Tootfinder

On generation by triality automorphisms
Danila O. Revin, Andrei V. Zavarnitsine
https://arxiv.org/abs/2508.02277 https://arxiv.org/pdf/2508.02277

On generation by triality automorphisms
We clarify the structure of subgroups generated by conjugate graph automorphisms of order $3$ of $O_8^+(2)$ and $O_8^+(3)$. As a result, we obtain a correction to a paper by S. Guest which, in turn, plays an important role in proving the solvable analogue of the Baer--Suzuki theorem.

Local Poisson Deconvolution for Discrete Signals
Shayan Hundrieser, Tudor Manole, Danila Litskevich, Axel Munk
https://arxiv.org/abs/2508.00824 https://arx…

Local Poisson Deconvolution for Discrete Signals
We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution $μ$, from a binned Poisson convolution model. This question is motivated, among others, by super-resolution laser microscopy applications, where precise estimation of $μ$ provides insights into spatial formations of cellular protein assemblies. Our main results quantify the local minimax risk of estimating $μ$ for a broad class of smooth convolution kernels. This local perspective en…

Tuning Incommensurate Charge Order in Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$
Prathum Saraf, Eleanor M. Clements, Danila Sokratov, Shanta Saha, Peter Zavalij, Thomas W. Heitmann, Jeffrey W. Lynn, Camille Bernal-Choban, Dipanjan Chaudhuri, Caitlin Kengle, Yue Su, Simon Bettler, Nathan Manning, Peter Abbamonte, Sananda Biswas, Roser Valent\'i, Johnpierre Paglione

Tuning Incommensurate Charge Order in Ba$_{1-x}$Sr$_x$Al$_4$ and Ba$_{1-y}$Eu$_y$Al$_4$
The BaAl$_4$-type structure family is home to a vast landscape of interesting and exotic properties, with descendant crystal structures hosting a variety of electronic ground states including magnetic, superconducting and strongly correlated electron phenomena. BaAl$_4$ itself hosts a non-trivial topological band structure, but is otherwise a paramagnetic metal. However, the other members of the $A$Al$_4$ family ($A$= alkali earth), including SrAl$_4$ and EuAl$_4$, exhibit symmetry-breaking gro…

On the chromatic numbers of Johnson type graphs
Danila Cherkashin
https://arxiv.org/abs/2508.19775 https://arxiv.org/pdf/2508.19775

On the chromatic numbers of Johnson type graphs
A Johnson type graph $J_{\pm}(n,k,t)$ is a graph whose vertex set consists of vectors from $\{-1,0,1\}^n$ of the length $\sqrt{k}$ and edges connect vertices with scalar product $t$. The paper determines the order of growth of the chromatic numbers of graphs $J_\pm(n,2,-1)$ and $J_\pm(n,3,-1)$ (logarithmic on $n$), and also $J_\pm(n,3,-2)$ (double logarithmic on $n$).

GRILE: A Benchmark for Grammar Reasoning and Explanation in Romanian LLMs
Adrian-Marius Dumitran, Alexandra-Mihaela Danila, Angela-Liliana Dumitran
https://arxiv.org/abs/2508.14279

GRILE: A Benchmark for Grammar Reasoning and Explanation in Romanian LLMs
LLMs (Large language models) have revolutionized NLP (Natural Language Processing), yet their pedagogical value for low-resource languages remains unclear. We present GRILE (Grammar Romanian Inference and Language Explanations) , the first open benchmark of 1,151 multiple-choice questions harvested from Romanian high-stakes exams (National Evaluation, Baccalaureate, university admissions). GRILE enables us to probe two complementary abilities of seven state-of-the-art multilingual and Romanian-…

On branching points in the Gilbert-Steiner problem
Danila Cherkashin
https://arxiv.org/abs/2507.13532 https://arxiv.org/pdf/2507.1353…

On branching points in the Gilbert-Steiner problem
The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transport plan. A specific feature of the problem is that the cost of transporting a mass $m$ along a segment of length $l$ is equal to $l \times m^p$ for a fixed $0 < p < 1$ and segments may end at points not belonging to the supports of given measures (branching points). Main result of this paper determines all pairs of…

Complex single-site magnetism and magnetotransport in single-crystalline Gd$_{2}$AlSi$_{3}$
Ram Kumar, Shanta R. Saha, Jarryd Horn, A. Ikeda, Danila Sokratov, Yash Anand, Prathum Saraf, Ryan Dorman, E. Hemley, K. K. Iyer, Johnpierre Paglione
https://arxiv.org/abs/2506.14687

Complex single-site magnetism and magnetotransport in single-crystalline Gd$_{2}$AlSi$_{3}$
We present a detailed investigation of single-crystal samples of the magnetic compound Gd$_{2}$AlSi$_{3}$, which crystallizes in the $α$-ThSi$_2$ type tetragonal structure. We report the temperature and magnetic field dependence of the magnetic susceptibility, magnetization, heat capacity, electrical resistivity, and magnetoresistance for magnetic fields applied along both the tetragonal $c$-axis and in the basal $ab$-plane. X-ray diffraction measurements confirm a centrosymmetric, $I4_{1}/amd…

Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
Oleg I. Utesov, Danila P. Budylev
https://arxiv.org/abs/2507.08407

Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets
High-temperature part of the phase diagram of tetragonal frustrated antiferromagnets is discussed within the framework of the mean-field approach. Based on recent experimental and theoretical studies, we consider a model including frustrated Heisenberg exchange, biquadratic exchange, anisotropic exchange, and magnetodipolar interaction. It is analytically demonstrated that a subtle interplay among these interactions results in a variety of phase diagrams in the temperature-magnetic field plane.…