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We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type…
Mathematical notations around the world are diverse. Not as much as requiring computing machines' makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics. In order to understand…
In the past decade, open science and science of science communities have initiated innovative efforts to address concerns about the reproducibility and replicability of published scientific research. In some respects, these efforts have…
This paper introduces a framework for measuring how much black-box decision-makers rely on variables of interest. The framework adapts a permutation-based measure of variable importance from the explainable machine learning literature. With…
The increasing impact of algorithmic decisions on people's lives compels us to scrutinize their fairness and, in particular, the disparate impacts that ostensibly-color-blind algorithms can have on different groups. Examples include credit…
Synthetic text generated by Large Language Models (LLMs) is increasingly used for further training and improvement of LLMs. Diversity is crucial for the effectiveness of synthetic data, and researchers rely on prompt engineering to improve…
Bilingual annotators were paid to link roughly sixteen thousand corresponding words between on-line versions of the Bible in modern French and modern English. These annotations are freely available to the research community from…
Gender bias, a systemic and unfair difference in how men and women are treated in a given domain, is widely studied across different academic fields. Yet, there are barely any studies of the phenomenon in the field of academic information…
Citations are an important indicator of the state of a scientific field, reflecting how authors frame their work, and influencing uptake by future scholars. However, our understanding of citation behavior has been limited to small-scale…
Let $\mathbb{K}$ be a field of characteristic $0$. For each choice of distinct $a_1, \ldots, a_n\in \mathbb{K}$ and distinct $b_1, \ldots, b_n\in \mathbb{K}$, consider the sum $S=\sum_{i=1}^n a_i b_{\pi(i)}$ as $\pi$ ranges over the…
In their letter to PNAS and a comprehensive set of notes on arXiv [arXiv:0909.5673v2], Christian Robert, Kerrie Mengersen and Carla Chen (RMC) represent our approach to model criticism in situations when the likelihood cannot be computed as…
We investigate the limits of the multivariable signature function $\sigma_L$ of a $\mu$-component link $L$ as some variable tends to $1$ via two different approaches: a three-dimensional and a four-dimensional one. The first uses the…
Online platforms increasingly rely on sequential decision-making algorithms to allocate resources, match users, or control exposure, while facing growing pressure to ensure fairness over time. We study a general online decision-making…
For each prime p other than 3, and each power q=p^k, we present two large classes of permutation polynomials over F_{q^2} of the form X^r B(X^{q-1}) which have at most five terms, where B(X) is a polynomial with coefficients in {1,-1}. The…
Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain…
A method is presented for evaluating authors on the basis of citations. It assigns to each author a citation score which depends upon the number of times he is cited, and upon the scores of the citers. The scores are found to be the…
This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for…
We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from $2003$ to the first half of…
Citation information in scholarly data is an important source of insight into the reception of publications and the scholarly discourse. Outcomes of citation analyses and the applicability of citation based machine learning approaches…
In qualitative statistics, permutation tests are very popular, mainly because of their finite-sample exactness under exchangeability. However, in non-exchangeable settings, the covariance structure of permuted statistics typically differs…