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Alexander Thomas

Publications and source records attributed to Alexander Thomas.

At least 19 recordsLinked to original sources

Evaluating Large Language Model Performance on International Maritime Dangerous Goods Code Compliance

The transport of dangerous goods by sea is a high-consequence activity governed by the International Maritime Dangerous Goods (IMDG) Code, a complex regulatory framework where errors in classification, packaging, stowage, or segregation can result in fire, explosion, toxic release, or loss of life or vessel. Correct compliance requires accurately interpreting hundreds of pages of interacting provisions, updated on a two-year amendment cycle. Practitioners increasingly use Large Language Models (LLMs) as decision-support tools, yet no systematic evaluation exists of whether they can reliably interpret IMDG requirements for safety-critical use. This paper introduces DGEval, the first benchmark for evaluating LLM knowledge of IMDG Amendment 42-24. Built from expert-written questions on the NCB Hazcheck e-learning platform and structured lookups from the Dangerous Goods List (DGL), it comprises 1,678 questions across multiple-choice, open-ended, DGL lookup, and regulatory identification tasks. We evaluate 13 models from six providers across multiple thinking configurations, including one maritime domain-specific fine-tuned model, and test the effect of web search. Although the best-performing model exceeds the human practitioner baseline on multiple-choice questions, all models are weakest in the operationally safety-critical areas of stowage, segregation, and regulatory recall. These results indicate that LLMs may support compliance tasks, particularly structured DGL lookups with web search, but unreliability in operational areas and regulatory-text recall means human oversight and authoritative source verification remain necessary before deployment in any safety-critical context. DGEval is designed as a safety assurance instrument to be applied continuously as models evolve, not as a settled characterisation of current capability.

cs.AI

Nuancing the unicity of $q$-rationals

We prove unicity of $q$-rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modular symmetry. We prove that there are exactly two deformations which deliver the usual $q$-integers: the original $q$-rationals defined by Morier-Genoud and Ovsienko, and another new one. Although the new family can be obtained by conjugacy from the old one, new positivity properties appear. In addition, this new family provides a direct computation of the Jones polynomial of rational knots.

math.QA

A Multi-Domain Red Teaming Framework for Safety, Robustness, and Fairness Evaluation of Medical Large Language Models

Large language models (LLMs) are increasingly deployed across healthcare, yet existing benchmarks fail to capture model behavior under adversarial or ethically complex conditions common in clinical practice. We developed a multi-domain red teaming framework evaluating eleven contemporary LLMs across 690 clinically grounded scenarios spanning nine domains and over 150 subcategories. Scenarios incorporated adversarial transformations, and responses were assessed using a seven-dimension rubric with LLM-assisted scoring and human-in-the-loop validation. Results revealed substantial performance variance, with mean scores ranging from 0.791 to 0.984. Critically, several high-performing systems produced complete failures in individual safety-critical scenarios, demonstrating that aggregate accuracy masks clinically meaningful risk. The highest-performing systems (X-BAI, GPT-5, Claude Opus 4.1) achieved scores above 0.97 with low variance, while performance varied significantly across domains. Equity-related tasks showed 10-20% error amplification with demographic modifications, and human reviewers identified clinically relevant failures missed by automated evaluation. Our findings demonstrate that performance variance and worst-case failures provide more clinically meaningful reliability indicators than mean accuracy alone, and that hybrid evaluation approaches combining automation with clinician oversight are essential for credible safety assessment.

cs.CL

Plane geometry of $q$-rationals and Springborn Operations

We study the geometry of $q$-rational numbers, introduced by Morier-Genoud and Ovsienko, for positive real $q$. In particular, we construct and analyse the deformed Farey triangulation and the deformed modular surface. We interpret every $q$-rational geometrically as a circle, similar to the famous Ford circles. Further, we define and study new operations on $q$-rationals, the Springborn operations, which can be seen as a quadratic version of the Farey addition. Geometrically, the Springborn operations correspond to taking the homothety centers of a pair of two circles. As an application, we derive a formula for the $q$-deformed midpoint of two Farey neighbors and we consider a new $q$-deformation of Markov numbers.

math.QA

Quantitative phase nano-imaging with a laboratory source

Investigating the structure of matter at the nanoscale non destructively is a key capability enabled by X-ray imaging. One of the most powerful nano-imaging methods is X-ray ptychography, a coherent diffraction imaging technique that has become the go-to method at synchrotron facilities for applications ranging from brain imaging to battery materials. However, the requirements in terms of X-ray beam quality have limited its use to large synchrotron facilities and, to date, only one attempt has been made to translate the technique to a small-scale laboratory. To unleash the power of this technique to the broad user community of laboratory X-ray sources, there are outstanding questions to answer including whether the quantitativeness of the information is preserved in a laboratory despite the drastic decrease in X-ray flux of several orders of magnitude, with respect to synchrotron instruments. In this study not only we demonstrate that the quantitativeness of X-ray ptychography is preserved in a laboratory setting, but we also apply the method to the imaging of a brain tissue phantom. Finally, we describe the current challenges and limitations, and we set the basis for further development and future directions of quantitative nano-imaging with laboratory X-ray sources.

