Abstract Real-time leakage detection based on pressure and flow data has become increasingly essential for water distribution systems (WDSs). Recent data-driven approaches have largely focused burst characterised as sudden outflow or drops but did not mention the ability to detect gradual events that do change could cause more loss. This study proposes an online system exponential weighted movi...

We study two generalizations of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras. To highlight difference between them, we develop new techniques construct incomparable in this setting. Furthermore, discuss relation with Tukey reducibility and prove that, assuming Continuum Hypothesis, there exist Cohen algebra which are RK-equivalent generalized sense but Tukey-incompara...

DOI: 10.5281/zenodo.55536 ABSTRACT Discrete Fourier Transform is a principal mathematical method for the frequency analysis and has wide applications in Engineering and Sciences. Because the DFT is so ubiquitous, fast methods for computing DFT have been studied extensively, and continuous to be an active research. The way of splitting the DFT gives out various fast algorithms. In this paper, we...

We discuss two general aspects of the theory of cardinal characteristics of the continuum, especially of proofs of inequalities between such characteristics. The first aspect is to express the essential content of these proofs in a way that makes sense even in models where the inequalities hold trivially (e.g., because the continuum hypothesis holds). For this purpose, we use a Borel version of...

The jackknife or “leave one out” procedure is a cross-validation technique first developed by Quenouille to estimate the bias of an estimator. John Tukey then expanded the use of the jackknife to include variance estimation and tailored the name of jackknife because like a jackknife—a pocket knife akin to a Swiss army knife and typically used by boy scouts—this technique can be used as a “quick...

The concept of location depth was introduced as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. The depth contours form a collection of nested polygons, and the center of the deepest contour is called the Tukey median. The only available implemented algor...