Searcharxiv⌕ Search

arXiv subjects

Nicholas Young

Publications and source records attributed to Nicholas Young.

5 recordsLinked to original sources
arXiv2026

A Framework for Human-AI Q-Matrix Refinement: A NeuralCDM Evaluation

Q-matrices are a cornerstone of theory-driven assessment and learning analytics, making item demands and students' underlying knowledge components and misconceptions explicit and actionable. However, Q-matrices are typically crafted by experts, making them time-consuming to build, prone to subjectivity, and difficult to validate empirically. We propose a framework for human-AI Q-matrix refinement in which large language models (LLMs) generate candidate Q-matrices using structured, misconception-aware prompting, and NeuralCDM provides an empirical evaluation layer to compare candidates based on how well they explain student response data. We apply the framework to a thermodynamics assessment dataset and benchmark locally deployed LLMs against cloud-served models. Results show that iteratively refined LLM-generated Q-matrices can exceed expert-baseline model fit (AUC 0.780 vs. 0.717), and that locally deployed models achieve comparable performance to cloud APIs, supporting privacy-preserving deployment.

cs.CY↗
arXiv2024

Function theory in the bfd-norm on an elliptical region

Let $E$ be the open region in the complex plane bounded by an ellipse. The B. and F. Delyon norm $\|\cdot\|_{\mathrm{bfd}}$ on the space $\mathrm{Hol}(E)$ of holomorphic functions on $E$ is defined by $$ \|f\|_{\mathrm{bfd}} \stackrel{\rm def}{=} \sup_{T\in \mathcal{F}_{\mathrm {bfd}}(E)}\|f(T)\|, $$ where $\mathcal{F}_{\mathrm {bfd}}(E)$ is the class of operators $T$ such that the closure of the numerical range of $T$ is contained in $E$. The name of the norm recognizes a celebrated theorem of the brothers Delyon, which implies that $\|\cdot\|_{\mathrm{bfd}}$ is equivalent to the supremum norm $\|\cdot\|_\infty$ on $\mathrm{Hol}(E)$. The purpose of this paper is to develop the theory of holomorphic functions of bfd-norm less than or equal to one on $E$. To do so we shall employ a remarkable connection between the bfd norm on $\mathrm{Hol}(E)$ and the supremum norm $\|\cdot\|_\infty$ on the space $\mathrm{H}^\infty(G)$ of bounded holomorphic functions on the symmetrized bidisc, the domain $G$ in $\mathbb{C}^2$ defined by \begin{align*} G & \stackrel{\rm def}{=} \{(z+w,zw): |z|<1, |w|<1\}. \end{align*} It transpires that there exists a holomorphic embedding $\tau:E \to G$ having the property that, for any bounded holomorphic function $f$ on $E$, \[ \|f\|_{\mathrm{bfd}} = \inf\{\|F\|_\infty: F \in {\mathrm H}^\infty(G), F\circ\tau=f\}, \] and moreover, the infimum is attained at some $F \in \mathrm{H}^\infty(G)$. This result allows us to derive, for holomorphic functions of bfd-norm at most one on $E$, analogs of the well-known model and realization formulae for Schur-class functions. We also give a second derivation of these models and realizations, which exploits the Zhukovskii mapping from an annulus onto $E$.

math.CV↗
arXiv2017

Possibilistic Fuzzy Local Information C-Means for Sonar Image Segmentation

Side-look synthetic aperture sonar (SAS) can produce very high quality images of the sea-floor. When viewing this imagery, a human observer can often easily identify various sea-floor textures such as sand ripple, hard-packed sand, sea grass and rock. In this paper, we present the Possibilistic Fuzzy Local Information C-Means (PFLICM) approach to segment SAS imagery into sea-floor regions that exhibit these various natural textures. The proposed PFLICM method incorporates fuzzy and possibilistic clustering methods and leverages (local) spatial information to perform soft segmentation. Results are shown on several SAS scenes and compared to alternative segmentation approaches.

cs.CV↗
arXiv2016

Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc

A set $V$ in a domain $U$ in $\mathbb{C}^n$ has the {\em norm-preserving extension property} if every bounded holomorphic function on $V$ has a holomorphic extension to $U$ with the same supremum norm. We prove that an algebraic subset of the {\em symmetrized bidisc} \[ G := \{(z+w,zw):|z|<1, |w| < 1 \} \] has the norm-preserving extension property if and only if it is either a singleton, $G$ itself, a complex geodesic of $G$, or the union of the set $\{(2z,z^2): |z|<1\}$ and a complex geodesic of degree $1$ in $G$. We also prove that the complex geodesics in $G$ coincide with the nontrivial holomorphic retracts in $G$. Thus, in contrast to the case of the ball or the bidisc, there are sets in $G$ which have the norm-preserving extension property but are not holomorphic retracts of $G$. In the course of the proof we obtain a detailed classification of the complex geodesics in $G$ modulo automorphisms of $G$. We give applications to von Neumann-type inequalities for $\Gamma$-contractions (that is, commuting pairs of operators for which the closure of $G$ is a spectral set) and for symmetric functions of commuting pairs of contractive operators. We find three other domains that contain sets with the norm-preserving extension property which are not retracts: they are the spectral ball of $2\times 2$ matrices, the tetrablock and the pentablock. We also identify the subsets of the bidisc which have the norm-preserving extension property for symmetric functions.

math.CV↗