Tootfinder

A Practical and Secure Byzantine Robust Aggregator
De Zhang Lee, Aashish Kolluri, Prateek Saxena, Ee-Chien Chang
https://arxiv.org/abs/2506.23183 https://

A Practical and Secure Byzantine Robust Aggregator
In machine learning security, one is often faced with the problem of removing outliers from a given set of high-dimensional vectors when computing their average. For example, many variants of data poisoning attacks produce gradient vectors during training that are outliers in the distribution of clean gradients, which bias the computed average used to derive the ML model. Filtering them out before averaging serves as a generic defense strategy. Byzantine robust aggregation is an algorithmic pri…

An Improved Inference for IV Regressions
Liyu Dou, Pengjin Min, Wenjie Wang, Yichong Zhang
https://arxiv.org/abs/2506.23816 https://a…

An Improved Inference for IV Regressions
Researchers often report empirical results that are based on low-dimensional IVs, such as the shift-share IV, together with many IVs. Could we combine these results in an efficient way and take advantage of the information from both sides? In this paper, we propose a combination inference procedure to solve the problem. Specifically, we consider a linear combination of three test statistics: a standard cluster-robust Wald statistic based on the low-dimensional IVs, a leave-one-cluster-out Lagra…

The spectral torsion for the one form rescaled Dirac operator
Jian Wang, Yong Wang
https://arxiv.org/abs/2505.23319 https://arxiv.org…

The spectral torsion for the one form rescaled Dirac operator
The spectral torsion is defined by three vector fields and Dirac operators and the noncommutative residue. Motivated by the spectral torsion and the one form rescaled Dirac operator, we give some new spectral torsion which is the extension of spectral torsion for Dirac operators, and compute the spectral torsion for the one form rescaled Dirac operator on even-dimensional spin manifolds without boundary.

A Dilation-based Seamless Multiscale Method For Elliptic Problems
Ziheng Chen, Bj\"orn Engquist
https://arxiv.org/abs/2506.22912 https://

A Dilation-based Seamless Multiscale Method For Elliptic Problems
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called, seamless methods have been introduced to reduce the requirement of scale separation. We will translate these methods to numerical homogenization problems and extend the technique to multiple dimensions. The initial step is to prove that a one-dimensional \sepia{s…

Replaced article(s) found for cond-mat.quant-gas. https://arxiv.org/list/cond-mat.quant-gas/new
[1/1]:
- Chirally-protected state manipulation by tuning one-dimensional statistics
F. Theel, M. Bonkhoff, P. Schmelcher, T. Posske, N. L. Harshman

This https://arxiv.org/abs/2407.10145 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Simplifying generic smooth maps to the 2-sphere and to the plane
We study how to construct explicit deformations of generic smooth maps from closed $n$--dimensional manifolds $M$ with $n \geq 2$ to the $2$--sphere $S^2$ and show that every smooth map $M \to S^2$ is homotopic to a $C^\infty$ stable map with at most one cusp point and with only folds of the middle absolute index. Furthermore, if $n$ is even, such a $C^\infty$ stable map can be so constructed that the restriction to the singular point set is a topological embedding. As a corollary, we show that…

Volumetric Parameterization for 3-Dimensional Simply-Connected Manifolds
Zhiyuan Lyu, Qiguang Chen, Gary P. T. Choi, Lok Ming Lui
https://arxiv.org/abs/2506.17025

Volumetric Parameterization for 3-Dimensional Simply-Connected Manifolds
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D data. However, the conventional approaches cannot control the bijectivity and local geometric distortions of the result mappings due to the complex structure of the solid manifolds. Moreover, prior methods mainly focus on one property instead of balancing differe…

All-Dielectric Metasurface with a Two-Dimensional Locally Flat Photonic Band
Minho Choi, Christopher Munley, Arnab Manna, Johannes Fr\"och, Arthur Barnard, Arka Majumdar
https://arxiv.org/abs/2506.20871

All-Dielectric Metasurface with a Two-Dimensional Locally Flat Photonic Band
Photonic flatbands offer promising light-matter interaction due to their unique slow-light nature. In recent years, flatbands have also attracted significant interest in optical engineering because of their angle-insensitive resonant characteristics. However, most photonic flatbands demonstrated to date occur only in one dimension and for a specific polarization, limiting their applicability. To date, no studies have reported the dispersionless behavior of flatbands under arbitrary two-dimensio…

On the isotopies of tangles in periodic 3-manifolds using finite covers
Yuka Kotorii, Sonia Mahmoudi, Elisabetta Matsumoto, Ken'ichi Yoshida
https://arxiv.org/abs/2505.20940

On the isotopies of tangles in periodic 3-manifolds using finite covers
A periodic tangle is a one-dimensional submanifold in $\mathbb{R}^3$ that has translational symmetry in one, two or three transverse directions. A periodic tangle can be seen as the universal cover of a link in the solid torus, the thickened torus, or the three-torus, respectively. Our goal is to study equivalence relations of such periodic tangles. Since all finite covers of a link lift to the same periodic tangle, it is necessary to prove that isotopies between different finite covers are pre…

Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds
Dmitry V. Bolotov
https://arxiv.org/abs/2506.19098 https://

Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds
In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation $\mathcal{F}$ of dimension one defined on a closed three-dimensional orientable manifold $M^3$ of negative curvature, which depends on the constants bounded the injectivity radius $inj(M^3)$, the volume $Vol(M^3)$, sectional curvature of the manifold $M^3$ and the mean curvature modulus of the leaves of the foliation $\mathcal{F}$.