Tootfinder

Sturmian lattices and Aperiodic tile sets
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
https://arxiv.org/abs/2506.19362 https://arxi…

Sturmian lattices and Aperiodic tile sets
We give aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope and we can produce infinitely many aperiodic tile sets whose underlying scaling constant is a unit of any real quadratic field. There are two key ingredients in our construction. The first one is ``Sturmian lattices'', an interesting grid structure generated by Sturmian words that emerged in an aperiodic monotile called Smith Turtle.The second is the bounded displacement …

Quadratic flatness and Regularity for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature
Mario Santilli, S{\l}awomir Kolasi\'nski
https://arxiv.org/abs/2507.18357

Quadratic flatness and Regularity for Codimension-One Varifolds with Bounded Anisotropic Mean Curvature
Given a uniformly convex norm $ ϕ$ on $ \mathbf{R}^{n+1} $ and a unit-density $ n $-dimensional varifold $ V $ in an open subset of $ \mathbf{R}^{n+1} $ with bounded mean $ ϕ$-curvature, under the hypothesis $$ \textrm{$\mathcal{H}^n \llcorner {\rm spt}\| V \| $ is absolutely continuous with respect to $ \| V \| $},$$ we prove that there exists an open dense $ \mathscr{C}^{1, α}$-regular part in $ {\rm spt} \| V \| $. Moreover we prove that the $ \mathscr{C}…

Finite-Horizon Strategy in Infinite-Horizon Linear-Quadratic Discrete-Time Dynamic Games
Shengyuan Huang, Xiaoguang Yang, Yifen Mu, Wenjun Mei
https://arxiv.org/abs/2506.19565

Finite-Horizon Strategy in Infinite-Horizon Linear-Quadratic Discrete-Time Dynamic Games
This paper explores a finite-horizon strategy, ``watching $T$ steps into the future and moving one step now,'' in an $N$-person infinite-horizon discrete-time linear-quadratic dynamic game. The game involves linear input/output/state dynamics and quadratic cost functions with heterogeneous discount factors. For the finite-horizon version, which forms the basis of the infinite-horizon game, we analyze the structure of the coupled generalized discrete Riccati difference equations related to the f…

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Derik T. Boonstra, Rakheon Kim, Dean M. Young
https://arxiv.org/abs/2506.19192

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address this problem, we develo…

Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials
Wen-Hao Bian, Jing Wang
https://arxiv.org/abs/2506.19378

Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials
We systematically investigate how static symmetry-breaking perturbations and dynamic Floquet terms via a polarized light manipulate the topological phase transitions in the two-dimensional quadratic-band-crossing-point (QBCP) materials. The Berry curvature shows distinct behavior in such two situations. It is linearly and quadratically proportional to the product of microstructural parameters $t_{x,z}$ for the former and the latter, respectively. The static perturbation eliminates the QBCP and …

The Asai--Flach Euler system in $p$-adic families
David Loeffler, Arshay Sheth
https://arxiv.org/abs/2506.19673 https://arxiv.org/pdf…

The Asai--Flach Euler system in $p$-adic families
We show that the Euler system for the Asai representation corresponding to a Hilbert modular eigenform over a real quadratic field, constructed by Lei, Loeffler and Zerbes (2018), can be interpolated $p$-adically as the Hilbert modular form varies in a Hida family. This work is used as an important input in recent work of Grossi, Loeffler and Zerbes (2025) on the proof of the Bloch--Kato conjecture in analytic rank zero for the Asai representation.

SADA: Stability-guided Adaptive Diffusion Acceleration
Ting Jiang, Yixiao Wang, Hancheng Ye, Zishan Shao, Jingwei Sun, Jingyang Zhang, Zekai Chen, Jianyi Zhang, Yiran Chen, Hai Li
https://arxiv.org/abs/2507.17135

SADA: Stability-guided Adaptive Diffusion Acceleration
Diffusion models have achieved remarkable success in generative tasks but suffer from high computational costs due to their iterative sampling process and quadratic attention costs. Existing training-free acceleration strategies that reduce per-step computation cost, while effectively reducing sampling time, demonstrate low faithfulness compared to the original baseline. We hypothesize that this fidelity gap arises because (a) different prompts correspond to varying denoising trajectory, and (b…

Optimized auxiliary functions for robust mitigation of finite-size errors in periodic hybrid density functional theory
Stephen Jon Quiton, Juan D. F. Pottecher, Xin Xing, Martin Head-Gordon, Lin Lin
https://arxiv.org/abs/2506.19157

Optimized auxiliary functions for robust mitigation of finite-size errors in periodic hybrid density functional theory
When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. In this work, we first investigate the performance of the SS method in …

Decision-Focused Learning for Neural Network-Constrained Optimization: Application to HVAC Management System
Pietro Favaro, Jean-Fran\c{c}ois Toubeau, Fran\c{c}ois Vall\'ee, Yury Dvorkin
https://arxiv.org/abs/2506.19717

Decision-Focused Learning for Neural Network-Constrained Optimization: Application to HVAC Management System
Heating, Ventilation, and Air Conditioning (HVAC) is a major electricity end-use with a substantial potential for grid services such as demand response. Harnessing this flexibility requires accurate modeling of the thermal dynamics of buildings, which is challenging due to their nonlinear and repetitive behavior (e.g., daily pattern), which reduce the value of historical data. To address this issue, this paper presents an HVAC management system formulated as a Mixed Integer Quadratic Program (M…

Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control
J\'an Boldock\'y, Shahriar Dadras Javan, Martin Gulan, Martin M\"onnigmann, J\'an Drgo\v{n}a
https://arxiv.org/abs/2506.19646

Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an explicit neural policy that maps control parameters to integer- and continuous-valued decision variables. This policy is optimized via stochastic gradient descent by differentiating the quadratic model predictive control objective through the closed-loop fin…