arXiv subjects

Paul Jennings

Publications and source records attributed to Paul Jennings.

15 recordsLinked to original sources

arXiv2026

Hyperspherical Trigonometry and Corresponding Elliptic Functions

We develop the basic formulae of hyperspherical trigonometry in multidimensional Euclidean space, using multidimensional vector products, and their conversion to identities for elliptic functions. We show that the basic addition formulae for functions on the 3-sphere embedded in 4-dimensional space lead to addition formulae for elliptic functions, associated with algebraic curves, which have two distinct moduli. We give an application of these formulae to the cases of a multidimensional Euler top, using them to provide a link to the Double Elliptic model.

math-ph↗

arXiv2026

Introducing a Novel Systems Thinking approach inspired by STPA: Road Safety Intervention design case study

According to the latest provisional statistics released by the UK Department for Transport, Great Britain recorded 1,633 road deaths in 2024, representing a slight increase from 2023 and raising concerns about safety progress, which indicates that preventable fatalities remain a challenge. The deployment of advanced mobility systems, even certified and safety-assessed, is not sufficient to deliver improved safety outcomes, and existing road infrastructure is not sufficiently equipped to prevent severe collisions. Successful application of the ``Safe System'' approach demands systems thinking in an integrated and holistic manner, encompassing all aspects of road safety. This paper argues that road safety must be managed as a complex socio-technical system where risk evolves dynamically and must be continuously monitored. To address these safety gaps, we propose a systems thinking approach that identifies factors contributing to fatal outcomes and mitigates them. The framework consists of four steps: 1) List stakeholders who influence road safety, 2) Model the interactions between these stakeholders, 3) List assumptions that might be identified as factors for fatalities, and 4) Monitor these assumptions throughout the system lifecycle. The approach is applied to the United Kingdom (UK) road network to demonstrate feasibility. The study provides actionable guidance and new KPIs categories for stakeholders to implement road safety monitoring and eliminate any unreasonable road safety risks.

physics.soc-ph↗

arXiv2025

Safety Analysis of eVTOL Operations based on STPA

Electric Vertical Take-Off and Landing (eVTOL) aircraft are expected to be quieter and more cost-effective than helicopters, offering major economic and social benefits through improved connectivity. Their adoption will require new ground infrastructure and airspace redesign, introducing risks involving multiple stakeholders (Regulators, eVTOL operators, Air navigation service providers, Vertiport operators, OEMs, Pilots, etc.). To assess these risks for the UK airspace, systems-thinking based System Theoretic Process Analysis (STPA) was conducted. To manage the large number of Unsafe Control Actions (UCAs) and requirements generated due to the complexity of the analysis, a novel extension to STPA for the prioritization of results was applied. 317 UCAs were identified in total out of which 110 high-priority UCAs were analyzed (Step-4), resulting in 377 causal factors and 432 requirements. These were prioritized to produce a targeted list of 124 distinct high-priority requirements, 56 of which were identified as gaps in existing aviation regulations, policies, or procedures.. These highlight opportunities for regulatory updates in areas such as organizational performance, certification processes, training, collision avoidance, energy management, and automation. The findings provide regulators with safety considerations that could shape new or updated regulations, compliance methods, and guidance materials for the safe deployment of eVTOLs.

eess.SY↗

arXiv2025

A Scalable Framework for Safety Assurance of Self-Driving Vehicles based on Assurance 2.0

