arXiv preprints from January 1, 2026 through September 27, 2026 — 13:59:58 EST
Pebble drift is an important mechanism for supplying the materials needed to build planets in the inner region of protoplanetary disks. Thus, constraining pebble drift's timescales and mass flux is essential to understanding planet formation history. Current pebble drift models suggest pebble fluxes can be constrained from the...
We study relaxation toward statistical equilibrium states of inviscid generalised two-dimensional flows, where the generalised vorticity $q$ is related to the streamfunction $ψ$ via $q=(-\nabla^2)^{\fracα{2}}ψ$, with the parameter $α$ controlling the strength of the nonlinear interactions. The equilibrium solutions exhibit an...
In this paper, we propose a novel information theoretic surrogate loss; normalized conditional mutual information (NCMI); as a drop in alternative to the de facto cross-entropy (CE) for training deep neural network (DNN) based classifiers. We first observe that the model's NCMI is inversely proportional to its accuracy. Building on...
We state and prove the spectral expansion of the theta series attached to the Rankin-Selberg spherical variety $(\mathrm{GL}_{n+1} \times \mathrm{GL}_n)/\mathrm{GL}_n$. This is a key result towards the fine spectral expansion of the Jacquet-Rallis trace formula. Our expansion is written in terms of regularized Rankin--Selberg periods...
Let $(X,ω)$ be a translation surface whose Veech group $Γ$ is a lattice. We prove that the generic orbit of the group of affine homeomorphisms of $(X,ω)$ can be used to approximate each point of $X$ with Diophantine precision. The proof utilizes an induced $SL_2(\mathbb{R})$-action on a fiber bundle $Y$ whose base is...
This article proposes new perspectives for developing derivative based numerical algorithms, supported by the introduction of a generalized derivative operators. It demonstrates that these operators have the potential to enhance and extend existing derivativebased numerical methods. To this end, two iterative derivative driven methods...
We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or reflecting boundary conditions. The hyperbolic formulation avoids the costly inversion of an elliptic operator present in the classical model. Our schemes...
While fluids near a solid surface are at the core of applications in energy storage/conversion, electrochemistry/electrowetting and adsorption/catalysis, their nanoscale behavior remains only partially deciphered. Beyond conventional effects (e.g. adsorption/reaction, interfacial transport, phase transition shifts), recent...
Purpose: Annotation of medical breast images is an essential step toward better diagnostic but a time consuming task. This research aims to focus on different selecting sample strategies within deep active learning on Breast Region Segmentation (BRS) to lessen computational cost of training and effective use of resources. Methods:...
Oblivious load-balancing in networks involves routing traffic from sources to destinations using predetermined routes independent of the traffic, so that the maximum load on any link in the network is minimized. We investigate oblivious load-balancing schemes for a $N\times N$ torus network under sparse traffic where there are at most...
Understanding real-world videos such as movies requires integrating visual and dialogue cues. Yet existing VideoQA benchmarks struggle to capture this multimodal reasoning and, given the difficulty of evaluating free-form answers, largely resort to simple multiple choice questions. We introduce a novel open-ended multimodal VideoQA...
Selecting a single high-quality output from multiple stochastic generations remains a fundamental challenge for large language models (LLMs), particularly in open-ended tasks where no canonical answer exists. While Best-of-N and self-consistency methods show that aggregating multiple generations can improve performance, existing...
Using VLT/MUSE data, we study the ionised-gas kinematics in a mass- and volume-limited ($M_* \geq 10^{10} M_\odot$, $D \leq 20$\,Mpc) sample of 21 nearby galaxies to identify signatures of extended shocks within their inner kiloparsec, which appear as coherent velocity jumps in kinematic maps. By removing angular momentum, shocks in...
The third interstellar object to be discovered, 3I/ATLAS, has a unique and continually unfolding story to tell about its nature and origin as it is monitored by telescopes on Earth, orbiting Earth and around the Solar System. Previous research into missions using chemical propulsion have only really addressed the direct case, where...
We study the parameterized complexity of the Cograph Deletion problem, which asks whether one can delete at most $k$ edges from a graph to make it $P_4$-free. This is a well-known graph modification problem with applications in computation biology and social network analysis. All current parameterized algorithms use a similar...
Cooking recipes are complex procedures that require not only a fluent and factual text, but also accurate timing, temperature, and procedural coherence, as well as the correct composition of ingredients. Standard training procedures are primarily based on cross-entropy and focus solely on fluency. Building on RECIPE-NLG, we...
We present Connection-Aware Motif Sequencing (CamS), a graph-to-sequence representation that enables decoder-only Transformers to learn molecular graphs via standard next-token prediction (NTP). For molecular property prediction, SMILES-based NTP scales well but lacks explicit topology, whereas graph-native masked modeling captures...
We propose a novel finite-sample procedure for testing composite null hypotheses. Traditional likelihood ratio tests based on asymptotic $χ^2$ approximations often exhibit substantial bias in small samples. Our procedure rejects the composite null hypothesis $H_0: θ\in Θ_0$ if the simple null hypothesis $H_0: θ= θ_t$ is rejected for...
We study a quasilinear chemotaxis system of singular type, where the diffusion operator is given by $Δu^m$ with $0<m<1$, corresponding to the fast diffusion regime, and where the chemotactic drift is nonlinear. Since Hölder continuity constitutes the optimal regularity class for weak solutions to the porous medium equation, we...
Astronomical measurements are often integrated over finite exposures, which can obscure latent variability on comparable timescales. Correctly accounting for exposure integration with Gaussian Processes (GPs) in such scenarios is essential but computationally challenging: once exposure times vary or overlap across measurements, the...
This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly infrastructure, and (2) verifying a social science theory using a model with sufficient data. The...
We study the accumulation of zeros of a polynomial arising from the enumeration of edge-coloured graphs along certain limit curves. The polynomial is a variant of an edge-chromatic polynomial, which specialises to the partition function of the ferromagnetic Ising model on a random regular graph. We call this accumulation behaviour a...
By modifying a construction of Abe and Tange, we exhibit arbitrarily large families of Lagrangian slice disks with Weinstein deformation equivalent exteriors. This answers a Lagrangian version of a question of Hitt and Sumners. We raise other open questions related to Lagrangian slice disks and their exteriors.
Artificial intelligence has advanced rapidly through large neural networks trained on massive datasets using thousands of GPUs or TPUs. Such training can occupy entire data centers for weeks and requires enormous computational and energy resources. Yet the optimization algorithms behind these runs have not kept pace. Most large scale...
We formalise recursive self-training in Large Language Models (LLMs) and Generative AI as a discrete-time dynamical system. We prove that if the proportion of exogenous, externally grounded signal $α_t$ vanishes asymptotically ($α_t \to 0$), the system undergoes degenerative dynamics. We derive two fundamental failure modes: (1)...