Roy Cerqueti

Edoardo Di Martino, Matteo Cinelli, Roy Cerqueti

Detecting multimodality in empirical distributions is a fundamental problem in statistics and data analysis, with applications ranging from clustering to the study of complex systems. In practice, however, assessing departures from unimodality in a consistent and comparable way remains challenging. Widely used methods such as Hartigan and Hartigan's Dip Test illustrate these difficulties, as the interpretation of their statistics depends strongly on sample size, requires calibration to determine significance, and, for large samples, exhibit increasing sensitivity, leading to rejection of unimodality for arbitrarily small deviations from the null. We introduce Z-Dip, a standardized measure of multimodality that addresses these limitations. By treating the Dip statistic as a random variable under the null hypothesis of unimodality and standardizing its observed value, the proposed approach yields scores that are directly comparable across datasets of different sizes. Using simulation-based calibration, we derive a universal decision threshold that closely reproduces classical Dip Test decisions without requiring sample-size-specific adjustments. Extensive validation on simulated data and on more than 88,000 empirical opinion distributions shows near-perfect agreement with the classical Dip Test while providing a more interpretable and comparable measure of modality. Finally, we propose a downsampling-based correction that mitigates residual sensitivity in extremely large samples. Open-source software and reference tables are provided to facilitate practical adoption.

Valerio Ficcadenti, Roy Cerqueti, Marcel Ausloos et al.

This paper deals with a quantitative analysis of the content of official political speeches. We study a set of about one thousand talks pronounced by the US Presidents, ranging from Washington to Trump. In particular, we search for the relevance of the rare words, i.e. those said only once in each speech -- the so-called hapaxes. We implement a rank-size procedure of Zipf-Mandelbrot type for discussing the hapaxes' frequencies regularity over the overall set of speeches. Starting from the obtained rank-size law, we define and detect the core of the hapaxes set by means of a procedure based on an Hirsch index variant. We discuss the resulting list of words in the light of the overall US Presidents' speeches. We further show that this core of hapaxes itself can be well fitted through a Zipf-Mandelbrot law and that contains elements producing deviations at the low ranks between scatter plots and fitted curve -- the so-called king and vice-roy effect. Some socio-political insights are derived from the obtained findings about the US Presidents messages.

Valerio Ficcadenti, Roy Cerqueti, Marcel Ausloos

This work presents a text mining context and its use for a deep analysis of the messages delivered by the politicians. Specifically, we deal with an expert systems-based exploration of the rhetoric dynamics of a large collection of US Presidents' speeches, ranging from Washington to Trump. In particular, speeches are viewed as complex expert systems whose structures can be effectively analyzed through rank-size laws. The methodological contribution of the paper is twofold. First, we develop a text mining-based procedure for the construction of the dataset by using a web scraping routine on the Miller Center website -- the repository collecting the speeches. Second, we explore the implicit structure of the discourse data by implementing a rank-size procedure over the individual speeches, being the words of each speech ranked in terms of their frequencies. The scientific significance of the proposed combination of text-mining and rank-size approaches can be found in its flexibility and generality, which let it be reproducible to a wide set of expert systems and text mining contexts. The usefulness of the proposed method and the speech subsequent analysis is demonstrated by the findings themselves. Indeed, in terms of impact, it is worth noting that interesting conclusions of social, political and linguistic nature on how 45 United States Presidents, from April 30, 1789 till February 28, 2017 delivered political messages can be carried out. Indeed, the proposed analysis shows some remarkable regularities, not only inside a given speech, but also among different speeches. Moreover, under a purely methodological perspective, the presented contribution suggests possible ways of generating a linguistic decision-making algorithm.