Assurance 2.0 is a modern framework developed to address the assurance challenges of increasingly complex, adaptive, and autonomous systems. Building on the traditional Claims-Argument-Evidence (CAE) model, it introduces reusable assurance theories and explicit counterarguments (defeaters) to enhance rigor, transparency, and adaptability. It supports continuous, incremental assurance, enabling innovation without compromising safety. However, limitations persist in confidence measurement, residual doubt management, automation support, and the practical handling of defeaters and confirmation bias. This paper presents \textcolor{black}{a set of decomposition frameworks to identify a complete set of safety arguments and measure their corresponding evidence.} Grounded in the Assurance 2.0 paradigm, the framework is instantiated through a structured template and employs a three-tiered decomposition strategy. \textcolor{black}{A case study regarding the application of the decomposition framework in the end-to-end (E2E) AI-based Self-Driving Vehicle (SDV) development is also presented in this paper.} At the top level, the SDV development is divided into three critical phases: Requirements Engineering (RE), Verification and Validation (VnV), and Post-Deployment (PD). Each phase is further decomposed according to its Product Development Lifecycle (PDLC). To ensure comprehensive coverage, each PDLC is analyzed using an adapted 5M1E model (Man, Machine, Method, Material, Measurement, and Environment). Originally developed for manufacturing quality control, the 5M1E model is reinterpreted and contextually mapped to the assurance domain. This enables a multi-dimensional decomposition that supports fine-grained traceability of safety claims, evidence, and potential defeaters.

cs.SE↗

arXiv2025

A Scalable Framework for the Management of STPA Requirements: a Case Study on eVTOL Operations

System-Theoretic Process Analysis (STPA) is a recommended method for analysing complex systems, capable of identifying thousands of safety requirements often missed by traditional techniques such as Failure Mode and Effects Analysis (FMEA) and Fault Tree Analysis (FTA). However, the absence of a structured framework for managing and prioritising these requirements presents challenges, particularly in fast-paced development environments. This paper introduces a scalable framework for prioritising STPA-derived requirements. The framework integrates outputs from each STPA step and incorporates expert evaluations based on four key factors: implementation time, cost, requirement type, and regulatory coverage. To reduce subjectivity, Monte-Carlo Simulation (MCS) is employed to calculate and stabilise requirement rankings. An automation toolchain supports the framework, enabling dynamic mapping of prioritised requirements in a scaling matrix. This visualisation aids decision-making and ensures traceability across development phases. The framework is applicable from early conceptualisation to more advanced stages, enhancing its utility in iterative system development. The framework was validated through a real-world case study focused on Electric Vertical Take-off and Landing (eVTOL) operations, conducted in collaboration with the UK Civil Aviation Authority. The findings contributed directly to CAP3141, a Civil Aviation Publication that identifies systemic operational risks and safety mitigations for regulators, operators, and vertiports. The prioritisation process supported decision-making by helping stakeholders identify and manage high-impact requirements efficiently. This work contributes a practical solution for managing STPA outputs, bridging gaps in requirement prioritisation and supporting safety-critical development in emerging technologies.

cs.SE↗

arXiv2024

ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbation

Text-to-Image (T2I) Diffusion Models (DMs) have shown impressive abilities in generating high-quality images based on simple text descriptions. However, as is common with many Deep Learning (DL) models, DMs are subject to a lack of robustness. While there are attempts to evaluate the robustness of T2I DMs as a binary or worst-case problem, they cannot answer how robust in general the model is whenever an adversarial example (AE) can be found. In this study, we first introduce a probabilistic notion of T2I DMs' robustness; and then establish an efficient framework, ProTIP, to evaluate it with statistical guarantees. The main challenges stem from: i) the high computational cost of the generation process; and ii) determining if a perturbed input is an AE involves comparing two output distributions, which is fundamentally harder compared to other DL tasks like classification where an AE is identified upon misprediction of labels. To tackle the challenges, we employ sequential analysis with efficacy and futility early stopping rules in the statistical testing for identifying AEs, and adaptive concentration inequalities to dynamically determine the "just-right" number of stochastic perturbations whenever the verification target is met. Empirical experiments validate the effectiveness and efficiency of ProTIP over common T2I DMs. Finally, we demonstrate an application of ProTIP to rank commonly used defence methods.

