arXiv preprints from January 1, 2026 through September 23, 2026 — 02:47:43 EST
The emergence of artificial intelligence (AI) accelerators like NVIDIA Tensor Cores offers new opportunities to speed up tensor-heavy scientific computations. However, applying them to quantum chemistry is challenging due to strict accuracy demands and irregular data patterns. We propose an adaptive precision algorithm to accelerate...
Vigoureux suggests replacing the usual linear superposition rule of quantum mechanics with a M"obius-type "composition law" $\oplus$, motivated by (i) bounded-domain composition laws in special relativity, (ii) familiar transfer-matrix formulas in multilayer optics, and (iii) an analogy with the inclusion-exclusion rule for classical...
Lithium-ion batteries (LIBs) are the leading technology used in consumer electronics, electric vehicles, and grid-level electrochemical energy storage applications. The ever-increasing use of LIBs has highlighted a gap in understanding of their behavior throughout their life cycle. Current monitoring systems rely on electrical and...
This paper introduces and investigates the structure of $δ$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $δ$. The authors define $δ$-Lie algebras, $δ$-Lie dialgebras, and $δ$-Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore,...
The impossibility of a transposable 12 semitone tuning of the octave arises from the mathematical fact that $2 \times 2^{7/12} \neq 3$ i.e., the second harmonic of the fifth can not exactly match the third harmonic of the fundamental. This in turn, stems from the whole number harmonic structure of western music, and the subsequent...
For a (possibly partial) Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ as well as a query complexity measure $M$ which maps Boolean functions to real numbers, define the composition limit of $M$ on $f$ by $M^*(f)=\lim_{k\to\infty} M(f^k)^{1/k}$. We study the composition limits of general measures in query complexity. We show this...
We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative non-integrable model. For these two systems, the normal-form transformation yields an interaction...
In this short paper, we advocate for the idea that continuation-based intermediate languages correspond to intermediate logics. The goal of intermediate languages is to serve as a basis for compiler intermediate representations, allowing to represent expressive program transformations for optimisation and compilation, while preserving...
Negative constraints (instructions of the form "do not use word X") represent a fundamental test of instruction-following capability in large language models. Despite their apparent simplicity, these constraints fail with striking regularity, and the conditions governing failure have remained poorly understood. This paper presents the...
In many applications, it becomes necessary for a set of distributed network nodes to agree on a common value or opinion as quickly as possible and with minimal communication overhead. The classical 2-choices rule is a well-known distributed algorithm designed to achieve this goal. Under this rule, each node in a network updates its...
Understanding the energetic efficiency of quantum computers is essential for assessing their scalability and for determining whether quantum technologies can outperform classical computation beyond runtime alone. In this work, we analyze the energy required to solve the Boson Sampling problem, a paradigmatic task for quantum...
Count-compositional data arise in many different fields, including high-throughput sequencing experiments, ecological surveys, and palaeoclimate studies, where a common, important goal is to understand how covariates relate to the observed compositions. Existing methods often fail to simultaneously address key challenges inherent in...
In this paper we present rigorously and as succintly as possible the theory of elliptic quasi-modular forms by means of moduli spaces and the Gauss-Manin connection, and deal with one of the main historical appearances of quasi-modular forms, which was the seminal case of mirror symmetry treated by Dijkgraaf.
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing backward reachability methods. In this work, we introduce new algorithms that compute both over- and...
Confidence estimation (CE) indicates how reliable the answers of large language models are and impacts user trust and decision-making. Existing evaluations mainly concern the alignment between confidence and correctness, but ignore the variability of language: confidence estimates should remain consistent under semantically equivalent...
Type Ia supernovae, type II supernovae, and asymptotic giant branch (AGB) stars are important sites of stellar nucleosynthesis, but they differ greatly in their rates, their location within a galaxy, and the mean thermal energy and abundance distribution of their ejecta. In earlier papers in this series we have shown that a...
To facilitate the review, evaluation and analysis of scientific literature, the lit-tag R Shiny application provides a convenient interface for users to generate a citation database with custom, user-defined tags and notes. Lit-tag is not subject-specific and is useful for any field of research. Starting with a table of citations...
Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted leaf-labeled phylogenetic networks in a variety of classes, finding that when the number of...
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is trained to autoregressively predict successive elements in human-generated text. We prove that...
We study stem-terminally differentiated (TD) lineages in small niches where demographic noise from discrete division and death events is non-negligible. Starting from a mechanistic five-channel, density-dependent CTMC (symmetric self-renewal, symmetric differentiation, asymmetric division, dedifferentiation, TD death), we derive its...
Non-orthogonal multiple access (NOMA) is a promising technique for optical wireless communication (OWC), enabling multiple users to share the optical spectrum simultaneously through the power domain. However, imperfect channel state information (CSI) and residual decoding errors deteriorate NOMA performance, especially in realistic...
High-resolution imaging of magnetic nanostructures is essential for understanding fundamental spin phenomena and designing advanced devices. Recent developments in three-dimensional (3D) nanomagnetism have highlighted the growing need for imaging techniques that can capture magnetic structures across curved or tilted surfaces with...
Chain-of-Thought (CoT) prompting has improved the reasoning performance of large language models (LLMs), but it remains unclear why it works and whether it is the unique mechanism for triggering reasoning in large language models. In this work, we study this question by directly analyzing and intervening on the internal...
The Hanano Puzzle is a one-player game with irreversible gravity, where the goal is to make colored blocks make contact with flowers of the corresponding color. The game Jelly no Puzzle shares similar mechanics. In general, determining if a given level of each of the two games is solvable is PSPACE-complete. There are also known...
Animal behavior reflects interactions between the nervous system, body, and environment. Therefore, biomechanics and environmental context must be considered to understand algorithms for behavioral control. Computational models that embed artificial neural controllers within body models in simulated environments, are a powerful tool...