physics.comp-ph

Photon Phase-Space Dynamics in a Plasma Wakefield Accelerator

Frequency up-shifting of laser light in a beam-driven plasma wakefield has the potential to provide high-intensity sources of short wavelength radiation. Simulations have demonstrated that a laser pulse can undergo large frequency shifts, limited only by the drive beam energy, when the plasma density is tailored to match the accelerating phase of the wake to the group velocity of the pulse. Here, we study the dynamical evolution of photons in the phase-space vicinity of the plasma wake-phase matching condition. Numerical calculations using a photon kinetic model are validated by direct comparison with full electromagnetic particle-in-cell simulations. These calculations form the basis of a linear theory of the photon dynamics which reveals several important results, including scalings for the properties of the witness pulse and a self-similar solution for the photon phase-space dynamics. One prediction of the theory is that the pulse can be compressed indefinitely with no lower bound on the duration. This predication suggests that photon acceleration can provide a novel source of sub-femtosecond, short wavelength radiation.

physics.plasm-ph

Circular Isoptics in Flatland

We explore convex shapes $S$ in the Euclidean plane which have the following property: there is a circle $C$ such that the angle between the two tangents from any point of $C$ to $S$ is constant equal to $\alpha$. A dynamical formulation allows to analyze the existence of such shapes. Interestingly, the existence of non-circular shapes depends in a non-trivial way on the angle $\alpha$.

math.MG

Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states

This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the foundational background needed to approach the frontiers of this rapidly evolving field, treating geometric and physical aspects in parallel. After surveying fundamental topics in algebra and geometry, a detailed introduction to higher-rank Teichm\"uller theory is developed, including Fock-Goncharov theory for Hitchin representations, maximal representations and the more recent notion of $\Theta$-positivity. Spectral networks are subsequently introduced, emphasizing their utility in the study of character varieties via the abelianization and non-abelianization maps they define. In parallel, key aspects of four-dimensional gauge dynamics with eight supercharges are explored, including electric-magnetic duality, Seiberg-Witten theory, and class $\mathcal S$ theories. The role of spectral networks as a framework for determining and analyzing BPS spectra in class $\mathcal S$ theories is then examined. The final chapter outlines recent applications of spectral networks across a range of contemporary research areas. This volume is intended for researchers and advanced students in either mathematics or physics who wish to enter the field.

math-ph

Seeing Through the Fog: A Cost-Effectiveness Analysis of Hallucination Detection Systems

This paper presents a comparative analysis of hallucination detection systems for AI, focusing on automatic summarization and question answering tasks for Large Language Models (LLMs). We evaluate different hallucination detection systems using the diagnostic odds ratio (DOR) and cost-effectiveness metrics. Our results indicate that although advanced models can perform better they come at a much higher cost. We also demonstrate how an ideal hallucination detection system needs to maintain performance across different model sizes. Our findings highlight the importance of choosing a detection system aligned with specific application needs and resource constraints. Future research will explore hybrid systems and automated identification of underperforming components to enhance AI reliability and efficiency in detecting and mitigating hallucinations.

cs.CL

Lightweight, Secure and Stateful Serverless Computing with PSL

We present PSL, a lightweight, secure and stateful Function-as-a-Serivce (FaaS) framework for Trusted Execution Environments (TEEs). The framework provides rich programming language support on heterogeneous TEE hardware for statically compiled binaries and/or WebAssembly (WASM) bytecodes, with a familiar Key-Value Store (KVS) interface to secure, performant, network-embedded storage. It achieves near-native execution speeds by utilizing the dynamic memory mapping capabilities of Intel SGX2 to create an in-enclave WASM runtime with Just-In-Time (JIT) compilation. PSL is designed to efficiently operate within an asynchronous environment with a distributed tamper-proof confidential storage system, assuming minority failures. The system exchanges eventually-consistent state updates across nodes while utilizing release-consistent locking mechanisms to enhance transactional capabilities. The execution of PSL is up to 3.7x faster than the state-of-the-art SGX WASM runtime. PSL reaches 95k ops/s with YCSB 100% read workload and 89k ops/s with 50% read/write workload. We demonstrate the scalability and adaptivity of PSL through a case study of secure and distributed training of deep neural networks.

cs.CR

Fock bundles and Hitchin components

We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character varieties of surface groups. Although similar to Higgs bundles, the crucial difference is that no complex structure is fixed on the underlying surface. Fock bundles are the gauge-theoretic realization of higher complex structures. We construct a canonical connection to a Fock bundle equipped with compatible symmetric pairing and hermitian structure. The space of flat Fock bundles maps to the character variety of the split real form. Determining the hermitian structure such that this connection is flat gives a non-linear PDE similar to Hitchin's equation. We explicitly construct solutions for Fock bundles in the Fuchsian locus. Ellipticity of the relevant linear operator provides a map from a neighborhood of the Fuchsian locus in the space of higher complex structures modulo higher diffeomorphisms to a neighborhood of the Fuchsian locus in the Hitchin component.

