Tootfinder

Robust Non-Linear Correlations via Polynomial Regression
Luca Giuliani, Michele Lombardi
https://arxiv.org/abs/2509.09380 https://arxiv.org/pdf/2509.09380

Robust Non-Linear Correlations via Polynomial Regression
The Hirschfeld-Gebelein-Rényi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal discovery. Recently, novel algorithms to estimate HGR in a differentiable manner have been proposed to facilitate its use as a loss regularizer in constrained machine learning applications. However, the inherent uncomputability of HGR requires a bias-variance trade-of…

A New Boundary Condition on Reionization
Sarah Libanore, Ely D. Kovetz, Julian B. Munoz, Yonatan Sklansky, Emilie Th\'elie
https://arxiv.org/abs/2509.08886 https://

A New Boundary Condition on Reionization
The epoch of reionization (EoR) marks the last phase transition of hydrogen in our Universe, as it evolves from cold and neutral to hot and ionized in the intergalactic medium (IGM). While its endpoint and duration can be estimated from current observations, albeit with large uncertainties, there is no known avenue to constrain its onset. We propose a novel method based on the Pearson cross-correlation coefficient between 21-cm brightness temperature maps and line-intensity maps tracing star-fo…

On independence testing using the (partial) distance correlation
Kontemeniotis Nikolaos, Vargiakakis Rafail, Tsagris Michail
https://arxiv.org/abs/2506.15659

On independence testing using the (partial) distance correlation
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and non-linear association between two univariate and or multivariate random variables. Partial distance correlation expands to the case of conditional independence. To test…

Entropy-Based Analysis of Urban Pollutant-Weather Correlations
Suchismita Banerjee, Koyena Ghosh, Moumita De, Urna Basu, Banasri Basu
https://arxiv.org/abs/2508.17453 https://…

Entropy-Based Analysis of Urban Pollutant-Weather Correlations
We employ statistical physics and information-theoretic methods to quantify the dependencies between key atmospheric pollutants and meteorological variables across multiple Indian cities. To capture both linear and nonlinear relationships, we introduce a Composite Correlation Index (CCI) that combines the Pearson correlation coefficient with entropy-based measures, including mutual information and conditional entropy. Based on the CCI values, cities are clustered into distinct groups, uncoverin…

Simplifying Strangeness Fluctuations through Balance Functions in Proton-Proton Collisions
Christian Bierlich, Peter Christiansen
https://arxiv.org/abs/2506.18375

Simplifying Strangeness Fluctuations through Balance Functions in Proton-Proton Collisions
Recent measurements of event-by-event fluctuations of multistrange baryons and kaons in proton-proton collisions by ALICE have been proposed as sensitive probes to distinguish between thermal and string-based hadronization mechanisms. We demonstrate that two key observables -- the normalized net-$Ξ$ second-order cumulant and the net-$K$--net-$Ξ$ Pearson correlation coefficient -- can be re-expressed in terms of balance function integrals, thereby revealing their underlying microscopic content…