arXiv preprints from January 1, 2026 through September 30, 2026 — 12:28:18 EST
We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite variation process. We first show existence and uniqueness. We then establish comparison and strict...
We show that the $C^*$-algebra of a countable directed graph is singly generated. As a consequence, any $C^*$-algebra generated by a countable family of projections and partial isometries satisfying Cuntz-Krieger relations is singly generated.
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In the Euclidean setting, the original minimization problem is approximated by a family of...
Artificial Intelligence (AI) is a transformative yet double-edged technology that can advance human welfare while also posing risks to humans and society. In response, the Human-Centered Artificial Intelligence (HCAI) approach has emerged as both a design philosophy and a methodological complement to prevailing technology-centered AI...
We quantize the regularity properties of classical graphs that determine spin models for singly-generated Yang-Baxter planar algebras, including the Kauffman polynomial, and construct explicit examples. A source of examples comes from deforming graphs using higher-idempotent splittings of quantum isomorphisms for which we prove that...
This paper is motivated by evaluating the benefits of patients receiving mechanical circulatory support (MCS) devices in end-stage heart failure management inference, in which hypothesis testing for a treatment effect on the risk of recurrent events is challenged in the presence of terminal events. Existing methods based on cumulative...
We present Racka, a lightweight, continually pretrained large language model designed to bridge the resource gap between Hungarian and high-resource languages such as English and German. Racka employs parameter-efficient continual pretraining via Low-Rank Adaptation (LoRA) on a Qwen-3 4B backbone, making the recipe practical on A100...
Hopping transport, characterized by carrier tunneling between localized states, is a key mechanism in disordered materials such as organic semiconductors, perovskites, nitride alloys, and 2D material-based inks. Two main regimes are typically observed: Variable Range Hopping and Nearest Neighbor Hopping, with a transition between them...
For a finite group $G$ and a sufficiently large (but fixed) prime power $q$ coprime to $G$ we obtain asymptotics for the number of regular Galois extensions $L/ \mathbb{F}_q(t)$, with $\mathrm{Gal}(L/\mathbb{F}_q(t)) \cong G$, ramified at a single place of $\mathbb{F}_q(t)$, thus making progress on a positive characteristic analog of...
Tool-augmented Large Language Model (LLM) agents create a new supply-chain surface: Model Context Protocol (MCP) tools are installed like third-party packages, yet their outputs can enter the agent's reasoning context. This enables confused-deputy risks in which attacker-controlled inputs cause otherwise benign tools to exercise...
Label assignment is a critical component in training dense object detectors. State-of-the-art methods typically assign each training sample a positive and a negative weight, optimizing the assignment scheme during training. However, these strategies often assign an insufficient number of positive samples to small objects, leading to a...
The rapid advancements in artificial intelligence have significantly accelerated the adoption of speech recognition technology, leading to its widespread integration across various applications. However, this surge in usage also highlights a critical issue: audio data is highly vulnerable to unauthorized exposure and analysis, posing...
Bayesian model selection commonly relies on Laplace approximation or the Bayesian Information Criterion (BIC), which assume that the effective model dimension equals the number of parameters. Singular learning theory replaces this assumption with the real log canonical threshold (RLCT), an effective dimension that can be strictly...
State Space Models (SSMs) have emerged as a promising alternative to Transformers for long-context sequence modeling, offering linear $O(N)$ computational complexity compared to the Transformer's quadratic $O(N^2)$ scaling. This paper presents a comprehensive benchmarking study comparing the Mamba SSM against the LLaMA Transformer on...
In this article, we consider the family $\mathcal{F}(α)$ defined for $α\in (0, 3]$ by \begin{align*} {\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right) > 1 - \fracα{2} \quad \text{for } z \in \mathbb{D}. \end{align*} Our primary objective is to show that this family possesses significant geometric and analytic properties, including...
In this paper we investigate the maximum size of finite semigroups of rational $n \times n$ matrices, with the goal of shedding more light on their structure. Such semigroups provide a rich generalisation of transition monoids of unambiguous (and, in particular, deterministic) finite automata. While in general such semigroups can be...
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group $S_n$. Using permutations suggested by AlphaEvolve (an evolutionary coding agent developed by Google DeepMind), we were led to an unusual situation in which the agent produced a pattern which performed well for the $n$ tested, and...
Hong Kong's education system is notably multicultural, including local, non-Chinese-speaking, and newly arrived students (NAS) (Mandarine Chinese-speaking). NAS can guess the meaning of vocabulary but cannot speak out, presenting unique challenges for them, particularly language barriers and cultural differences. These challenges...
Composite commits, which entangle multiple unrelated concerns, are prevalent in software development and significantly hinder program comprehension and maintenance. Existing automated untangling methods, particularly state-of-the-art graph clustering-based approaches, are fundamentally limited by two issues. (1) They over-rely on...
Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic collapse of neural extrapolation at scales beyond $10^{16}$ -- caused by standard floating-point...
Imagine a world where beauty and technology move in perfect harmony, revealing tiny masterpieces hidden in the water. This world is Nature, and diatoms are the stars. Masters of assembling complex hierarchical glass structures, these microscopic algae are true technological gems, and their potential is boundless when it comes to...
This paper proposes a low-power and low-noise instrumentation amplifier (IA) tailored for bioimpedance sensing applications. The design originates from a gain-boosted flipped voltage follower (FVF) transconductance (TC) stage and integrates two complementary circuit techniques to improve the noise performance. To achieve an optimal...
Background: While digital access has expanded rapidly in resource-constrained contexts, satisfaction with digital learning platforms varies significantly among students with seemingly equal connectivity. Traditional digital divide frameworks fail to explain these variations. Purpose: This study introduces the "Dependency Divide", a...
We present results from a seven-season (2018-2024) monitoring campaign of the gravitationally lensed quasar system PS J2305+3714 using the 1.5-m Maidanak Telescope in the optical R-band. From these data, the amplitude of possible microlensing variability does not exceed 10 mmag on a 7-yr timescale. Additionally, we measure a time...
Accurate fMRI analysis requires sensitivity to temporal structure across multiple scales, as BOLD signals encode cognitive processes that emerge from fast transient dynamics to slower, large-scale fluctuations. Existing deep learning (DL) approaches to temporal modeling face challenges in jointly capturing these dynamics over long...