arXiv preprints from January 1, 2026 through July 28, 2026 — 22:17:23 EST
We investigate Wold-type decompositions and unitary extension problems for multivariable isometric covariant representations associated with product systems of $C^*$-correspondences. First, we establish an operator-theoretic characterization for the existence of a Wold decomposition for the tuple $(σ, T_1, T_2, \ldots, T_n)$, where...
BiD codes, which are a new family of algebraic codes of length $3^m$, achieve the erasure channel capacity under bit-MAP decoding and offer asymptotically larger minimum distance than Reed-Muller (RM) codes. In this paper we propose fast maximum-likelihood (ML) and max-log-MAP decoders for first-order BiD codes. For second-order...
In this letter, we construct an explicit rephasing transformation that converts an arbitrary unitary matrix into the Kobayashi--Maskawa (KM) parameterization and identify all independent CP phases in the mixing matrix as the arguments of its matrix elements. Furthermore, by applying this rephasing transformation to the fermion...
The preparation of quantum states is one of the most fundamental tasks in quantum computing, and a key primitive in many quantum algorithms. Of particular interest to areas such as quantum simulation and linear-system solvers are sparse quantum states, which contain only a small number $s$ of non-zero computational basis states...
In the interstellar medium, cosmic rays (CRs) generate a field of ultraviolet (UV) photons via the excitation and subsequent radiative decay of $\rm H_2$ molecules. This UV field is a major agent of ionization and dissociation in the inner regions of molecular clouds that are shielded from the effects of the interstellar radiation...
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving hypersurface as its thickness tends to zero, we rigorously derive a limit problem by showing the weak...
The recent surge in open-source Multimodal Large Language Models (MLLM) frameworks, such as LLaVA, provides a convenient kickoff for artificial intelligence developers and researchers. However, most of the MLLM frameworks take vision as the main input modality, and provide limited in-depth support for the modality of speech, audio,...
Cell-Free Multiple-Input Multiple-Output (MIMO) and Open Radio Access Network (O-RAN) have been active research topics in the wireless communication community in recent years. As an open-source software implementation of the 3rd Generation Partnership Project (3GPP) 5th Generation (5G) protocol stack, OpenAirInterface (OAI) has become...
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete numerical method that relies on a continuous finite element approach and a semi-implicit...
In data-driven scientific discovery, a challenge lies in classifying well-characterized phenomena while identifying novel anomalies. Current semi-supervised clustering algorithms do not always fully address this duality, often assuming that supervisory signals are globally representative. Consequently, methods often enforce rigid...
The Crack Topology Score (CTS) is a recently proposed metric that focuses on evaluating the topological correctness of crack segmentation outputs. While pixel-wise metrics such as IoU or F1-score fail to capture structural validity, CTS offers a skeleton-based matching framework to measure the preservation of connectivity. This paper...
Current large language model agents predominantly operate under a reactive paradigm, responding only to immediate user queries within short-term sessions. This limitation hinders their ability to maintain long-term user's intents and dynamically adapt to evolving external environments. In this paper, we propose a novel interaction...
In this paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these...
Large-scale LED lighting systems degrade through gradual package degradation and abrupt driver outages, while acceptability is determined by spatio-temporal illuminance compliance rather than component reliability alone. This paper proposes a performance-driven, simulation-in-the-loop framework for opportunistic maintenance...
The role of interface states and dielectric mismatch is studied in ultrathin P-doped silicon-on-insulator (SOI) films with thickness of the device layer ($H_{SOI}$) varying from 30 to 8 nm and dopant concentration ($n_{D}$) ranging from 10$^{18}$ to nearly 10$^{20}$ cm$^{-3}$. P concentration is determined by Time-of-Flight Secondary...
Robotic stacking of van der Waals heterostructures has been at the verge thanks to the convergence between artificial intelligence (AI) and two-dimensional (2D) materials research. Key ingredients to fulfill this pursuit often include algorithms to identify layer compounds on chips, hard-wares to realize sophisticated operations of...
Diffusion models conditioned on identity embeddings enable the generation of synthetic face images that consistently preserve identity across multiple samples. Recent work has shown that introducing an additional negative condition through classifier-free guidance during sampling provides a mechanism to suppress undesired attributes,...
Generating safe and reliable trajectories for autonomous vehicles in long-tail scenarios remains a significant challenge, particularly for high-lateral-acceleration maneuvers such as sharp turns, which represent critical safety situations. Existing trajectory planners exhibit systematic failures in these scenarios due to data...
The autonomous motion of liquid crystal oil droplets in micellar media arises from spontaneous breaking of time reversal symmetry via nonlinear coupling between Marangoni stresses and surfactant transport. While this phenomenon has been widely studied, the influence of micellar solute structure remains unexplored. By modifying...
This paper develops a complete framework for understanding when a dual truncated Toeplitz operator (DTTO) attains its norm. Given a nonconstant inner function $u$, the DTTO associated with a symbol $\varphi \in L^{\infty}(\mathbb{T})$ acts on the orthogonal complement ${\mathcal{K}_u}^{\perp} = uH^{2} \oplus H^{2}_{-}$ of the model...
Parkinson's disease (PD) is a chronic neurodegenerative disease. Early diagnosis is essential to mitigate the progressive deterioration of patients' quality of life. The most characteristic motor symptoms are very mild in the early stages, making diagnosis difficult. Recent studies have shown that the use of patient voice recordings...
In fault-tolerant quantum computing, a large number of physical qubits are required to construct a single logical qubit, and a single quantum node may be able to hold only a small number of logical qubits. In such a case, the idea of distributed fault-tolerant quantum computing (DFTQC) is important to demonstrate large-scale quantum...
Do Large Language Models (LLMs) genuinely grasp the compositional semantics of events, or do they rely on surface-level probabilistic heuristics? We investigate the Imperfective Paradox, a logical phenomenon where the past progressive aspect entails event realization for activities (e.g., running $\to$ ran) but not for accomplishments...
Zero-Knowledge (ZK) proof systems are cryptographic protocols that can (with overwhelming probability) demonstrate that the pair $(X, W)$ is in a relation $R$ without revealing information about the private input $W$. This membership checking is captured by a complex arithmetic circuit: a set of polynomial equations over a finite...
We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the functional quantile autocorrelation framework leverages quantile-based excursion sets to robustly...