arXiv preprints from January 1, 2026 through September 24, 2026 — 01:05:05 EST
In this paper, we include some new results for the Lucas calculus. A Lucas-Pantograph type exponential function is introduced. Additionally, we define Lucas-Pantograph type trigonometric functions, and some of their most notable identities are given: parity, sum and difference formulas, Pythagorean identities, double-angle identities,...
Let $k$ be a perfect field with $\mathrm{char}(k)\neq 2,3$, set $K=k(t)$, and let $\mathcal{W}_n^{\min}$ be the moduli stack of minimal elliptic curves over $K$ of Faltings height $n$, constructed via the height-moduli framework of Bejleri-Park-Satriano applied to $\overline{\mathcal{M}}_{1,1}\simeq\mathcal{P}(4,6)$. The Shioda-Tate...
Bouncing cosmologies offer an alternative to inflation by resolving the initial singularity through a contracting phase followed by a bounce into expansion. In many such models, the contracting phase is dominated by a single matter component, typically pressureless dust, which leads to an almost scale-invariant spectrum of scalar...
We propose a CompliantVLA-adaptor that augments the state-of-the-art Vision-Language-Action (VLA) models with vision-language model (VLM)-informed context-aware variable impedance control (VIC) to improve the safety and effectiveness of contact-rich robotic manipulation tasks. Existing VLA systems (e.g., RDT, Pi0.5, OpenVLA-oft)...
Deep learning models, particularly Transformers, are often criticized as "black boxes" and lack interpretability. We propose Prism, a white-box attention-based architecture derived from the principles of Maximizing Coding Rate Reduction ($\text{MCR}^2$). By modeling the attention mechanism as a gradient ascent process on a distinct...
Early detection of malignant skin lesions is critical for improving patient outcomes in aggressive, metastatic skin cancers. This study evaluates a comprehensive system for preliminary skin lesion assessment that combines the clinically established ABCD rule of dermoscopy (analyzing Asymmetry, Borders, Color, and Dermoscopic...
Machine unlearning aims to remove specific knowledge (e.g., copyrighted or private data) from a trained model without full retraining. In practice, models are often quantized (e.g., 4-bit) for deployment, but we find that quantization can catastrophically restore forgotten information [1]. In this paper, we (1) analyze why low-bit...
The practical utility of Speech Emotion Recognition (SER) systems is undermined by their fragility to domain shifts, such as speaker variability, the distinction between acted and naturalistic emotions, and cross-corpus variations. While domain adaptation and fine-tuning are widely studied, they require either source data or labelled...
The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income distributions. In a previous study, we demonstrated that the macroscopic behavior of the model...
We show that quantum information scrambling can enable a generic SWAP gate between collective degrees of freedom in systems without universal local control. Our protocol combines the Hayden-Preskill recovery scheme, associated with the black hole information paradox, with quantum teleportation and runs them in parallel and in opposite...
The global demand for green hydrogen and its derivatives is growing rapidly as a cornerstone for decarbonizing hard-to-abate sectors. Morocco, endowed with abundant solar and wind resources, ambitions to capture up to 4% of the global PtX market by 2030, positioning itself as a strategic partner for Europe's energy transition. Yet,...
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have been successfully generalized and internalized within tangent categories. Over the past decade,...
A world model is an AI system that simulates how an environment evolves under actions, enabling planning through imagined futures rather than reactive perception. Current world models, however, suffer from visual conflation: the mistaken assumption that high-fidelity video generation implies an understanding of physical and causal...
Unmanned aerial vehicles (UAVs) with multi-connectivity (MC) capabilities efficiently and reliably transfer data between terrestrial networks (TNs) and non-terrestrial networks (NTNs). However, optimally sharing and allocating spectrum and power resources to maintain MC while ensuring reliable connectivity and optimal performance...
We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the approach introduced in arXiv:2507.07428 to conically averaged operators, thus including iteration...
Alzheimer's disease (AD), defined as an abnormal buildup of amyloid plaques and tau tangles in the brain can be diagnosed with high accuracy based on protein biomarkers via PET or CSF analysis. However, due to the invasive nature of biomarker collection, most AD diagnoses are made in memory clinics using cognitive tests and evaluation...
Code-mixing and code-switching (CSW) remain challenging phenomena for large language models (LLMs). Despite recent advances in multilingual modeling, LLMs often struggle in mixed-language settings, exhibiting systematic degradation in grammaticality, factuality, and safety behavior. This work provides a comprehensive overview of CSW...
Phasor Measurement Units (PMUs) convert high-speed waveform data into low-speed phasor data, which are fundamental to wide-area monitoring and control in power systems, with oscillation detection and localization among their most prominent applications. However, representing electrical waveform signals with oscillations using PMU...
Large Language Model (LLM)-based question-answering systems offer significant potential for automating customer support and internal knowledge access in small businesses, yet their practical deployment remains challenging due to infrastructure costs, engineering complexity, and security risks, particularly in retrieval-augmented...
The Web is a rich source of structured data in the form of tables, from product catalogs and knowledge bases to scientific datasets. However, the heterogeneity of the structure and semantics of these tables makes it challenging to build a unified method that can effectively leverage the information they contain. Meanwhile, Large...
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted from this polynomial relation and the bijection between permutations involved in the proof of the identity.
We study the frog model on $\mathbb{Z}$ with particle wise discrete Weibull lifetimes. Each particle has an i.i.d. survival parameter $π\in(0,1)$; conditionally on $π=p$, its lifetime $Ξ$ satisfies \[ P(Ξ\ge k\mid π=p)=p^{k^γ},\qquad k\in\mathbb{N}_0,γ>0. \] The law of $π$ has right edge density \[...
The ab-initio thermodynamic properties of simple cubic polonium (α-Po) were studied within the quasi-harmonic approximation (QHA), where both lattice vibrations (phonons) and electronic excitations contributions are included in the Helmholtz free energy. We investigate the influence of spin-orbit coupling (SOC) by comparing the scalar...
A filling pair $(α, β)$ of a surface $S_g$ is a pair of simple closed curves in minimal position such that the complement of $α\cupβ$ in $S_g$ is a disjoint union of topological disks. A filling pair is said to be minimally intersecting if the number of intersections between them, or equivalently, the number of complementary disks, is...
The Fokker-Planck equation models rare events across sciences, but blue{direct solution of the PDE is intractable for classical computers due to } its high-dimensional nature. Classical stochastic methods circumvent this curse-of-dimensionality, and serve as the de facto standard for practicing computational scientists. Quantum...