arXiv preprints from January 1, 2026 through September 21, 2026 — 10:55:38 EST
It has been observed in numerous experiments, simulations, and various theoretical treatments that the spreading of particles can be modeled by the continuous-time random walk. We consider two well-known cases, i.e., Gaussian displacements and discrete displacements, to compute the position distribution and demonstrate the emergence...
This study investigates the minimal seed for laminar-to-turbulent transition in a supersonic boundary layer at $M=3.0$ and $Re=300$ using adjoint-based nonlinear non-modal analysis. While linear theory identifies oblique waves as the optimal disturbances for transient growth, we demonstrate that nonlinear effects fundamentally alter...
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a \textit{spherical \(t\)-design} if the average value of any polynomial of degree at most \(t\) over \(X_N\)...
Most systems exhibit significant variability in their dynamics, including variations in system parameters and large high-frequency dynamic uncertainties. Traditional uncertainty modelling techniques consolidate all such variations into a single uncertainty block, often yielding overly conservative representations of the true plant...
In this paper we present a conjecture on the construction of generalised elliptic units above number fields with exactly one complex place. These elliptic units obtained as values of multiple elliptic Gamma functions. These form a collection of multivariate meromorphic functions which were studied in the late 1990s and early 2000s in...
Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses. We argue that this is a misleading inductive bias: the optimization-optimal trajectory distribution favors informative gradients, whereas the...
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the efficiency of quantum algorithms based on contour integral representation for eigenvalue...
Understanding how dark matter affects the immediate environment of black holes (BHs) is crucial for interpreting horizon-scale observations. We study rotating BHs surrounded by perfect fluid dark matter (PFDM), exploring their observable features through both analytical and numerical approaches. Using the existence criterion of the...
Can fully agentic AI nowcast stock returns? We deploy a state-of-the-art Large Language Model to evaluate the attractiveness of each Russell 1000 stock daily, starting from April 2025 when AI web interfaces enabled real-time search. Our data contribution is unique along three dimensions. First, the nowcasting framework is completely...
Overlapping calendar invitations force busy professionals to repeatedly decide which meetings to attend, reschedule, or decline. We refer to this preference-driven decision process as calendar conflict resolution. Automating this decision process is crucial yet challenging. Scheduling logistics can drain hours, and human delegation...
Reliable reasoning in Large Language Models (LLMs) is challenged by their propensity for hallucination. While augmenting LLMs with Knowledge Graphs (KGs) improves factual accuracy, existing KG-augmented methods fail to quantify epistemic uncertainty in both the retrieved evidence and LLMs' reasoning. To bridge this gap, we introduce...
A broadband silicon polarization beam splitter (PBS) is proposed and experimentally demonstrated based on Floquet-engineered directional couplers. The total length of the coupling structure is 20 um . By periodically modulating the waveguide width of the directional couplers, the power exchange between the two waveguides for the...
The rapid advancement of quantum computing has led to the development of various quantum libraries, empowering compilation, simulation, and hardware backend interfaces. However, ensuring the correctness of these libraries remains a fundamental challenge due to the lack of mature testing methodologies. The state-of-the-art tools often...
Dynamic graphs have attracted increasing attention due to their ability to model complex and evolving relationships in real-world scenarios. Traditional approaches typically pre-train models using dynamic link prediction and directly apply the resulting node temporal embeddings to specific downstream tasks. However, the significant...
Constrained Reinforcement Learning (CRL) aims to maximize cumulative rewards while satisfying constraints. However, existing CRL algorithms often encounter significant constraint violations during training, limiting their applicability in safety-critical scenarios. In this paper, we identify the underestimation of the cost value...
Box-free model watermarking has gained significant attention in deep neural network (DNN) intellectual property protection due to its model-agnostic nature and its ability to flexibly manage high-entropy image outputs from generative models. Typically operating in a black-box manner, it employs an encoder-decoder framework for...
Existing anomaly detection methods for Wireless Sensor Networks (WSNs) generally suffer from insufficient extraction of spatio-temporal correlation features, reliance on either timedomain or frequencydomain information alone, and high computational overhead. To address these limitations, this paper proposes a topology-enhanced...
A transient (LPA J0108+13) with repeated bursts was detected on the Large Phased Array (LPA) radio telescope at a central frequency of 110.4 MHz in the direction of the radio galaxy 3C 33. The flux density of bursts ranges from tens to hundreds of Jy, and the duration of the bursts is \approx 1^m - 4^m. In daily observations, the...
Extreme weather events are becoming more common, with severe storms, floods, and prolonged precipitation affecting communities worldwide. These shifts in climate patterns pose a direct threat to the insurance industry, which faces growing exposure to weather-related damages. As claims linked to extreme weather rise, insurance...
Compared with IP multicast, Overlay Multicast (OM) offers better compatibility and flexible deployment in heterogeneous, cross-domain networks. However, traditional OM struggles to adapt to dynamic traffic due to unawareness of physical resource states, and existing reinforcement learning methods fail to decouple OM's tightly coupled...
This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error system is shown to achieve any prescribed decay rate by leveraging the Berezin-Li-Yau inequality...
Biological matrices are rich in information related to life processes, serving as invaluable media for assessing an individual's overall physiological status and its dynamic fluctuations, as well as crucial foundations for disease diagnosis. However, the inherent complexity of these matrices, coupled with our incomplete understanding...
Modelling fluid dynamics with machine learning (ML) has advanced rapidly, yet most data driven approaches remain opaque because they rely on complex architectures to capture nonlinear flow behaviour. This lack of interpretability limits the reliability and hinders the understanding of when and why some models succeed or fail. To...
Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary and indicate the presence of at least one defective item in the test, we study the cascaded group...
Preterm infants (born between 28 and 37 weeks of gestation) face elevated risks of neurodevelopmental delays, making early identification crucial for timely intervention. While deep learning-based volumetric segmentation of brain MRI scans offers a promising avenue for assessing neonatal neurodevelopment, achieving accurate...