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Fast X-ray transients (FXTs) are brief, luminous bursts of soft X-ray emission whose physical origins remain uncertain. The Einstein Probe (EP) mission has recently enabled prompt discovery of these events, providing opportunities for rapid…

Computational costs often make smoothing procedures prohibitive for high-dimensional data assimilation problems. To address this challenge, we propose a dynamical low-rank approximation (DLRA) methodology for smoothing concerning frameworks…

We introduce and study continued fractions defined by Schneider-like maps over polynomial rings, where the maps are associated with a fixed polynomial of arbitrary degree. In particular, we prove the existence and uniqueness of the…

The study of Target Speaker Extraction (TSE) aims to isolate a desired speaker from overlapping speech mixture given auxiliary cues. Existing systems are typically designed for specific cue types, limiting flexibility when cue availability…

Entity Resolution (ER) is a fundamental problem in data management, playing a critical role in tasks like data cleaning and knowledge graph construction. The existing ER approaches range from traditional rule-based to deep learning…

The capacity region of the $K$-user discrete memoryless broadcast channel is fully characterized when non-signaling (NS) assistance is available to the transmitter and all $K$ receivers. The NS-assisted capacity region is shown to coincide…

We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break…

We propose dynamical low-rank (DLR) type filters for data-assimilation problems based on stochastic differential equations (SDEs). In detail, first we derive a DLRA filter for minimizing jointly the mean and covariance error, as well as a…

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference…

Extracting intrinsic magnetic Hamiltonians directly from magnetometry is challenging due to the high dimensionality of the parameter space and the degeneracy induced by ensemble averaging. Here, we introduce a collection of deep…

LLM-agent systems can solve complex tasks through dynamic self-organization and emergent cooperation. Auditing this process is essential because plausible intermediate or final outputs can conceal incomplete or unsupported work and poorly…

Medical imaging has served as primary proving ground for clinical artificial intelligence (AI), yet a decade of intense research has not translated into proportionate bedside impact. We argue that this gap is not primarily a product of…

Gaussian Process Regression (GPR) is a robust framework for uncertainty quantification, yet its $O(n^3)$ complexity limits its scalability. Low-rank Nystr\"om approximations can reduce this burden to $O(nm^2)$, but their accuracy depends…

Ensemble-averaged models of polydisperse bubbly flows require statistics of the evolving bubble population. Prior quadrature-based moment formulations close bubble pressure with a polytropic relation that omits heat and mass transfer at the…

It is a famous property that a longitude of a classical knot lies in the second commutator subgroup of the knot group. We observe that the same property holds for a longitude of a virtual knot.

We present a comprehensive first-principles investigation of all symmetrically inequivalent low-index surfaces of $\beta$-Ga$_2$O$_3$, examining their structural properties and thermodynamic stability across experimentally relevant growth…

This paper concerns a variational system of nonlinear elliptic equations that generalizes the classical Brezis-Nirenberg problem. In addition to considering vector-valued unknown functions in place of scalar-valued unknown functions, the…

Good action rankings do not make a contrastive critic safe to maximize. These critics increasingly act as value-like objectives for best-of-$K$ selection, planning, and critic-guided generation. Unbounded bilinear scores can let large…

Intent classification is a core component of task-oriented dialogue systems, yet practitioners have limited systematic guidance for selecting deployable open-weight language models under compute, latency, and robustness constraints. We…

Humanity's Last Exam (HLE) is widely used to evaluate frontier language models. HLE organizes its questions into eight subject-domain categories, whose subscores are often interpreted as evidence of distinct capabilities. However, no study…