Tootfinder

Space-Efficient Hierholzer: Eulerian Cycles in O(m) Time and O(n) Space
Ziad Ismaili Alaoui, Detlef Plump, Sebastian Wild
https://arxiv.org/abs/2508.05251 https://

Space-Efficient Hierholzer: Eulerian Cycles in O(m) Time and O(n) Space
We describe a simple variant of Hierholzer's algorithm that finds an Eulerian cycle in a (multi)graph with $n$ vertices and $m$ edges using $\mathrm{O}(n \lg m)$ bits of working memory. This substantially improves the working space compared to standard implementations of Hierholzer's algorithm, which use $\mathrm{O}(m \lg n)$ bits of space. Our algorithm runs in linear time, like the classical versions, but avoids an $\mathrm{O}(m)$-size stack of vertices or storing information for each edge. T…

Auto-Doubly Robust Estimation of Causal Effects on a Network
Jizhou Liu, Dake Zhang, Eric J. Tchetgen Tchetgen
https://arxiv.org/abs/2506.23332 https://

Auto-Doubly Robust Estimation of Causal Effects on a Network
This paper develops new methods for causal inference in observational studies on a single large network of interconnected units, addressing two key challenges: long-range dependence among units and the presence of general interference. We introduce a novel network version of Augmented Inverse Propensity Weighted, which combines propensity score and outcome models defined on the network to achieve doubly robust identification and estimation of both direct and spillover causal effects. Under a ne…

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Xia Liao, Xiping Zhang
https://arxiv.org/abs/2505.24236 https://

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(γ\cdot \ind_U)$ of the restriction of a constructible function $γ$ on $U$. We globalise Ginzburg's local sharp construction and introduce the log transversality condition, which is a new transversality condition about the relative position of $γ$ and $D$. We prove that the log transversality condition is satisfied if either $D$ is normal…

SuSAM-v2: improved superscaling description of electron and CC neutrino quasielastic scattering using effective mass dynamics
V. L. Martinez-Consentino, P. R. Casale, J. E. Amaro
https://arxiv.org/abs/2506.03934

SuSAM-v2: improved superscaling description of electron and CC neutrino quasielastic scattering using effective mass dynamics
We present an improved version of the Superscaling Analysis with Relativistic Effective Mass, denoted as SuSAM-v2. In the original SuSAM model, a universal scaling function was fitted to a selected set of quasielastic electron scattering (e,e') cross section data, using a phenomenological ansatz inspired by the Relativistic Mean Field model of nuclear matter. In this work, we refine the procedure by first fitting a longitudinal scaling function directly to experimental longitudinal response dat…

Hive is PSPACE-Hard
Dani\"el Andel, Benjamin Rin
https://arxiv.org/abs/2506.03492 https://arxiv.org/pdf/2506.03492

Hive is PSPACE-Hard
Hive is an abstract strategy game played on a table with hexagonal pieces. First published in 2001, it was and continues to be highly popular among both casual and competitive players. In this paper, we show that for a suitably generalized version of the game, the computational problem of determining whether a given player in an arbitrary position has a winning strategy is PSPACE-hard. We do this by reduction from a variant of Generalized Geography we call Formula Game Geography.

Commissioning of the NUCLEUS Experiment at the Technical University of Munich
H. Abele, G. Angloher, B. Arnold, M. Atzori Corona, A. Bento, E. Bossio, F. Buchsteiner, J. Burkhart, F. Cappella, M. Cappelli, N. Casali, R. Cerulli, A. Cruciani, G. Del Castello, M. del Gallo Roccagiovine, S. Dorer, A. Erhart, M. Friedl, S. Fichtinger, V. M. Ghete, M. Giammei, C. Goupy, D. Hauff, F. Jeanneau, E. Jericha, M. Kaznacheeva, H. Kluck, A. Langenk\"amper, T. Lasserre, D. Lhuillier, M. Mancuso…

Commissioning of the NUCLEUS Experiment at the Technical University of Munich
The NUCLEUS experiment aims to detect coherent elastic neutrino-nucleus scattering of reactor antineutrinos on CaWO$_4$ targets in the fully coherent regime, using gram-scale cryogenic calorimeters. The experimental apparatus will be installed at the Chooz nuclear power plant in France, in the vicinity of two 4.25 GW$_{\text{th}}$ reactor cores. This work presents results from the commissioning of an essential version of the experiment at the shallow Underground Laboratory of the Technical Univ…

Improved girth approximation in weighted undirected graphs
Avi Kadria, Liam Roditty, Aaron Sidford, Virginia Vassilevska Williams, Uri Zwick
https://arxiv.org/abs/2507.13869

Improved girth approximation in weighted undirected graphs
Let $G = (V,E,\ell)$ be a $n$-node $m$-edge weighted undirected graph, where $\ell: E \rightarrow (0,\infty)$ is a real \emph{length} function defined on its edges, and let $g$ denote the girth of $G$, i.e., the length of its shortest cycle. We present an algorithm that, for any input, integer $k \geq 1$, in $O(kn^{1+1/k}\log{n} + m(k+\log{n}))$ expected time finds a cycle of length at most $\frac{4k}{3}g$. This algorithm nearly matches a $O(n^{1+1/k}\log{n})$-time algorithm of \cite{KadriaRSWZ…

Chow cohomology and Lefschetz (1,1)-theorem
Ananyo Dan, Inder Kaur
https://arxiv.org/abs/2506.13220 https://arxiv.org/pdf/2506.13220

Chow cohomology and Lefschetz (1,1)-theorem
Any smooth, projective variety satisfies the Hodge conjecture in codimension one, known as the Lefschetz (1,1) theorem. Totaro formulated a version for singular varieties. He asked whether the natural Bloch-Gillet-Soulé cycle class map from the operational Chow group to the (1,1)-classes in the weight graded piece of the cohomology group is surjective? In this short article, we give a sufficient criterion for this to hold. In particular, we show that several singular varieties with at worst is…

This https://arxiv.org/abs/2408.06616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gromov-Witten invariants in family and quantum cohomology
A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r…