cs.CV↗

arXiv2023

STPA for Learning-Enabled Systems: A Survey and A New Practice

Systems Theoretic Process Analysis (STPA) is a systematic approach for hazard analysis that has been used across many industrial sectors including transportation, energy, and defense. The unstoppable trend of using Machine Learning (ML) in safety-critical systems has led to the pressing need of extending STPA to Learning-Enabled Systems (LESs). Although works have been carried out on various example LESs, without a systematic review, it is unclear how effective and generalisable the extended STPA methods are, and whether further improvements can be made. To this end, we present a systematic survey of 31 papers, summarising them from five perspectives (attributes of concern, objects under study, modifications, derivatives and processes being modelled). Furthermore, we identify room for improvement and accordingly introduce DeepSTPA, which enhances STPA from two aspects that are missing from the state-of-the-practice: (i) Control loop structures are explicitly extended to identify hazards from the data-driven development process spanning the ML lifecycle; (ii) Fine-grained functionalities are modelled at the layer-wise levels of ML models to detect root causes. We demonstrate and compare DeepSTPA and STPA through a case study on an autonomous emergency braking system.

cs.SE↗

arXiv2023

Domain Knowledge Distillation from Large Language Model: An Empirical Study in the Autonomous Driving Domain

Engineering knowledge-based (or expert) systems require extensive manual effort and domain knowledge. As Large Language Models (LLMs) are trained using an enormous amount of cross-domain knowledge, it becomes possible to automate such engineering processes. This paper presents an empirical automation and semi-automation framework for domain knowledge distillation using prompt engineering and the LLM ChatGPT. We assess the framework empirically in the autonomous driving domain and present our key observations. In our implementation, we construct the domain knowledge ontology by "chatting" with ChatGPT. The key finding is that while fully automated domain ontology construction is possible, human supervision and early intervention typically improve efficiency and output quality as they lessen the effects of response randomness and the butterfly effect. We, therefore, also develop a web-based distillation assistant enabling supervision and flexible intervention at runtime. We hope our findings and tools could inspire future research toward revolutionizing the engineering of knowledge-based systems across application domains.

cs.CL↗

arXiv2023

Visual Sensor Pose Optimisation Using Visibility Models for Smart Cities

Visual sensor networks are used for monitoring traffic in large cities and are promised to support automated driving in complex road segments. The pose of these sensors, i.e. position and orientation, directly determines the coverage of the driving environment, and the ability to detect and track objects navigating therein. Existing sensor pose optimisation methods either maximise the coverage of ground surfaces, or consider the visibility of target objects (e.g. cars) as binary variables, which fails to represent their degree of visibility. For example, such formulations fail in cluttered environments where multiple objects occlude each other. This paper proposes two novel sensor pose optimisation methods, one based on gradient-ascent and one using integer programming techniques, which maximise the visibility of multiple target objects. Both methods are based on a rendering engine that provides pixel-level visibility information about the target objects, and thus, can cope with occlusions in cluttered environments. The methods are evaluated in a complex driving environment and show improved visibility of target objects when compared to existing methods. Such methods can be used to guide the cost effective deployment of sensor networks in smart cities to improve the safety and efficiency of traffic monitoring systems.

cs.CV↗

arXiv2020

Deep Learning-based Vehicle Behaviour Prediction For Autonomous Driving Applications: A Review

Behaviour prediction function of an autonomous vehicle predicts the future states of the nearby vehicles based on the current and past observations of the surrounding environment. This helps enhance their awareness of the imminent hazards. However, conventional behaviour prediction solutions are applicable in simple driving scenarios that require short prediction horizons. Most recently, deep learning-based approaches have become popular due to their superior performance in more complex environments compared to the conventional approaches. Motivated by this increased popularity, we provide a comprehensive review of the state-of-the-art of deep learning-based approaches for vehicle behaviour prediction in this paper. We firstly give an overview of the generic problem of vehicle behaviour prediction and discuss its challenges, followed by classification and review of the most recent deep learning-based solutions based on three criteria: input representation, output type, and prediction method. The paper also discusses the performance of several well-known solutions, identifies the research gaps in the literature and outlines potential new research directions.

