Related papers: Mathematical reflections on modified fractional co…
Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of…
World University rankings have become well-established tools that students, university managers and policy makers read and use. Each ranking claims to have a unique methodology capable of measuring the 'quality' of universities. The purpose…
The 'macro F1' metric is frequently used to evaluate binary, multi-class and multi-label classification problems. Yet, we find that there exist two different formulas to calculate this quantity. In this note, we show that only under rare…
In causal inference, estimating the average treatment effect is a central objective, and in the context of competing risks data, this effect can be quantified by the cause-specific cumulative incidence function (CIF) difference. While…
Key doctrines, including novelty (patent), originality (copyright), and distinctiveness (trademark), turn on a shared empirical question: whether a body of work is meaningfully distinct from a relevant reference class. Yet analyses…
In this paper we study saturated fractions of a two-factor design under the simple effect model. In particular, we define a criterion to check whether a given fraction is saturated or not, and we compute the number of saturated fractions.…
The multifractal formalism for measures in its original formulation is checked for special classes of measures such as doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to…
Two journal-level indicators, respectively the mean ($m^i$) and the standard deviation ($v^i$) are proposed to be the core indicators of each journal and we show that quite several other indicators can be calculated from those two core…
Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to generalize the classical continued fractions. In this paper, we propose an introductive fundamental study about MCFs in the field of the $p$--adic…
We cardinally and ordinally rank distribution functions (CDFs). We present a new class of statistics, maximal adjusted quantiles, and show that a statistic is invariant with respect to cardinal shifts, preserves least upper bounds with…
Computers are increasingly used to make decisions that have significant impact in people's lives. Often, these predictions can affect different population subgroups disproportionately. As a result, the issue of fairness has received much…
A formulation towards quantifying resource count used in a measurement, that is independent of the model of the measurement dynamics(Quantum/Classical), is considered. For any general measurement with $(M+1)$ discrete outcomes, it is found…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
In this work we propose a metric to assess academic productivity based on publication outputs. We are interested in knowing how well a research group in an area of knowledge is doing relatively to a pre-selected set of reference groups,…
Entity rankings (e.g., institutions, journals) are a core component of academia and related industries. Existing approaches to institutional rankings have relied on a variety of data sources, and approaches to computing outcomes, but remain…
Text-to-image generation and image captioning are recently emerged as a new experimental paradigm to assess machine intelligence. They predict continuous quantity accompanied by their sampling techniques in the generation, making evaluation…
Economists often estimate causal effects of policies on multiple outcomes and summarize them into scalar measures of cost-effectiveness or welfare, such as the Marginal Value of Public Funds (MVPF). In many settings, microdata underlying…
There are various mathematical models proposed in the recent literature for estimating the h-index through bibliometric measures, such as number of articles (P) and citations received (C). These models have been previously empirically…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…