arXiv preprints from January 1, 2026 through September 23, 2026 — 17:21:31 EST
The Fueter-Sce theorem is one of the most important results in hypercomplex analysis, providing a two-step procedure for constructing axially monogenic functions starting from holomorphic functions of one variable. In the first step, the so-called slice operator is applied to holomorphic functions of one variable, producing the class...
We study diffusion-controlled growth of a spherical droplet with a moving boundary using a physics-informed neural network (PINN) formulation. The governing diffusion equation is coupled to the interfacial mass balance, with the droplet radius treated as an additional trainable function of time. The PINN accurately reproduces the...
We discuss the initial value problem for the Einstein equations in Hitchin's generalised geometry for the case of closed divergence (which correspond to the equations of motion in the bosonic part of the NS-NS sector in type II ten-dimensional supergravity) and establish the existence of a maximal globally hyperbolic development...
This work investigates the optical properties of a static, spherically symmetric, electrically charged black hole in f(R) gravity coupled to Euler-Heisenberg(EH) nonlinear electrodynamics(NLED). By analyzing photon trajectories in this background spacetime, we show how the model parameters affect light propagation, leading to wider...
Deep Research (DR) Agents powered by advanced Large Language Models (LLMs) have fundamentally shifted the paradigm for completing complex research tasks. Yet, a comprehensive and live evaluation of their forecasting performance on real-world, research-oriented tasks in high-stakes domains (e.g., finance) remains underexplored. We...
Retrieval-Augmented Generation (RAG) helps LLMs stay accurate, but feeding long documents into a prompt makes the model slow and expensive. This has motivated context compression, ranging from token pruning and summarization to embedding-based compression. While researchers have tried ''compressing'' these documents into smaller...
The Taub-NUT and Eguchi-Hanson gravitational instantons, along with the self-dual Plebanski-Demianski metric, form a set of Euclidean metrics which can naturally be called `self-dual black holes', as they arise from self-dual slices of the most general vacuum, asymptotically flat black hole metric. These self-dual black holes are of...
Quantum generative modeling is a very active area of research in looking for practical advantage in data analysis. Quantum generative adversarial networks (QGANs) are leading candidates for quantum generative modeling and have been applied to diverse areas, from high-energy physics to image generation. The latent style-based QGAN,...
In this paper, we present a patch-based representation of surfaces, PolyFit, which is obtained by fitting jet functions locally on surface patches. Such a representation can be learned efficiently in a supervised fashion from both analytic functions and real data. Once learned, it can be generalized to various types of surfaces. Using...
The concept of Critical Batch Size, as pioneered by OpenAI, has long served as a foundational principle for large-scale pre-training. However, with the paradigm shift towards the Warmup-Stable-Decay (WSD) learning rate scheduler, we observe that the original theoretical framework and its underlying mechanisms fail to align with new...
Demand forecasting in supply chain management (SCM) is critical for optimizing inventory, reducing waste, and improving customer satisfaction. Conventional approaches frequently neglect external influences like weather, festivities, and equipment breakdowns, resulting in inefficiencies. This research investigates the use of machine...
The temporal evolution of the propagation environment plays a central role in integrated sensing and communication (ISAC) systems. A slow-time evolution manifests as channel aging in communication links, while a fast-time one is associated with non-zero Doppler clutter. Nevertheless, the joint impact of these two phenomena on ISAC...
When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in...
Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the expectation of a convex function. In this paper, we establish rigorous refinements of this inequality...
Greedy Sampling Methods (GSMs) are widely used to construct approximate solutions of Configuration Optimization Problems (COPs), where a loss functional is minimized over finite configurations of points in a compact domain. While effective in practice, deterministic convergence analyses of greedy-type algorithms are often restrictive...
Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect symmetries that might arise in real-world applications. This has motivated the development of...
Retrieval-Augmented Generation (RAG) improves generation quality by incorporating evidence retrieved from large external corpora. However, most existing methods rely on statically selecting top-k passages based on individual relevance, which fails to exploit combinatorial gains among passages and often introduces substantial...
We introduce monomial divisibility diagrams (MDDs), a data structure for monomial ideals that supports insertion of new generators and fast membership tests. MDDs stem from a canonical tree representation by maximally sharing equal subtrees, yielding a directed acyclic graph. We establish basic complexity bounds for membership and...
Let $ (T(t))_{t\geq0} $ be a positive $C_{0}$-semigroup with generator $A$ on a C$^*$-algebra or on the predual of a W$^*$-algebra. Then the growth bound $ω_{0}$ equals $s(A)$. If the spectrum of $A$ is not empty, then $s(A)$, the spectral bound of $A$, is a spectral value.
In this paper, we employ contour integration and residue calculus to derive explicit parity formulas for (cyclotomic) multiple zeta values (MZVs). A key innovation lies in applying double shuffle regularization to the contour integrals, which leads to two distinct regularized parity formulas-one via shuffle and one via stuffle...
This paper investigates the finite-time blow-up phenomena to a quasilinear two-species chemotaxis system with two chemicals \begin{align}\tag{$\star$} \begin{cases} u_t = \nabla \cdot \left(D_1(u) \nabla u\right) - \nabla \cdot \left(u \nabla v\right), & x \in Ω, \ t > 0, 0 = Δv - μ_2 + w, \quad μ_2=\fint_Ωw, & x \in Ω, \ t > 0,...
Realistic, large-scale, and well-labeled cybersecurity datasets are essential for training and evaluating Intrusion Detection Systems (IDS). However, they remain difficult to obtain due to privacy constraints, data sensitivity, and the cost of building controlled collection environments such as testbeds and cyber ranges. This paper...
Brain networks exhibit remarkable structural properties, including high local clustering, short path lengths, and heavy-tailed weight and degree distributions. While these features are thought to enable efficient information processing with minimal wiring costs, the fundamental principles that generate such complex network...
The next generation of Earth observation satellites will seek to deploy intelligent models directly onboard the payload in order to minimize the latency incurred by the transmission and processing chain of the ground segment, for time-critical applications. Designing neural architectures for onboard execution, particularly for...
Recent Large Reasoning Models trained via reinforcement learning exhibit a "natural" alignment with human cognitive costs. However, we show that the prevailing paradigm of reasoning distillation -- training student models to mimic these traces via Supervised Fine-Tuning (SFT) -- fails to transmit this cognitive structure. Testing the...