arXiv subjects

Daniel Thompson

Publications and source records attributed to Daniel Thompson.

17 recordsLinked to original sources

arXiv2025

From Description to Score: Can LLMs Quantify Vulnerabilities?

Manual vulnerability scoring, such as assigning Common Vulnerability Scoring System (CVSS) scores, is a resource-intensive process that is often influenced by subjective interpretation. This study investigates the potential of general-purpose large language models (LLMs), namely ChatGPT, Llama, Grok, DeepSeek, and Gemini, to automate this process by analyzing over 31{,}000 recent Common Vulnerabilities and Exposures (CVE) entries. The results show that LLMs substantially outperform the baseline on certain metrics (e.g., \textit{Availability Impact}), while offering more modest gains on others (e.g., \textit{Attack Complexity}). Moreover, model performance varies across both LLM families and individual CVSS metrics, with ChatGPT-5 attaining the highest precision. Our analysis reveals that LLMs tend to misclassify many of the same CVEs, and ensemble-based meta-classifiers only marginally improve performance. Further examination shows that CVE descriptions often lack critical context or contain ambiguous phrasing, which contributes to systematic misclassifications. These findings underscore the importance of enhancing vulnerability descriptions and incorporating richer contextual details to support more reliable automated reasoning and alleviate the growing backlog of CVEs awaiting triage.

cs.CR↗

arXiv2025

Quantum-assured magnetic navigation achieves positioning accuracy better than a strategic-grade INS in airborne and ground-based field trials

Modern navigation systems rely critically on GNSS, which in many cases is unavailable or unreliable (e.g. due to jamming or spoofing). For this reason there is great interest in augmenting backup navigation systems such as inertial navigation systems (INS) with additional modalities that reduce positioning error in the absence of reliable GNSS. Magnetic-anomaly navigation is one such approach, providing passive, non-jammable navigation through periodic position fixes obtained by comparing local measurements of Earth's crustal field against known anomaly maps. Despite its potential, existing MagNav efforts have been limited by magnetometer performance and platform noise; solutions addressing these problems have proven either too brittle or impractical for realistic deployment. Here we demonstrate a quantum-assured MagNav solution based on proprietary quantum magnetometers with by a novel denoising and map-matching algorithms. The system fits on fixed-wing drones or in the avionics bay of a commercial airliner. We present trials at altitudes up to 19000 feet, testing onboard and outboard quantum magnetometers comparing against a strategic-grade INS. Our MagNav solution achieves superior performance, delivering up to 46x better positioning error than the velocity-aided INS; the best final positioning accuracy we achieve is 22m or 0.006% of the flight distance. Airborne trials consistently achieve at least 11x advantage over the INS across varying conditions, altitudes, and flight patterns. The system learns model parameters online without special vehicle maneuvers providing robustness to various configuration changes (e.g. changing payload or latitude). Our trials also include the first successful MagNav performed in a ground vehicle using publicly-available anomaly maps, delivering bounded positioning error 7x lower than the INS, with both systems in strapdown configuration.

quant-ph↗

arXiv2024

System and sub-system energy resilience during public safety power shutoffs (PSPS) in California -- An evidence-based argument

This study examines historical relationships between Public Safety Power Shutoffs (PSPS) events enacted by California's investor-owned utilities (IOUs), at the system and sub-system levels, along with other disruptions to macro electricity systems. This study contributes to understanding the balance between system-wide resilience goals, such as wildfire hazard mitigation, and sub-system-level priorities, such as minimizing the frequency and duration of localized disruptions. Focusing on circuit-level data from 2018 to 2023 as a proxy for sub-systems, we evaluate differences in outage frequency, duration, and customer impact across three major IOUs in California. Results highlight a differentiation between 'higher impact' de-energization events, which have occurred less frequently, and circuits impacted frequently but with lower customer or duration impacts. Study outcomes suggest that resilience, from the perspective of PSPS events, may be more temporal, which in this case is driven by infrastructure and planning investments by IOUs. Future work aims to incorporate socio-demographic factors, including urban-rural divide, to identify further opportunities to enhance resilience at the circuit and sub-circuit levels.

econ.GN↗

arXiv2024

Pull-back and push-forward functors for holonomic modules over Cherednik algebras

