arXiv preprints from January 1, 2026 through September 25, 2026 — 09:57:45 EST
Let $F$ be a $k\times \ell$ (0,1)-matrix. A matrix is simple if it is a (0,1)-matrix with no repeated columns. A (0,1)-matrix $A$ is said to have a $F$ as a configuration if there is a submatrix of $A$ which is a row and column permutation of $F$. In the language of sets, a configuration is a trace. Let $\mathrm{Avoid}(m,F)$ be all...
The widespread deployment of 5G networks, together with the coexistence of 4G/LTE networks, provides mobile devices a diverse set of candidate cells to connect to. However, associating mobile devices to cells to maximize overall network performance, a.k.a. cell (re)selection, remains a key challenge for mobile operators. Today, cell...
Aluminum (Al) remains the central material for superconducting qubits, and considerable effort has been devoted to optimizing its deposition and patterning for quantum devices. However, post-processing strategies focused on oxide removal of niobium (Nb) and tantalum (Ta) -based resonators using buffered oxide etch (BOE), which can not...
A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the literature. In this note, it is argued that the most natural paradefinite logic relative to...
We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as Gödel's $G_3$, a superintuitionistic logic of importance in logic programming. Our method adapts a recent interpolation technique that operates on classically encoded logic...
We study the total variation distance under two information-erasing maps on inhomogeneous Bernoulli product measures: summation and homogenization. While summation is a Markov kernel and hence satisfies the usual data processing inequality, homogenization -- which maps each Bernoulli parameter to the cumulative mean -- is not....
We study pattern densities in binary sequences, finding optimal limit sequences with fixed pattern densities.
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse scattering transform, Hamiltonian methods in soliton theory and Lie point symmetries. No knowledge...
We work in the context of a complete totally transcendental theory $T = T^{eq}$. We consider the prime model $M_{A}$ over a set $A$. For intermediate sets $B$ with $A\subseteq B \subseteq M_{A}$ which are normal ($Aut(M_{A}/A)$-invariant) and ``minimal" we give a full Galois correspondence between intermediate definably closed sets...
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth order combined sparse grid solution. In the analysis, working in a general dimension, we...
In this paper we propose and investigate a multi-dimensional opinion dynamics model where people are characterised by both opinions and importance weights across these opinions. Opinion changes occur through binary interactions, with a novel coupling mechanism: the change in one topic depends on the weighted similarity across the full...
Large Multimodal Models (LMMs) have demonstrated impressive capabilities in video reasoning via Chain-of-Thought (CoT). However, the robustness of their reasoning chains remains questionable. In this paper, we identify a critical failure mode termed textual inertia, where once a textual hallucination occurs in the thinking process,...
Fast phase logic (FPL) is a novel digital superconductor electronic (SCE) logic family that employs multiple junction types, including switching 0-Josephson junctions (0-JJs), non-switching 0-JJ stacks, and $π$-JJs. FPL enables flexible, automatable cell layouts, faster pulse propagation, reduced bias current via phase-shifting...
Phasor Agents are dynamical systems whose internal state is a Phasor Graph: a weighted graph of coupled Stuart-Landau oscillators. A Stuart-Landau oscillator is a minimal stable "rhythm generator" (the normal form near a Hopf bifurcation); each oscillator is treated as an abstract computational unit (inspired by, but not claiming to...
We tackle a common domain adaptation setting in causal systems. In this setting, the target variable is observed in the source domain but is entirely missing in the target domain. We aim to impute the target variable in the target domain from the remaining observed variables under various shifts. We frame this as learning a compact,...
The transition from secondary to higher education represents a critical point in academic trajectories, particularly in programmes with a strong emphasis on basic sciences. Across different higher education systems, introductory Mathematics and Physics courses consistently concentrate high rates of early failure and attrition, yet...
A unified autoregressive model is a Transformer-based framework that addresses diverse multimodal tasks (e.g., text, image, video) as a single sequence modeling problem under a shared token space. Such models rely on the KV-cache mechanism to reduce attention computation from O(T^2) to O(T); however, KV-cache size grows linearly with...
In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may achieve better energy efficiency and performance, a theoretical characterization of the resource...
In contemporary educational systems, academic performance indicators play a central role in institutional evaluation and in the interpretation of student trajectories. However, under conditions of rapid technological change, the inferential validity of such indicators becomes increasingly fragile. This article examines how, in...
Contact-rich manipulation requires reliable estimation of extrinsic contacts-the interactions between a grasped object and its environment which provide essential contextual information for planning, control, and policy learning. However, existing approaches often rely on restrictive assumptions, such as predefined contact types,...
We present a systematic study of the evolution of low- and intermediate-mass X-ray binaries (L/IMXBs) consisting of a $1.4\,M_{\odot}$ neutron star (NS) and a donor star of mass $1-8\,M_{\odot}$. Using grids of detailed MESA simulations, we show that for donor masses of $2-8\,M_{\odot}$, mass transfer may be dynamically unstable,...
Large-scale neural recording with high spatio-temporal resolution is essential for understanding information processing in brain, yet current neural interfaces fall far short of comprehensively capturing brain activity due to extremely high neuronal density and limited scalability. Although recent advances have miniaturized neural...
The tautological $\mathbb{Q}$-subalgebra $\mathsf{R}^*(\mathcal{A}_g) \subset \mathsf{CH}^*(\mathcal{A}_g)$ of the Chow ring of the moduli space of principally polarized abelian varieties is generated by the Chern classes of the Hodge bundle. There is a canonical $\mathbb{Q}$-linear projection operator $\mathsf{taut}:...
This study presents a comprehensive comparative analysis of custom-built Convolutional Neural Networks (CNNs) against popular pre-trained architectures (ResNet-18 and VGG-16) using both feature extraction and transfer learning approaches. We evaluated these models across five diverse image classification datasets from Bangladesh:...
We introduce a two-parameter framework that refines several classical graph invariants by imposing higher-order constraints along bounded-length geodesics. For integers $k,d\ge1$, a vertex set is called $k,d$-independent if every shortest path of length at most $d$ contains fewer than $k$ vertices of the set, giving rise to...