math.DG

Structure constants for simple Lie algebras from principal $\mathfrak{sl}_2$-triple

For a simple complex Lie algebra $\mathfrak{g}$, fixing a principal $\mathfrak{sl}_2$-triple and highest weight vectors induces a basis of $\mathfrak{g}$ as vector space. For $\mathfrak{sl}_n$, we describe how to compute the Lie bracket in this basis using transvectants. This generalizes a well-known rule for $\mathfrak{sl}_2$ using Poisson brackets and degree 2 monomials in two variables. Our proof method uses a graphical calculus for classical invariant theory. Other Lie algebra types are discussed.

math.RT

Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra

We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and $q$-deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to $q$-deformed M\"obius transformations acting on the hyperbolic plane.

math.QA

SCL: A Secure Concurrency Layer For Paranoid Stateful Lambdas

We propose a federated Function-as-a-Service (FaaS) execution model that provides secure and stateful execution in both Cloud and Edge environments. The FaaS workers, called Paranoid Stateful Lambdas (PSLs), collaborate with one another to perform large parallel computations. We exploit cryptographically hardened and mobile bundles of data, called DataCapsules, to provide persistent state for our PSLs, whose execution is protected using hardware-secured TEEs. To make PSLs easy to program and performant, we build the familiar Key-Value Store interface on top of DataCapsules in a way that allows amortization of cryptographic operations. We demonstrate PSLs functioning in an edge environment running on a group of Intel NUCs with SGXv2. As described, our Secure Concurrency Layer (SCL), provides eventually-consistent semantics over written values using untrusted and unordered multicast. All SCL communication is encrypted, unforgeable, and private. For durability, updates are recorded in replicated DataCapsules, which are append-only cryptographically-hardened blockchain with confidentiality, integrity, and provenance guarantees. Values for inactive keys are stored in a log-structured merge-tree (LSM) in the same DataCapsule. SCL features a variety of communication optimizations, such as an efficient message passing framework that reduces the latency up to 44x from the Intel SGX SDK, and an actor-based cryptographic processing architecture that batches cryptographic operations and increases throughput by 81x.

cs.CR

Cerberus: A Formal Approach to Secure and Efficient Enclave Memory Sharing

Hardware enclaves rely on a disjoint memory model, which maps each physical address to an enclave to achieve strong memory isolation. However, this severely limits the performance and programmability of enclave programs. While some prior work proposes enclave memory sharing, it does not provide a formal model or verification of their designs. This paper presents Cerberus, a formal approach to secure and efficient enclave memory sharing. To reduce the burden of formal verification, we compare different sharing models and choose a simple yet powerful sharing model. Based on the sharing model, Cerberus extends an enclave platform such that enclave memory can be made immutable and shareable across multiple enclaves via additional operations. We use incremental verification starting with an existing formal model called the Trusted Abstract Platform (TAP). Using our extended TAP model, we formally verify that Cerberus does not break or weaken the security guarantees of the enclaves despite allowing memory sharing. More specifically, we prove the Secure Remote Execution (SRE) property on our formal model. Finally, the paper shows the feasibility of Cerberus by implementing it in an existing enclave platform, RISC-V Keystone.

cs.CR

A Gentle Introduction to the Non-Abelian Hodge Correspondence

We aim at giving a pedagogical introduction to the non-abelian Hodge correspondence, a bridge between algebra, geometric structures and complex geometry. The correspondence links representations of a fundamental group, the character variety, to the theory of holomorphic bundles. We focus on motivations, key ideas, links between the concepts and applications. Among others we discuss the Riemann--Hilbert correspondence, Goldman's symplectic structure via the Atiyah--Bott reduction, the Narasimhan--Seshadri theorem, Higgs bundles, harmonic bundles and hyperk\"ahler manifolds.

math.DG

Differential Operators on Surfaces and Rational WKB Method

In this paper, we give a simple and geometric, but formal, description of an open subset of the character variety of surface groups into $\mathrm{SL}_n(\mathbb{C})$. The main ingredient is a modified version of the WKB method, which we call rational WKB method. The geometric interpretation uses higher complex structures introduced by Vladimir Fock and the author. More precisely, the character variety is parametrized by the cotangent bundle of the moduli space of higher complex structures. This generalizes the well-known description of the moduli space of flat $\mathrm{SL}_2(\mathbb{C})$-connections by the cotangent bundle of Teichm\"uller space.

math.DG

Topological quantum field theories from Hecke algebras

We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent polynomial for punctured surfaces. There is a graphical way to compute the invariant using minimal colored graphs. We give explicit formulas in terms of the Schur elements of the Hecke algebra and prove positivity properties for the invariants when the Coxeter group is of classical type, or one of the exceptional types $H_3$, $E_6$ and $E_7$.

math.QA