{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:33:36Z","timestamp":1760243616866,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2012,5,9]],"date-time":"2012-05-09T00:00:00Z","timestamp":1336521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently, a novel method has been introduced to estimate the statistical significance of clustering in the direction distribution of objects. The method involves a multiscale procedure, based on the Kullback\u2013Leibler divergence and the Gumbel statistics of extreme values, providing high discrimination power, even in presence of strong background isotropic contamination. It is shown that the method is: (i) semi-analytical, drastically reducing computation time; (ii) very sensitive to small, medium and large scale clustering; (iii) not biased against the null hypothesis. Applications to the physics of ultra-high energy cosmic rays, as a cosmological probe, are presented and discussed.<\/jats:p>","DOI":"10.3390\/e14050865","type":"journal-article","created":{"date-parts":[[2012,5,9]],"date-time":"2012-05-09T12:14:00Z","timestamp":1336565640000},"page":"865-879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Entropic Approach to Multiscale Clustering Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Manlio","family":"De Domenico","sequence":"first","affiliation":[{"name":"School of Computer Science, University of Birmingham, Edgbaston B15 2TT Birmingham, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Insolia","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia, Universit\u00e1 di Catania and INFN, Via S. 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