arXiv preprints from January 1, 2026 through September 17, 2026 — 04:22:17 EST
We investigate the Keller--Segel--(Navier--)Stokes system posed in a smooth bounded domain \(Ω\subset \mathbb{R}^N\) with \(N = 2,3\): \begin{equation*} \begin{cases} n_t + u \cdot \nabla n = Δn - \nabla \cdot \big( n S(n)\nabla c \big), \\[2mm] u \cdot \nabla c = Δc - c + n, \\[2mm] u_t + κ(u \cdot \nabla) u = Δu - \nabla P + n...
In this paper, we consider the following logarithmic Schrödinger equation \[ -Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}. \] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R)\), \(V\) is bounded away from zero, and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative variational approach to overcome the...
Predicting problem-difficulty in large language models (LLMs) refers to estimating how difficult a task is according to the model itself, typically by training linear probes on its internal representations. In this work, we study the multilingual geometry of problem-difficulty in LLMs by training linear probes using the AMC subset of...
The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are...
One of the central challenges in visual place recognition (VPR) is learning a robust global representation that remains discriminative under large viewpoint changes, illumination variations, and severe domain shifts. While visual foundation models (VFMs) provide strong local features, most existing methods rely on a single model,...
We report the discovery of multiple compact molecular features exhibiting extremely broad velocity widths toward the W44 molecular cloud. ALMA CO $J$=3--2 data reveal eight ``Petit--Bullets'' surrounding the previously known ``Bullet.'' Each Petit--Bullet shows a distinct V-shaped structure in position--velocity space, reminiscent of...
The article focuses on the differences in mathematics performance between girls and boys visible from the first four months of compulsory schooling in the French education system. The influence of gender stereotypes in the evaluation practices of teachers and the threat of the gender stereotype on student performance are questioned....
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these methods have shown their efficiency, the first part of the strategy often involves heavy...
Long contexts challenge transformers: attention scores dilute across thousands of tokens, critical information is often lost in the middle, and models struggle to adapt to novel patterns at inference time. Recent work on test-time adaptation addresses this by maintaining a form of working memory -- transient parameters updated on the...
We solve the two-electron problem on a square lattice with d-wave altermagnetism, considering both on-site and nearest-neighbor attractive interactions. The altermagnetic spin-splitting in the single-particle dispersion naturally gives rise to a ground state of two-electron bound pairs with nonzero center-of-mass momentum. The...
Retrieval-Augmented Generation enhances Large Language Models by integrating external knowledge, which reduces hallucinations but increases prompt length. This increase leads to higher computational costs and longer Time to First Token (TTFT). To mitigate this issue, existing solutions aim to reuse the preprocessed KV cache of each...
Temporal Graph Clustering (TGC) is a new task with little attention, focusing on node clustering in temporal graphs. Compared with existing static graph clustering, it can find the balance between time requirement and space requirement (Time-Space Balance) through the interaction sequence-based batch-processing pattern. However, there...
This document provides an assessment of the overall structure of the BNEUF system and how it operates within the framework of the Initiative for Digital Development in French speaking Universities (IDNEUF). This report aims to support the AUF's new strategy for 2021-2025, with its new structural and governance foundations for the...
Diffusion-based planners have emerged as a promising approach for human-like trajectory generation in autonomous driving. Recent works incorporate reinforcement fine-tuning to enhance the robustness of diffusion planners through reward-oriented optimization in a generation-evaluation loop. However, they struggle to generate...
The continuous-review (s,S) inventory model is a cornerstone of stochastic inventory theory, yet its analysis becomes analytically intractable when dealing with non-Markovian systems. In such systems, evaluating long-run performance measures typically relies on costly simulation. This paper proposes a supervised learning framework...
Motivated by the recent progress in the moiré superlattice systems and spin-1/2 triangular lattice antiferromagnets, we revisit the triangular-lattice spin liquids and study their magnetic responses. While the magnetic responses on the ordered phases can be mundane, the orbital magnetic flux and the Zeeman coupling have synergetic...
A bi-Cayley graph over a cyclic group $\mathbb{Z}_n$ is called a bicirculant graph. Let $Γ=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=R^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $T=T^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $S\subseteq \mathbb{Z}_n$. In this paper, using Chebyshev polynomials, we obtain a...
We study bi-Lipschitz right-equivalence of holomorphic function germs $f:(\mathbb{C}^2,0)\to(\mathbb{C},0)$ via polar arcs and gradient canyons. For a polar arc $γ$ we consider the Newton polygon of $f_x(X+γ(Y),Y)$ and define its augmentation by adjoining the point $(0,\operatorname{ord} f(γ(y),y)-1)$. We prove that the resulting...
These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a...
The proliferation of sophisticated generative AI models has significantly escalated the threat of synthetic manipulations in identity documents, particularly through face swapping and text inpainting attacks. This paper presents TwoHead-SwinFPN, a unified deep learning architecture that simultaneously performs binary classification...
Diffusion Policy has dominated action generation due to its strong capabilities for modeling multi-modal action distributions, but its multi-step denoising processes make it impractical for real-time visuomotor control. Existing caching-based acceleration methods typically rely on $\textit{static}$ schedules that fail to adapt to the...
In this paper, we present a remarkably simple expression for the exact solution to the $D = 5$, $\mathcal{N} = 2$ supergravity coupled to three vector multiplets with the prepotential $\mathcal{V} = STU -W^2U \equiv 1$, which represents a five-dimensional static Kaluza-Klein black hole with squashed $S^3$ horizons and four independent...
Test time adaptation (TTA) has emerged as a promising solution to adapt pre-trained models to new, unseen data distributions using unlabeled target domain data. However, most TTA methods are designed for independent data, often overlooking the time series data and rarely addressing forecasting tasks. This paper presents AdaNODEs, an...
Halide perovskites have emerged as promising materials for next-generation photovoltaics, laser sources and X-ray detectors. There is intense debate as to whether some photoactive halide perovskites exhibit ferroelectric behaviour and whether it might be possible to utilise the bulk photovoltaic effect to enhance the performance of...
Quantum dot-superconductor hybrids have been established as a suitable platform for realizing Kitaev chains hosting Majorana bound states. Implementing these structures in a qubit architecture is expected to result in coherence times that scale exponentially with the lengths of the chains. To scale to longer systems, the phase...