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Finding congruences with the WZ method
Li-Quan Feng, Qing-Hu Hou
https://arxiv.org/abs/2506.19221 https://arxiv.org/pdf/2506.19221

Finding congruences with the WZ method
We utilize the Wilf-Zeilberger (WZ) method to establish congruences related to truncated Ramanujan-type series. By constructing hypergeometric terms $f(k, a, b, \ldots)$ with Gosper-summable differences and selecting appropriate parameters, we derive several congruences modulo $p$ and $p^2$ for primes $p > 2$. For instance, we prove that for any prime $p > 2$, \[ \sum_{n=0}^{p-1} \frac{10n+3}{2^{3n}}\binom{3n}{n}\binom{2n}{n}^2 \equiv 0 \pmod{p},\] and \[ \sum_{n=0}^{p-1} \frac{(-1)^n(20n^2+8n+…

🦩 Mit bis zu zwei Metern #Flügelspannweite und auffallend roten Beinen und Schnabel ist der majestätische #Weißstorch nicht zu übersehen. Doch der #Lebensraumverlust und …

Weißstorch (Ciconia ciconia): Gefährdet durch menschliche Aktivitäten
Der Weißstorch: Wissenswertes über den majestätischen Vogel – Lebensweise, Nahrung, Brut und Schutz.

Reducing the Cost of Energy Differences in Variational Monte Carlo with Spotlight Sampling
Sonja Bumann, Eric Neuscamman
https://arxiv.org/abs/2507.18930 https://

Reducing the Cost of Energy Differences in Variational Monte Carlo with Spotlight Sampling
We investigate an approximate sampling scheme that can significantly reduce the cost scaling of variational Monte Carlo when it is employed to predict the energy differences associated with local chemical changes. Inspired by side-chaining and embedding methods, this spotlight sampling approach adopts an approximate fragmented Hamiltonian and correlated sampling to reduce cost scaling to the point that it is essentially linear with system size, with the potential to go sub-linear if certain con…

Quantum Boltzmann Machines using Parallel Annealing for Medical Image Classification
Dani\"elle Schuman, Mark V. Seebode, Tobias Rohe, Maximilian Balthasar Mansky, Michael Schroedl-Baumann, Jonas Stein, Claudia Linnhoff-Popien, Florian Krellner
https://arxiv.org/abs/2507.14116

Quantum Boltzmann Machines using Parallel Annealing for Medical Image Classification
Exploiting the fact that samples drawn from a quantum annealer inherently follow a Boltzmann-like distribution, annealing-based Quantum Boltzmann Machines (QBMs) have gained increasing popularity in the quantum research community. While they harbor great promises for quantum speed-up, their usage currently stays a costly endeavor, as large amounts of QPU time are required to train them. This limits their applicability in the NISQ era. Following the idea of Noè et al. (2024), who tried to allev…

The coalescent of a sample from a linear-fractional branching process
Natalia Cardona-Tob\'on, Sandra Palau
https://arxiv.org/abs/2506.17470 https://…

The coalescent of a sample from a linear-fractional branching process
In this article, we focus on Bienaymé-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli sampling, where each individual is selected independently with a given probability, or through uniform sampling, where a fixed number of individuals are chosen uniformly at random. We analyze the genealogical trees generated by the sampled individuals. In particul…

Galton-Watson processes, simple varieties of trees and Khinchin families
V\'ictor J. Maci\'a
https://arxiv.org/abs/2506.18370 https://

Galton-Watson processes, simple varieties of trees and Khinchin families
In this note, we introduce a unified analytic framework that connects simple varieties of trees, Bienayme-Galton-Watson processes and Khinchin families. Using Lagrange's inversion formula, we derive new coefficient-based expressions for extinction probabilities and reinterpret them as boundary phenomena tied to the domain of the inverse of the solution to Lagrange's equation. This perspective reveals a structural bridge between combinatorial and probabilistic models, simplifying classical argum…

Smooth manifolds in $G_{n,2}$ and $\mathbb{C} P^{N}$ defined by symplectic reductions of $T^n$-action
Victor M. Buchstaber, Svjetlana Terzi\'c
https://arxiv.org/abs/2507.04582

Smooth manifolds in $G_{n,2}$ and $\mathbb{C} P^{N}$ defined by symplectic reductions of $T^n$-action
Plücker coordinates define the $T^n$-equivariant embedding $p : G_{n,2}\to \mathbb{C} P^{N}$ of a complex Grassmann manifold $G_{n,2}$ into the complex projective space $\mathbb{C} P^{N}$, $N=\binom{n}{2}-1$ for the canonical $T^n$-action on $G_{n,2}$ and the $T^n$-action on $\mathbb{C} P^{N}$ given by the second symmetric power representation $T^n\to T^{N}$ and the standard $T^{N}$-action. Let $μ: G_{n,2}\to Δ_{n,2}\subset \mathbb{R} ^{n}$ and $\tildeμ: \mathbb{C} P^{N}\to Δ_{n,2}\subset …

VERTICO IX: Signatures of environmental processing of the gas in Virgo cluster spiral galaxies through mapping of CO isotopologues
Timothy A. Davis, Toby Brown, Maria J. Jimenez-Donaire, Christine D. Wilson, Dhruv Bisaria, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Sara Ellison, Bumhyun Lee, Ian D. Roberts, Kristine Spekkens, Vicente Villanueva, Nikki Zabel

VERTICO IX: Signatures of environmental processing of the gas in Virgo cluster spiral galaxies through mapping of CO isotopologues
In this work we study CO isotopologue emission in the largest cluster galaxy sample to date: 48 VERTICO spiral galaxies in Virgo. We show for the first time in a significant sample that the physical conditions within the molecular gas appear to change as a galaxy's ISM is affected by environmental processes. 13CO is detected across the sample, both directly and via stacking, while C18O is detected in a smaller number of systems. We use these data to study trends with global and radial galaxy pr…

Distributed Approximation Algorithms for Minimum Dominating Set in Locally Nice Graphs
Marthe Bonamy, Cyril Gavoille, Timoth\'e Picavet, Alexandra Wesolek
https://arxiv.org/abs/2507.04960

Distributed Approximation Algorithms for Minimum Dominating Set in Locally Nice Graphs
We give a new, short proof that graphs embeddable in a given Euler genus-$g$ surface admit a simple $f(g)$-round $α$-approximation distributed algorithm for Minimum Dominating Set (MDS), where the approximation ratio $α\le 906$. Using tricks from Heydt et al. [European Journal of Combinatorics (2025)], we in fact derive that $α\le 34 +\varepsilon$, therefore improving upon the current state of the art of $24g+O(1)$ due to Amiri et al. [ACM Transactions on Algorithms (2019)]. It also improves…