Tootfinder

\'Etale algebras and the Kummer theory of finite Galois modules
Evan M. O'Dorney
https://arxiv.org/abs/2506.11310 https://arx…

Étale algebras and the Kummer theory of finite Galois modules
Galois cohomology groups $H^i(K,M)$ are widely used in algebraic number theory, in such contexts as Selmer groups of elliptic curves, Brauer groups of fields, class field theory, and Iwasawa theory. The standard construction of these groups involves maps out of the absolute Galois group $G_K$, which in many cases of interest (e.g. $K = \mathbb{Q}$) is too large for computation or even for gaining an intuitive grasp. However, for finite $M$, an element of $H^i(K,M)$ can be described by a finite …

Fourth- and Higher-order Interface Tracking of Three or More Materials with Arbitrarily Complex Topology and Geometry
Yan Tan, Yixiao Qian, Zhiqi Li, Qinghai Zhang
https://arxiv.org/abs/2506.11897

Fourth- and Higher-order Interface Tracking of Three or More Materials with Arbitrarily Complex Topology and Geometry
For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) accurately and efficiently represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) maintains a $(r,h)$-regularity condition of the interface so that the distance between any pair of adjacent markers is within a user-specified range that may vary according to the local curvature, (c) applies to multiple materials with arbitraril…

On frequentist confidence intervals in a non-Gaussian regime
Shubham Barua, Shantanu Desai, Mauricio Lopez-Hernandez, Eoin \'O Colg\'ain
https://arxiv.org/abs/2508.10633

On frequentist confidence intervals in a non-Gaussian regime
We study frequentist confidence intervals based on graphical profile likelihoods (Wilks' theorem, likelihood integration), and the Feldman-Cousins (FC) prescription, a generalisation of the Neyman belt construction, in a setting with non-Gaussian Markov chain Monte Carlo (MCMC) posteriors. Our simplified setting allows us to recycle the MCMC chain as an input in all methods, including mock simulations underlying the FC approach. We find all methods agree to within $10 \%$ in the close to Gaussi…

Linear-quadratic stochastic nonzero-sum differential games between graphon teams
De-xuan Xu, Zhun Gou, Nan-jing Huang
https://arxiv.org/abs/2506.11468 http…

Linear-quadratic stochastic nonzero-sum differential games between graphon teams
We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common social cost function. On the other hand, these two groups compete with each other, forming a Nash game between two graphon teams. We note that the original problem can be equivalently formulated as an infinite-dimensional two-agent Nash game. Applying the dynamic …

An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups
Daniel Str\"ombom, Catherine Futterman
https://arxiv.org/abs/2509.11083 https://

An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups
Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the pred…

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
Meghanil Sinha, S. Surendra Singh
https://arxiv.org/abs/2506.11171

Impact of Buchdahl metric potential on thin-shell gravastar framework in de Rham-Gabadadze-Tolley like massive gravity
This paper presents a study on gravitational vacuum stars (gravastars) with an isotropic matter distribution in de Rham-Gabadadze-Tolley (dRGT) massive gravity incorporating Buchdahl metric function. Here we have conducted an analysis on thin-shell singularity-free gravastar configuration. The study demonstrates the viability of gravastars as alternatives to black holes (BHs) in this massive gravity. Our research yields singularity free analytical solutions for gravastar interior and without ev…

A note on intrinsic topologies of groups
S. Bardyla, L. Elliott, J. D. Mitchell, Y. P\'eresse
https://arxiv.org/abs/2506.11500 https://

A note on intrinsic topologies of groups
We investigate topologies on groups which arise naturally from their algebraic structure, including the Frechét-Markov, Hausdorff-Markov, and various kinds of Zariski topologies. Answering a question by Dikranjan and Toller, we show that there exists a countable abelian group in which no bounded version of the Zariski topology coincides with the full Zariski topology. Complementing a recent result by Goffe and Greenfeld, we show that on any group with no algebraicity the semigroup Zariski topo…

Topology-Aware Virtualization over Inter-Core Connected Neural Processing Units
Dahu Feng, Erhu Feng, Dong Du, Pinjie Xu, Yubin Xia, Haibo Chen, Rong Zhao
https://arxiv.org/abs/2506.11446

Topology-Aware Virtualization over Inter-Core Connected Neural Processing Units
With the rapid development of artificial intelligence (AI) applications, an emerging class of AI accelerators, termed Inter-core Connected Neural Processing Units (NPU), has been adopted in both cloud and edge computing environments, like Graphcore IPU, Tenstorrent, etc. Despite their innovative design, these NPUs often demand substantial hardware resources, leading to suboptimal resource utilization due to the imbalance of hardware requirements across various tasks. To address this issue, prio…

The permutation dimension of the Klein 4-group
Henry Harman
https://arxiv.org/abs/2507.11469 https://arxiv.org/pdf/2507.11469

The permutation dimension of the Klein 4-group
Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation dimension. Following Walsh's success with cyclic groups of prime order, we compute the (global) $p$-permutation dimension of the Klein 4-group in characteristic $p := 2$, along with the dimensions for each of its indecomposable modules.

Isoperimetric behavior of generalized Stallings-Bieri groups
Noel Brady, Pratit Goswami, Rob Merrell
https://arxiv.org/abs/2509.09939 https://arxiv.org/pdf…

Isoperimetric behavior of generalized Stallings-Bieri groups
We introduce the notion of $n$-split for an epimorphism from a group to a finite rank free abelian group. This is used to provide bounds for the Dehn functions of certain coabelian subgroups of direct products of finitely presented groups. Such subgroups include and significantly generalize the Stallings-Bieri groups.