arXiv preprints from January 1, 2026 through September 22, 2026 — 11:53:07 EST
We determine the frame set of the first Hermite function, proving a conjecture of Lyubarskii and Nes. We use a characterization of semi-regular Gabor frames due to Gröchenig, Romero, and Stöckler to transform the problem into a question about the existence of a nonzero Gaussian shift-invariant entire function $F$, with bounded...
The yielding transition marks the onset of irreversible plastic deformation in amorphous solids and plays a central role in determining the mechanical stability and failure of metallic glasses, colloidal suspensions, and biological assemblies. Despite extensive research, the microscopic factors governing the nature of yielding,...
The LUX-ZEPLIN (LZ) Collaboration recently reported one event consistent with a $248$ keV nuclear recoil in a $2.84$ tonne-year exposure, with a maximum local significance of $3.4σ$ and a global significance of $2.6σ$. We investigate whether the dark matter (DM)--nucleon interactions favored by this high-energy event can arise from...
This paper investigates the global dynamics of a doubly degenerate nutrient-taxis system with indirect consumption: \begin{equation*} \left\{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\nabla \cdot (u^{2}v\nabla v)+\ell vw,&x\in Ω,\, t>0,\\ & v_{t}=Δv-vw,&x\in Ω,\, t>0,\\ &w_t=Δw-w+u,&x\inΩ,t>0 \end{aligned} \right....
Loneliness is a critical public health issue among older adults, linked to higher risks of depression, cognitive decline, and mortality. Scalable, objective methods for its detection remain limited, particularly in natural conversational contexts. We analyzed speech and language markers of loneliness in 310 older adults using...
The Mini-Girona Intervention Autonomous Underwater Vehicle (I-AUV) represents an advancement in accessible underwater robotics, designed to bridge the gap between costly, specialized research AUVs and basic Remotely Operated Vehicles (ROVs). Developed with a focus on affordability and usability, the Mini-Girona, priced at...
We prove the Lonely Runner Conjecture for fourteen runners by a computer-assisted extension of the finite-checking framework of Sungkawichai and Trakulthongchai. With one runner stationary, their thirteen-runner result supplies the induction input, and their reduction leaves finitely many modular calculations indexed by primes. We...
Transition metal dichalcogenides (TMDs) in their monolayer form offer a premier platform for next-generation optoelectronics, particularly through the local manipulation of their robust excitonic states using nanoscale electric fields. These localized states can be dynamically controlled through spatial structuring as well as through...
We present a systematic study of the transition form factors for the semileptonic decays $D\rightarrow Pe^{+}v_{e}$ and $D\rightarrow Pμ^{+}\bar{v}_μ$ using QCD light-cone sum rules with chiral currents, with emphasis on the nonperturbative structure of the pion. The distribution amplitudes of the meson $π$, including twist-2 and...
The Calderón-Zygmund theory establishes the boundedness of singular integral operators on $L^p$ spaces for $1 < p < \infty$, yet it encounters a failure at the endpoint $p = 1$. While radial counterexamples in $\mathbb{R}^n$ are well-documented, Pan-Shao-Wang-Wu \cite{psww2026} has showed that every nonconstant holomorphic function...
Reliable epidemic monitoring often requires inferring regional infection burden and transmission heterogeneity from noisy, spatially aggregated, and potentially sparse surveillance data. Agent-based models (ABMs) are attractive for this task because they represent individual behavior, contact heterogeneity, and localized...
Predicting transcriptional responses to specific perturbations is critical for understanding cellular regulatory mechanisms and accelerating drug discovery. Single-cell RNA sequencing destroys each measured cell, yielding only unpaired populations of control and perturbed cells. However, existing methods typically model perturbation...
When the rates of ligand binding are measured by methods such as surface plasmon resonance, it is common practice to use the observed rate constants for the onset and offset of binding to estimate an equilibrium constant for ligand binding. If this agrees with the equilibrium constant found as the EC50 for binding at equilibrium, this...
Here we present the Active Visual Semantics (AVS) dataset, a large-scale collection of magnetoencephalography (MEG) and eye-tracking data recorded while five participants freely explored 4,080 natural scenes over 10 sessions each, yielding more than 200,000 fixation epochs in total. Unlike existing neuroimaging datasets that rely on...
Token aggregation converts token-level representations into fixed-dimensional sample representations, but most pooling methods operate only in the original token space. We introduce Frequency-Domain Latent-attention Gated Pooling (FLaG), a plug-in aggregation module that re-expresses encoder outputs in the Fourier domain before final...
Geometric eigenmodes provide a compact and biologically grounded representation of large-scale neural activity. Previous work demonstrated that they can mitigate the underdetermined nature of electroencephalographic (EEG) and magnetoencephalographic (MEG) source localisation, an ill-posed inverse problem in which neural activity is...
Many natural and engineered systems are large complex networks of interacting components, and external perturbations drive them along different dynamical paths. Identifying which perturbation occurred matters for diagnosis, control, and prediction. Yet often times only a few components can be jointly monitored. Which components should...
Single-cell studies are typically initiated from predefined research questions, leaving much of the biological information encoded within existing data unexplored. We formalize open-ended discovery as an analytical paradigm, in which data-derived signals are identified before biological context is interrogated and subsequently...
Like pairwise distances, quartets can be highly redundant and correlated on a phylogenetic tree, and their number grows on the order of n^4 rather than n^2. I explore BME-like weights for reweighting quartet scores before summing them to score a full tree. Three weights are considered on an unrooted binary tree:...
At the water-land interface, amphibious fishes encounter wet flowable substrates made of granular solid-water mixtures, which can stay solid or flow like a fluid. As these substrates become wetter or drier, their yield strength (at which solid-fluid transition occurs) and cohesion (how sticky they are) both change, challenging...
Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are...
The corticothalamic circuit supports rhythms with timescales that differ by orders of magnitude: sleep spindles, the sigma-band events of non-rapid-eye-movement (NREM) sleep, and infra-slow fluctuations near 0.02Hz that organize when spindles occur. Because the anatomy is the same in both cases, architecture alone cannot determine...
Antibody-specific language models pretrained via masked language modeling (MLM) learn representations that are critical for downstream sequence design and property prediction tasks. Yet, the corruption process itself is rarely leveraged as a source of inductive bias during pretraining. While preferentially masking...
We study optimal sampling recovery in reproducing kernel Hilbert spaces (RKHS) in the uniform norm. For every RKHS with bounded kernel, we establish new comparisons between linear sampling widths and Gelfand widths that overcome the known square-root gap, without requiring a measure or a Christoffel-type condition. Our bounds rely on...
Let $X$ be a smooth complex projective variety of dimension $n$, and let $L$ be an ample Cartier divisor. We prove that $K_X+mL$ is globally generated for every integer $m\geq\lceil C_0n\rceil$, where $C_0=1.77629\ldots$ is an explicit constant. In particular, $K_X+2nL$ is globally generated. Our main input is a new estimate for the...