{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T18:32:25Z","timestamp":1772217145509,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,8]],"date-time":"2015-05-08T00:00:00Z","timestamp":1431043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We have used the Kolmogorov complexities and the Kolmogorov complexity spectrum to quantify the randomness degree in river flow time series of seven rivers with different regimes in Bosnia   and Herzegovina, representing their different type of courses, for the period 1965\u20131986. In particular, we have examined: (i) the Neretva, Bosnia and the Drina (mountain and lowland parts), (ii) the Miljacka and the Una (mountain part) and the Vrbas and the Ukrina (lowland part) and then calculated the Kolmogorov complexity (KC) based on the Lempel\u2013Ziv Algorithm (LZA) (lower\u2014KCL and upper\u2014KCU), Kolmogorov complexity spectrum highest value (KCM) and overall Kolmogorov complexity (KCO) values for each time series. The results indicate that the KCL, KCU, KCM and KCO values in seven rivers show some similarities regardless of the amplitude differences in their monthly flow rates. The KCL, KCU and KCM complexities as information measures do not \u201csee\u201d a difference between time series which have different amplitude variations but similar random components. However, it seems that the KCO information measures better takes into account both the amplitude and the place of the components in a time series.<\/jats:p>","DOI":"10.3390\/e17052973","type":"journal-article","created":{"date-parts":[[2015,5,8]],"date-time":"2015-05-08T10:56:41Z","timestamp":1431082601000},"page":"2973-2987","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Kolmogorov Complexity Based Information Measures Applied to the Analysis of Different River Flow Regimes"],"prefix":"10.3390","volume":"17","author":[{"given":"Dragutin","family":"Mihailovi\u0107","sequence":"first","affiliation":[{"name":"Department of Field Crops and Vegetables, Faculty of Agriculture, University of Novi Sad,  Novi Sad 21000, Serbia"}]},{"given":"Gordan","family":"Mimi\u0107","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad 21000, Serbia"}]},{"given":"Nusret","family":"Dre\u0161kovi\u0107","sequence":"additional","affiliation":[{"name":"Department of Geography, Faculty of Sciences, University of Sarajevo, Sarajevo 71000, Bosnia and Herzegovina"}]},{"given":"Ilija","family":"Arseni\u0107","sequence":"additional","affiliation":[{"name":"Department of Field Crops and Vegetables, Faculty of Agriculture, University of Novi Sad,  Novi Sad 21000, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/02626660209492913","article-title":"Discussion of \u201cEvidence of chaos in rainfall-runoff process\u201d. Which chaos in rainfall-runoff process?","volume":"47","author":"Schertzer","year":"2002","journal-title":"Hydrol. Sci. J"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"557","DOI":"10.5194\/npg-12-557-2005","article-title":"Aggregation and sampling in deterministic chaos: implications for chaos identification in hydrological processes","volume":"12","author":"Salas","year":"2005","journal-title":"Nonlinear Proc. Geoph"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"046210","DOI":"10.1103\/PhysRevE.86.046210","article-title":"Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach","volume":"86","author":"Zunino","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.physa.2013.09.062","article-title":"Complexity analysis of the turbulent environmental fluid flow time series","volume":"395","year":"2014","journal-title":"Physica A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.3390\/e15041289","article-title":"HydroZIP: How hydrological knowledge can be used to improve compression of hydrological data","volume":"15","author":"Weijs","year":"2013","journal-title":"Entropy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3171","DOI":"10.5194\/hess-17-3171-2013","article-title":"Data compression to define information content of hydrological time series","volume":"17","author":"Weijs","year":"2013","journal-title":"Hydrol. Earth Syst. Sc"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1140\/epjst\/e2013-01858-3","article-title":"Ordinal patterns and statistical complexity analysis of daily stream flow time series","volume":"222","author":"Lange","year":"2013","journal-title":"Eur. Phys. J. ST"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1007\/s00477-013-0825-8","article-title":"Complexity\u2014entropy analysis of daily stream flow time series in the continental United States","volume":"28","author":"Serinaldi","year":"2014","journal-title":"Stoch. Env. Res. Risk A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1287\/orsc.1090.0481","article-title":"From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations","volume":"20","author":"Andriani","year":"2009","journal-title":"Organ. Sci"},{"key":"ref_10","unstructured":"Thompson, M., and Young, L. The complexities of measuring complexity. Available online: http:\/\/www.impgroup.org\/uploads\/papers\/7846.pdf."