arXiv preprints from January 1, 2026 through September 15, 2026 — 04:10:17 EST
The application of the standard static Geometric Brownian Motion (GBM) model for cryptocurrency risk management resulted in a systemic failure, evidenced by a 80.67% chance of loss in the 5% value-at-risk benchmark. This study addresses a critical literature gap by comparatively testing three conditional volatility models the...
We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it includes three parts with the first and third part relatively short, and the values in the middle...
Academic Clinical Trial Units frequently face fragmented statistical workflows, leading to duplicated effort, limited collaboration, and inconsistent analytical practices. To address these challenges within an oncology Clinical Trial Unit, we developed grstat, an R package providing a standardised set of tools for routine statistical...
Large Language Models (LLMs) increasingly automate software engineering tasks. While recent studies highlight the accelerated adoption of ``AI as a teammate'' in Open Source Software (OSS), developer interaction patterns remain under-explored. In this work, we investigated project-level guidelines and developers' interactions with...
Aiming at the core problem that it is difficult for a fixed inertia coefficient to balance transient disturbance suppression and long-term stability in complex network synchronization systems, an adaptive inertia control strategy based on variational optimization is proposed. Taking the Kuramoto model with inertia as the research...
Large reasoning models (LRMs) have achieved remarkable success in complex problem-solving, yet they often suffer from computational redundancy or reasoning unfaithfulness. Current methods for shaping LRM behavior typically rely on reinforcement learning or fine-tuning with gold-standard reasoning traces, a paradigm that is both...
Natural disaster monitoring through continuous satellite observation requires processing multi-temporal data under strict operational constraints. This paper addresses flood detection, a critical application for hazard management, by developing an onboard change detection system that operates within the memory and computational limits...
In this article, we investigate the quantitative form of the classical Hardy inequality. In our first result, we prove the following quantitative bound under the assumption that the $\mathbb{M}^N$ is a Riemannian model satisfying the centered isoperimetric inequality: We prove that $$ \|\nabla_g u\|^2_{L^{2}(\mathbb{M}^N)} -...
Large language models (LLMs) are increasingly employed for decision-support across multiple domains. We investigate whether these models display a systematic preferential bias in favor of artificial intelligence (AI) itself. Across three complementary experiments, we find consistent evidence of pro-AI bias. First, we show that LLMs...
Accurate epileptic seizure prediction from electroencephalography (EEG) remains challenging because pre-ictal dynamics may span long time horizons while clinically relevant signatures can be subtle and transient. Many deep learning models face a persistent trade-off between capturing local spatiotemporal patterns and maintaining...
We decompose linear $\mathrm{G}_2$-structure in canonical ways adapted to 3-dimensional subspaces, in terms of certain natural 1-forms and definite triple of 2-forms, and apply the decompositions to the study of $\mathrm{G}_2$-structure with $\mathbb{T}^3$-symmetry. Closed $\mathrm{G}_2$-structures $\varphi$ with an effective...
We investigate Hamiltonian fluid reductions of the one-dimensional Vlasov-Poisson equation. Our approach utilizes the hydrodynamic Poisson bracket framework, which allows us to systematically identify fundamental normal variables derived from the analysis of the Casimir invariants of the resulting Poisson bracket. This framework is...
Wi-Fi gesture recognition based on Channel State Information (CSI) is challenged by high-dimensional noise and resource constraints on edge devices. Prevailing end-to-end models tightly couple feature extraction with classification, overlooking the inherent time-frequency sparsity of CSI and leading to redundancy and poor...
We propose a statistical proxy framework for retrieval-augmented generation (RAG) that formalizes how language models balance internal predictions with retrieved evidence. We derive an optimal query-level gate, analyze hallucination via retrieval discordance, model query-memory mismatch, and validate the framework numerically on...
We present BioNIC, a multi-layer feedforward neural network for emotion classification, inspired by detailed synaptic connectivity graphs from the MICrONs dataset. At a structural level, we incorporate architectural constraints derived from a single cortical column of the mouse Primary Visual Cortex(V1): connectivity imposed via...
Signal Temporal Logic (STL) has been widely adopted as a specification language for specifying desirable behaviors of hybrid systems. By monitoring a given STL specification, we can detect the executions that violate it, which are often referred to as counterexamples. In practice, these counterexamples may arise from different causes...
Large Language Model (LLM) judges exhibit strong reasoning capabilities but are limited to textual content. This leaves current automatic Speech-to-Speech (S2S) evaluation methods reliant on opaque and expensive Audio Language Models (ALMs). In this work, we propose TRACE (Textual Reasoning over Audio Cues for Evaluation), a novel...
We prove an abstract theorem of maximal hypoellipticy showing that in an abstract calculus under some natural assumptions, an operator is maximally hypoelliptic if and only if its principal symbol is left invertible. We then show that our theorem implies various known results in the literature like regularity theorem for elliptic...
On-chip generation of high-purity single photons is essential for scalable photonic quantum technologies. Spontaneous parametric down-conversion (SPDC) is widely used to generate photon pairs for heralded single-photon sources, but intrinsic spectral correlations of the pairs often limit the purity and interference visibility of the...
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion in interaction representation is written as a generalized one-turn twist map. One can imagine...
We estimate the probability that the discrete Gaussian free field on a planar domain with Dirichlet boundary conditions stays positive in the bulk. Improving upon the result by Bolthausen, Deuschel and Giacomin from 2001, we derive the order of the subleading term of this probability when a sequence of discretized scale-ups of given...
This paper presents the flexible RIM Hand, a biomimetic robotic hand that precisely replicates the carpometacarpal (CMC) joints and employs superelastic Nitinol wires throughout its skeletal framework. By modeling the full carpal-to-metacarpal anatomy, the design enables realistic palm deformation through tendon-driven fingers while...
Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex nilpotent Lie algebras of arbitrary dimension via pseudobosonic operators. We involve the...
Probabilistic confidence metrics are increasingly adopted as proxies for reasoning quality in Best-of-N selection, under the assumption that higher confidence reflects higher reasoning fidelity. In this work, we challenge this assumption by investigating whether these metrics truly capture inter-step causal dependencies necessary for...
Principle-based alignment often lacks context sensitivity and completeness. Grounded in Theory of Mind, we propose role conditioning as a compact alternative: social roles (e.g., mother, judge) implicitly encode both values and the cognitive schemas required to apply them. We introduce a training-free pipeline featuring a...