particle physics. We detail a roadmap for their implementation, software and hardware resource requirements, collaborative initiatives with the data science community, academia and industry, and training the particle physics community in data science. The main objective of the document is to connect and motivate these areas of research and development with the physics drivers of the High-Luminosity Large Hadron Collider and future neutrino experiments and identify the resource needs for their implementation. Additionally we identify areas where collaboration with external communities will be of great benefit.

physics.comp-ph↗
arXiv2019

Semi-free actions with manifold orbit spaces

In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply connected $5$-manifolds admitting a smooth, semi-free circle action with fixed-point components of codimension $4$ are connected sums of $S^3$-bundles over $S^2$. Furthermore, the Betti numbers of the $5$-manifolds and of the quotient $4$-manifolds are related by a simple formula involving the number of fixed-point components. We also investigate semi-free $S^3$ actions on simply connected $8$-manifolds with quotient a $5$-manifold and show, in particular, that there are strong restrictions on the topology of the $8$-manifold.

math.DG↗
arXiv2018

Lifelong Testing of Smart Autonomous Systems by Shepherding a Swarm of Watchdog Artificial Intelligence Agents

Artificial Intelligence (AI) technologies could be broadly categorised into Analytics and Autonomy. Analytics focuses on algorithms offering perception, comprehension, and projection of knowledge gleaned from sensorial data. Autonomy revolves around decision making, and influencing and shaping the environment through action production. A smart autonomous system (SAS) combines analytics and autonomy to understand, learn, decide and act autonomously. To be useful, SAS must be trusted and that requires testing. Lifelong learning of a SAS compounds the testing process. In the remote chance that it is possible to fully test and certify the system pre-release, which is theoretically an undecidable problem, it is near impossible to predict the future behaviours that these systems, alone or collectively, will exhibit. While it may be feasible to severely restrict such systems\textquoteright \ learning abilities to limit the potential unpredictability of their behaviours, an undesirable consequence may be severely limiting their utility. In this paper, we propose the architecture for a watchdog AI (WAI) agent dedicated to lifelong functional testing of SAS. We further propose system specifications including a level of abstraction whereby humans shepherd a swarm of WAI agents to oversee an ecosystem made of humans and SAS. The discussion extends to the challenges, pros, and cons of the proposed concept.

cs.AI↗
arXiv2015

Equivariant Alexandrov geometry and orbifold finiteness

Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivariant Gromov--Hausdorff topology, then the limit space is equivariantly homeomorphic to spaces in the tail of the sequence. As a consequence, the class of Riemannian orbifolds of dimension $n$ defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is finite up to orbifold homeomorphism.

math.DG↗
arXiv2015

Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by Lie homomorphisms. Additional lower bounds on curvature and volume strengthen this result to convergence by monomorphisms, so that symmetries can only increase on passing to the limit.

math.MG↗
arXiv2014

G-actions with close orbit spaces

The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit spaces is "close" to a limit orbit space, in some suitable sense, within a larger ambient orbit space, the G-spaces in the tail of the sequence are strongly equivalent to the limit G-space.

math.GN↗