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Weisberg, S. (2005). Applied Linear Regression, Wiley. [3rd].","DOI":"10.1002\/0471704091"},{"key":"ref_12","unstructured":"Shalizi, C.R. Available online: http:\/\/www.stat.cmu.edu\/~cshalizi\/350\/lectures\/28\/lecture-28.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4236\/ojmh.2011.11001","article-title":"ARMA modelling of Benue river flow dynamics: Comparative study of par model","volume":"1","author":"Otache","year":"2011","journal-title":"Open J. Modern Hydrol"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, M., and Vitanyi, P. (1997). An Introduction to Kolmogorov Complexity and its Applications, Springer. [2nd].","DOI":"10.1007\/978-1-4757-2606-0"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/TIT.1976.1055501","article-title":"On the complexity of finite sequences","volume":"22","author":"Lempel","year":"1976","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","first-page":"1","article-title":"Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis","volume":"13","year":"2015","journal-title":"Open Phys"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/S0375-9601(97)00855-4","article-title":"Measures of Statistical Complexity: Why?","volume":"238","author":"Feldman","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/TIT.1968.1054210","article-title":"Logical basis for information theory and probability theory","volume":"IT-14","author":"Kolmogorov","year":"1968","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"902","DOI":"10.3390\/e13040902","article-title":"Algorithmic relative complexity","volume":"13","author":"Cerra","year":"2011","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1103\/PhysRevA.36.842","article-title":"Easily calculable measure for the complexity of spatiotemporal patterns","volume":"36","author":"Kaspar","year":"1987","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1109\/10.966601","article-title":"EEG complexity as a measure of depth of anesthesia of patients","volume":"48","author":"Zhang","year":"2001","journal-title":"IEEE Trans. Biomed. Eng"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1142\/S0218127400001092","article-title":"An alternative partitioning technique to quantify the regularity of complex time series","volume":"10","author":"Radhakrishnan","year":"2000","journal-title":"Int. J. Bifurcation Chaos"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Small, M. (2005). Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance, World Scientific.","DOI":"10.1142\/9789812567772"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/TBME.2006.873543","article-title":"Comparison of entropy and complexity measures for the assessment of depth of sedation","volume":"53","author":"Ferenets","year":"2006","journal-title":"IEEE Trans. Biomed. Eng"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2606","DOI":"10.1109\/TBME.2006.883825","article-title":"Analysis of biomedical signals by the Lempel\u2013Ziv complexity: the effect of finite data size","volume":"53","author":"Hu","year":"2006","journal-title":"IEEE Trans. Biomed. Eng"},{"key":"ref_26","unstructured":"Thai, Q. Available online: http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/38211-calclzcomplexity."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1659\/0276-4741(2001)021[0034:ANTFMA]2.0.CO;2","article-title":"A new typology for mountains and other relief classes: An application to global continental water resources and population distribution","volume":"21","author":"Meybeck","year":"2001","journal-title":"Mt. Res. Dev"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"557","DOI":"10.5194\/npg-12-557-2005","article-title":"Aggregation and sampling in deterministic chaos: Implications for chaos identification in hydrological processes","volume":"12","author":"Salas","year":"2005","journal-title":"Nonlinear Process. Geophys"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4942","DOI":"10.1016\/j.physa.2010.06.025","article-title":"Multifractal detrended cross-correlation analysis of sunspot numbers and river flow fluctuations","volume":"389","author":"Hajian","year":"2010","journal-title":"Physica A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2973\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:46:01Z","timestamp":1760215561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2973"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,8]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052973"],"URL":"https:\/\/doi.org\/10.3390\/e17052973","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,8]]}}}