arXiv preprints from January 1, 2026 through September 23, 2026 — 16:55:59 EST
We propose a definition of the reduction type of a curve over a discretely valued field in terms of the special fibre of an arbitrary regular model. We show that under this definition, the reduction type in terms of the minimal regular model determines and reduction type in terms of the minimal regular normal crossings model and vice...
Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The major efficiency gap now lies in the updating of zigzag representatives. In this paper, we propose efficient algorithms for updating zigzag representatives...
This paper establishes a new characterization of simple closed curves on a closed orientable surface. Let $Γ$ be the fundamental group of a closed orientable surface. We prove that if an element $g\inΓ$ has the same possible images as a given simple closed curve $γ\in Γ$ under epimorphisms from $Γ$ to every finite group, then $g$...
A random sequence sampled from a known continuous distribution is observed with the objective to choose an item with the overall rank one. A rejected item cannot be recalled and is immediately erased from the memory. Under this memory constraint, the choice problem is not amenable to recursive methods of optimal stopping and becomes a...
We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewise smooth and arise from a nonlinear overdetermined elliptic boundary value problem associated with a stream-function formulation. A distinguishing feature...
We study randomly advected incompressible Navier-Stokes equations, where the advecting field is a mean-zero, divergence-free, space-time stationary velocity field with smooth order-one correlations. We introduce a two-parameter family of models in which the advection is accelerated on a fast temporal scale $\varepsilon^2$ and has...
We show that the Erdős-Rogers function $f_{s,s+1}(n)$ satisfies $$f_{s,s+1}(n) = Θ( \sqrt{n \log n} )$$ for every $s \ge 2$. More precisely, we construct a $K_{s+1}$-free graph on $n$ vertices in which every set of at least $C(s)\sqrt{n \log n}$ vertices contains a copy of $K_s$ for some constant $C(s)$, which implies the upper bound....
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics...
It is well-known that combinatorial circuits are modeled mathematically by string diagrams in monoidal categories. Given a gate set $Σ$, the circuits over $Σ$ can be thought of as string diagrams in the free monoidal category generated by $Σ$. In this model, circuit semantics are then given by monoidal functors out of this free...
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...