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Analysis

This paper presents a novel Time Projection Chamber (TPC) system designed for low-background beta radiation measurements. The system's effectiveness is demonstrated through experimental validation using a $^{90}$Sr beta source and a Geant4-based simulation. The study highlights the system's ability to discriminate between beta signals and background radiation, achieving a low background rate. The paper also identifies the sources of background radiation and proposes optimizations for further improvement, making it relevant for applications requiring sensitive beta detection.
Reference

The system achieved a background rate of 0.49 $\rm cpm/cm^2$ while retaining more than 55% of $^{90}$Sr beta signals within a 7 cm diameter detection region.

Analysis

This paper investigates the maximum number of touching pairs in a packing of congruent circles in the hyperbolic plane. It provides upper and lower bounds for this number, extending previous work on Euclidean and specific hyperbolic tilings. The results are relevant to understanding the geometric properties of circle packings in non-Euclidean spaces and have implications for optimization problems in these spaces.
Reference

The paper proves that for certain values of the circle diameter, the number of touching pairs is less than that from a specific spiral construction, which is conjectured to be extremal.

Diameter of Random Weighted Spanning Trees

Published:Dec 26, 2025 10:48
1 min read
ArXiv

Analysis

This paper investigates the diameter of random weighted uniform spanning trees. The key contribution is determining the typical order of the diameter under specific weight assignments. The approach combines techniques from Erdős-Rényi graphs and concentration bounds, offering insights into the structure of these random trees.
Reference

The diameter of the resulting tree is typically of order $n^{1/3} \log n$, up to a $\log \log n$ correction.