cs.CV↗

arXiv2015

Cabling in the Skyrme-Faddeev model

The Skyrme-Faddeev model is a three-dimensional non-linear field theory that has topological soliton solutions, called hopfions, which are novel string-like solutions taking the form of knots and links. Solutions found thus far take the form of torus knots and links of these, however torus knots form only a small family of known knots. It is an open question whether any non-torus knot hopfions exist. In this paper we present a construction of knotted fields with the form of cable knots to which an energy minimisation scheme can be applied. We find the first known hopfions which do not have the form of torus knots, but instead take the form of cable and hyperbolic knots.

hep-th↗

arXiv2013

Integration of Omics Data and Systems Biology Modeling: Effect of Cyclosporine A on the Nrf2 Pathway in Human Renal Kidneys Cells

In a recent paper, Wilmes et al. demonstrated a qualitative integration of omics data streams to gain a mechanistic understanding of cyclosporine A toxicity. One of their major conclusions was that cyclosporine A strongly activates the nuclear factor (erythroid-derived 2)-like 2 pathway (Nrf2) in renal proximal tubular epithelial cells exposed in vitro. We pursue here the analysis of those data with a quantitative integration of omics data with a differential equation model of the Nrf2 pathway. That was done in two steps: (i) Modeling the in vitro pharmacokinetics of cyclosporine A (exchange between cells, culture medium and vial walls) with a minimal distribution model. (ii) Modeling the time course of omics markers in response to cyclosporine A exposure at the cell level with a coupled PK-systems biology model. Posterior statistical distributions of the parameter values were obtained by Markov chain Monte Carlo sampling. Data were well simulated, and the known in vitro toxic effect EC50 was well matched by model predictions. The integration of in vitro pharmacokinetics and systems biology modeling gives us a quantitative insight into mechanisms of cyclosporine A oxidative-stress induction, and a way to predict such a stress for a variety of exposure conditions.

q-bio.QM↗

arXiv2013

On an elliptic extension of the Kadomtsev-Petviashvili equation

A generalisation of the Lattice Potential Kadomtsev-Petviashvili (LPKP) equation is presented, using the method of Direct Linearisation based on an elliptic Cauchy kernel. This yields a (3+1)-dimensional lattice system with one of the lattice shifts singled out. The integrability of the lattice system is considered, presenting a Lax representation and soliton solutions. An associated continuous system is also derived, yielding a (3+1)-dimensional generalisation of the potential KP equation associated with an elliptic curve.

nlin.SI↗

arXiv2013

Broken planar Skyrmions -- statics and dynamics

The broken planar Skyrme model is a theory that breaks global O(3) symmetry to the dihedral group D_N. It has been shown that the single soliton solution is formed of N constituent parts, named partons, that are topologically confined. The multi-soliton solutions have already been computed for N = 3 and were shown to be related to polyiamonds. We extend this for larger N and demonstrate that this polyform structure continues (planar figures formed by regular N-gons joined along their edges, of which polyiamonds are the N=3 subset). Furthermore, we numerically simulate the dynamics of this model for the first time. It will be demonstrated that the time dependent behaviour of these solutions can be broken down into the interactions of its constituent partons. The results are then compared with those of the standard planar Skyrme model.

hep-th↗

arXiv2013

The dynamics of domain wall Skyrmions

It has recently been shown that Skyrmions with a fixed size can exist in theories without a Skyrme term, providing the Skyrmion is located on a domain wall. Here we numerically compute domain wall Skyrmions of this type, in a (2+1)-dimensional O(3) sigma model with a potential term. Moreover, we investigate Skyrmion dynamics, to study both Skyrmion stability and the scattering of multi-Skyrmions. We demonstrate that scattering events in which both Skyrmions remain on the same domain wall are effectively one-dimensional, and at low speeds are well-approximated by kink scattering in the integrable sine-Gordon model. However, more exotic fully two-dimensional scatterings are also presented, in which Skyrmions that are initially on different domain walls emerge on the same domain wall.

hep-th↗