In this article we continue the study of holonomic modules over sheaves of Cherednik algebras, initiated by the third author in [Tho18]. Under mild assumptions on the parameters, we first develop a theory of b-functions to prove that push-forward along open embeddings preserves holonomicity. This implies that pull-back along closed embeddings also preserves holonomicity. We use these facts to show that both push-forward and pull-back under any melys morphism preserves holonomicity. Since duality preserves holonomicity, we deduce that extraordinary push-forward and extraordinary pull-back also exist for holonomic modules. As a consequence, we give a general classification of irreducible holonomic modules similar to the classification of irreducible holonomic $\mathscr{D}$-modules as minimal extensions of integrable connections on locally closed subsets. Finally, we prove that Ext-groups between holonomic modules are finite-dimensional and explore applications of our work to the classification of aspherical parameters and existence of finite-dimensional modules for sheaves of Cherednik algebras.

math.QA↗

arXiv2021

Division algebras and MRD codes from skew polynomials

Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Using skew polynomials $f\in R$, we construct division algebras and a generalization of maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include a class of codes constructed by Sheekey (in particular, generalized Gabidulin codes), as well as Jha Johnson semifields.

math.RA↗

arXiv2020

Weakly linked embeddings of pairs of complete graphs in $\mathbb{R}^3$

Let $G$ and $H$ be disjoint embeddings of complete graphs $K_m$ and $K_n$ in $\mathbb{R}^3$ such that some cycle in $G$ links a cycle in $H$ with non-zero linking number. We say that $G$ and $H$ are *weakly linked* if the absolute value of the linking number of any cycle in $G$ with a cycle in $H$ is $0$ or $1$. Our main result is an algebraic characterisation of when a pair of disjointly embedded complete graphs is weakly linked. As a step towards this result, we show that if $G$ and $H$ are weakly linked, then each contains either a vertex common to all triangles linking the other or a triangle which shares an edge with all triangles linking the other. All families of weakly linked pairs of complete graphs are then characterised by which of these two cases holds in each complete graph.

math.GT↗

arXiv2020

The norm of a skew polynomial

Let $D$ be a finite-dimensional division algebra over its center and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Under certain assumptions on $\delta$ and $\sigma$, the ring of central quotients $D(t;\sigma,\delta) = \{f/g \,|\, f \in D[t;\sigma,\delta], g \in C(D[t;\sigma,\delta])\}$ of $D[t;\sigma,\delta]$ is a central simple algebra with reduced norm $N$. We calculate the norm $N(f)$ for some skew polynomials $f\in R$ and investigate when and how the reducibility of $N(f)$ reflects the reducibility of $f$.

math.RA↗

arXiv2020

Learning medical triage from clinicians using Deep Q-Learning

Medical Triage is of paramount importance to healthcare systems, allowing for the correct orientation of patients and allocation of the necessary resources to treat them adequately. While reliable decision-tree methods exist to triage patients based on their presentation, those trees implicitly require human inference and are not immediately applicable in a fully automated setting. On the other hand, learning triage policies directly from experts may correct for some of the limitations of hard-coded decision-trees. In this work, we present a Deep Reinforcement Learning approach (a variant of DeepQ-Learning) to triage patients using curated clinical vignettes. The dataset, consisting of 1374 clinical vignettes, was created by medical doctors to represent real-life cases. Each vignette is associated with an average of 3.8 expert triage decisions given by medical doctors relying solely on medical history. We show that this approach is on a par with human performance, yielding safe triage decisions in 94% of cases, and matching expert decisions in 85% of cases. The trained agent learns when to stop asking questions, acquires optimized decision policies requiring less evidence than supervised approaches, and adapts to the novelty of a situation by asking for more information. Overall, we demonstrate that a Deep Reinforcement Learning approach can learn effective medical triage policies directly from expert decisions, without requiring expert knowledge engineering. This approach is scalable and can be deployed in healthcare settings or geographical regions with distinct triage specifications, or where trained experts are scarce, to improve decision making in the early stage of care.

cs.AI↗

arXiv2019

Division algebras that generalize Dickson semifields

We generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2s^2$ by doubling central division algebras of degree $s$. Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

math.RA↗

arXiv2019

A generalisation of Dickson's commutative division algebras

Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not restricting us to the classical setup where a cyclic field extension is taken. The latter case yields algebras which are no longer commutative nor associative. Conditions for when the algebras are division algebras are given that canonically generalise the classical ones known up to now. We investigate when we obtain non-isomorphic algebras and compute all the automorphisms, including the structure of the automorphism group in some cases.

