arXiv preprints from January 1, 2026 through September 12, 2026 — 01:54:12 EST
We prove $L^p\rightarrow L^4$ Fourier adjoint restriction estimates for three-dimensional quadratic surfaces in $\mathbb{R}^5$. These estimates are sharp up to the endpoint, and improve results by Oberlin and Guo--Oh.
We prove that every $n$-vertex simple planar graph with no copy of $C_8$ has at most \[ \frac{69}{25}(n-2) \] edges, for every $n\ge 8$. This improves the best known bound \[ \frac{323}{108}n-6 \qquad \text{for every } n\ge 27. \]
We study the flip dynamics on perfect matchings of graphs, where a flip consists of replacing the edges of a perfect matching along an even cycle with the complementary alternating edges. In particular, we want to bound the minimum length of cycles such that any two perfect matchings are related by flips of such cycles. Given a...
Parking functions correspond with preferences of $n$ cars which enter sequentially to park on a one-way street where (1) each car parks in the first available spot greater than or equal to its preference and (2) all cars successfully park. We generalize parking functions to parking completions: Here, we are given that some cars have...
We provide a proof that the empirical spatial distribution estimator in $\mathbb R^d$ as well as the corresponding plug-in estimator of the spatial depth are uniformly $L^1$-consistent. The consistency rate only depends on the sample size $n$, not on the dimension $d$ or any tuning or regularization parameters. This is a rare...
This paper illustrates the Pick-to-Learn methodology applied to the calibration of a Model Predictive Control policy. While developed around a specific example, the presentation is meant to highlight a methodology of broad applicability. The example concerns an aircraft traveling from an origin point to a destination point in the...
Motivated by the celebrated Lonely Runner Conjecture, we study a variant in which the runners have time-dependent velocities. Let $n \geq 3$ runners start from the same point on the unit circle, where each runner $i\in[n]$ has a locally integrable velocity function $ν_i\in L^1_{\mathrm{loc}}(\mathbb{R}_{>0})$Assume that their...
We establish asymptotic formulas for abelian extensions of global function fields ordered by conductor and subject to prescribed local conditions. Our proof combines harmonic analysis with a theory of frobenian functions over global function fields developed in this paper. We interpret our result via equidistribution on algebraic stacks.
We consider the $hp$-FEM applied to the Helmholtz scattering problem with wavenumber $k$, truncated with a perfectly-matched layer. The scatterer consists of a combination of Dirichlet, Neumann, and penetrable obstacles together with variable coefficients. Provided that the Helmholtz solution operator is polynomially bounded in $k$,...
An $n \times n$ matrix $W$ with exactly $w$ non-zero entries taken from the set of $k^{\rm th}$ complex roots of unity in each row and column satisfying $WW^{\ast} = wI_n$ is a complex generalised weighing matrix $CGW(n,w;k)$. We study such matrices through the centraliser algebras of monomial representations of finite groups. Using...
Let $d \geq 3$, \[ D \subsetneq \{ 0,1,\dots,d-1\}, \qquad |D| \geq 2, \ 0 \in D \] be a finite alphabet, and define the integer Cantor set \begin{align} \mathcal{C} := \mathcal{C}_{D} := \bigcup_{J \geq 0} \Big\{ \sum_{j =0}^J a_j d^j : a_j \in D \Big\}. \end{align} We prove that for any $σ$-finite measure-preserving system,...
Corrosion of Ni-Cr structural alloys in molten fluoride salts is a persistent material degradation problem, yet the atomistic role of grain boundaries in this process remains poorly understood. Here we use reactive molecular dynamics to investigate corrosion of NiCr alloys in molten FLiNaK across four representative grain boundaries...
Quantum LPDC codes provide a substantial reduction in qubit overhead required for fault-tolerant quantum computation compared to surface code, thanks to their high encoding rate. However, operating simultaneously on multiple logical qubits encoded in the same block is more challenging and may slow down logical operations. Prior work...
Surface brightness fluctuations (SBF), the pixel-to-pixel variations in flux that arise from the statistical distribution of stars in galaxy images, provide a powerful tool to measure redshift-independent distances from photometric data alone. This method is particularly important in the era of large imaging surveys, such as those...
In this work, we investigate the prospects for probing primordial non-Gaussianity and associated symmetry of parity through scalar-induced gravitational waves (SIGWs), with third-generation gravitational-wave detectors. We develop a framework that accounts for contributions to the energy density spectrum of GWs arising from the scalar...
Solar energetic particle (SEP) event forecasting often involves integrating heterogeneous observations that differ in cadence, temporal coverage, format, and historical availability, posing challenges for reproducible analysis of data-driven approaches. This paper presents SEP-PRISM Data, a curated multi-source dataset designed for...
We examine $f(R,T)=R+λT^ε$ gravity models by finding the best fit parameters for various values of $ε$. This is accomplished by analyzing data from the cosmic microwave background, baryon acoustic oscillation observations, cosmic chronometer, and Type Ia supernovae introducing correlations and radiation effects to our previous work....
Shallow-water ocean forcing provides strong broadband passive Scholte-wave illumination along a seabed distributed acoustic sensing cable on the Texas Gulf Coast. We exploit this illumination through direct processing of the uncorrelated wavefield, long-duration frequency-wavenumber stacking, and a multi-aperture strategy that...
We study elastic deformations of thin-shell black holes and wormholes in AdS$_3$ gravity. These geometries are sourced by line defects in the dual conformal field theory, and their shape and mass distribution define elastic moduli of the gravitational saddle. We compute the quadratic response of the partition function to these...
The excursion-set formalism provides a key connection between primordial density fluctuations and the abundance of cosmic structures such as dark matter halos and voids, traditionally assuming Gaussian random walks. In this work, we extend this framework to fluctuations whose distribution presents strongly non-Gaussian tails. Such...
Interactions of cosmic rays and other forms of ionizing radiation pose a significant challenge to the reliable operation of state-of-the-art quantum devices and error correction in quantum computing based on superconducting circuits which are typically fabricated on semiconductor substrates. Shielded by 2 km of rock overburden, the...
Strange metals exemplify highly collective quantum many-body systems that call for new means of characterization, and there is considerable potential for quantum information approaches contributing to the cause. We investigate multipartite entanglement across the quantum phase transition of a Kondo lattice model using the quantum...
A central problem in fluid mechanics is the identification of self-similarity, which reveals the underlying scaling behaviour of a flow. Recently, a data-driven framework proposed by Bempedelis et al. (2025 J. Fluid Mech., vol. 1020, A11) has enabled the extraction of single-scale self-similarity from data, without prior knowledge of...
Using the stress-energy tensor response functions obtained in the Anderson-Witting model of kinetic theory with non-zero mass, we verify that these response functions satisfy the required analytic conditions and are fully consistent with the recently derived Kubo formulas in Ref.[1].
In this work we demonstrate that a single transformer-based generative model can capture Standard Model structure spanning five decades of invariant mass, from the sub-GeV regime to the TeV continuum, a range that no single Monte Carlo sample covers. To achieve this we design \textsc{ShellFlow}, a Riemannian conditional flow matching...