math.RA↗

arXiv2018

Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials

Let $(\otimes_{j=1}^nV_j)[0]$ be the zero weight subspace of a tensor product of finite-dimensional irreducible $\frak{sl}_2$-modules. The dynamical elliptic Bethe algebra is a commutative algebra of differential operators acting on $(\otimes_{j=1}^nV_j)[0]$-valued functions on the Cartan subalgebra of $\frak{sl}_2$. The algebra is generated by values of the coefficient $S_2(x)$ of a certain differential operator $D=(d/dx)^2+S_2(x)$, defined to V. Rubtsov, A. Silantyev, D. Talalaev in 2009. We express $S_2(x)$ in terms of the KZB operators introduced by G. Felder and C. Wieszerkowski in 1994. We study the eigenfunctions of the dynamical elliptic Bethe algebra by the Bethe ansatz method. Under certain assumptions we show that such Bethe eigenfunctions are in one-to-one correspondence with ordered pairs of theta-polynomials of certain degree. The correspondence between Bethe eigenfunctions and two-dimensional spaces, generated by the two theta-polynomials, is an analog of the non-dynamical non-elliptic correspondence between the eigenvectors of the $\frak{gl}_2$ Gaudin model and the two-dimensional subspaces of the vector space $\Bbb C[x]$, due to E. Mukhin, V. Tarasov, A. Varchenko. We obtain a counting result for, equivalently, certain solutions of the Bethe ansatz equation, certain fibers of the elliptic Wronski map, or ratios of theta polynomials, whose derivative is of a certain form. We give an asymptotic expansion for Bethe eigenfunctions in a certain limit, and deduce from that that the Weyl involution acting on Bethe eigenfunctions coincides with the action of an analytic involution given by the transposition of theta-polynomials in the associated ordered pair.

math-ph↗

arXiv2016

Holonomic modules over Cherednik algebras, I

The goal of this paper is to generalize several basic results from the theory of $\cal{D}$-modules to the representation theory of rational Cherednik algebras. We relate characterizations of holonomic modules in terms of singular support and Gelfand-Kirillov dimension. We study pullback, pushforward, and dual on the derived category of (holonomic) Cherednik modules for certain classes of maps between varieties. We prove, in the case of generic parameters for the rational Cherednik algebra, that pushforward with respect to an open affine inclusion preserves holonomicity.

math.RT↗

arXiv2016

The image of the KZ functor for Cherednik algebras of varieties with finite group actions

We prove that the KZ functor from a certain category of modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is essentially surjective. Then we begin to use this result to study the analog of category O for Cherednik algebras on Riemann surfaces and on products of elliptic curves. In particular we give conditions on the parameters under which these categories are nonzero.

math.RT↗

arXiv2010

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.

hep-th↗

arXiv2008

A variational principle for topological pressure for certain non-compact sets

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form \[ \{x \in X : \lim_{n \ra \infty} \frac{1}{n} \sum_{i = 0}^{n-1} \varphi (f^i (x)) = \alpha \}. \] Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non-uniformly expanding interval maps.

math.DS↗

arXiv2008

The Irregular Set for Maps with the Specification Property has Full Topological Pressure

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $φ: X \mapsto \IR$ a continuous function. We consider the set of points for which the Birkhoff average of $φ$ does not exist (which we call the irregular set for $φ$) and show that this set is either empty or carries full topological pressure (in the sense of Pesin and Pitskel). We formulate various equivalent natural conditions on $φ$ that completely describe when the latter situation holds and give examples of interesting systems to which our results apply but were not previously known. As an application, we show that for a suspension flow over a continuous map with specification, the irregular set carries full topological entropy.

math.DS↗

arXiv2008

A Thermodynamic Definition of Topological Pressure for Non-Compact Sets

We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an equilibrium state. We study the properties of this new quantity and compare it with existing notions of topological pressure. We are particularly interested in the situation when the ambient metric space is assumed to be compact. We motivate the naturality of our definition by applying it to some interesting examples, including the level sets of the pointwise Lyapunov exponent for the Manneville-Pomeau family of maps.

math.DS↗