Abstract:We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to di erent time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four di erent geophysical phenomena (dynamics of: river ow, long term precipitation, indoor Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained o er deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

ABSTRACT:We considered shifts in the Köppen climate zones and the corresponding impact on the crop yields in Serbia by comparing (1) the results of downscaling with the ECMWF Hamburg Atmospheric Model 5 (ECHAM5) and regional Eta Belgrade University (EBU)-Princeton Ocean Model (POM) model for the A1B and A2 scenarios over 2001-2030 and 2071-2100 and (2) the present climate simulations for the period 1961−1990. We analyzed the EBU-POM regional climate model complexity by calculating the corresponding metrics. The yields of winter wheat, maize and soybeans were evaluated with the Decision Support System for Agrotechnology Transfer (DSSAT) model.In the future, the Köppen climate zones of Serbia will shift in coverage percentage and altitude from the present climate simulations toward warmer and drier climate zones. The calculated climate indices feature changes in the following parameters: increases in the mean annual temperature, growing season temperature, number of growing degree days (higher than 5 ∘ C) and the frequency of tropical days; and decreases in the mean annual precipitation, growing season precipitation and frequency of frost days. Yields of crops (winter wheat, maize and soybeans) will increase on average under both scenarios, with the exception of maize in non-irrigated conditions and under the A2 scenario.

We have used the Kolmogorov complexities, sample and permutation entropies to quantify the randomness degree in river flow time series of two mountain rivers in Bosnia and Herzegovina, representing the turbulent environmental fluid, for the period . In particular, we have examined the monthly river flow time series from two rivers (Miljacka and Bosnia) in mountain part of their flow and then calculated the Kolmogorov Complexity (KL) based on the Lempel-Ziv Algorithm (LZA) (Lower -KLL and Upper -KLU), Sample Entropy (SE) and Permutation Entropy (PE) values for each time series.The results indicate that the KLL, KLU, SE and PE values in two rivers are close to each other regardless of the amplitude differences in their monthly flow rates. We have illustrated the changes in mountain river flow complexity by experiments using (i) the data set for the Bosnia River and (ii) anticipated human activities and projected climate changes. We have explored the sensitivity of considered measures in dependence on the length of time series. In addition, we have divided the period 1926-1990 into three subintervals: (a) 1926 -1945, (b) 1946-1965, (c) 1966-1990, and calculated the KLL, KLU, SE, PE values for the various time series in these subintervals. It is found that during the period 1946 -1965, there is a decrease in their complexities, and corresponding changes in the SE and PE, in comparison to the period 1926-1990. This complexity loss may be primarily attributed to (i) human interventions, after the Second World War, on these two rivers because of their use for water consumption and (ii) climate change in recent time.

Motivated by the One Health paradigm, we found the expected changes in temperature and UV radiation (UVR) to be a common trigger for enhancing the risk that viruses, vectors, and diseases pose to human and animal health. We compared data from the mosquito field collections and medical studies with regional climate model projections to examine the impact of climate change on the spreading of one malaria vector, the circulation of West Nile virus (WNV), and the incidence of melanoma. We analysed data obtained from ten selected years of standardised mosquito vector sampling with 219 unique location-year combinations, and 10 years of melanoma incidence. Trends in the observed data were compared to the climatic variables obtained by the coupled regional Eta Belgrade University and Princeton Ocean Model for the period 1961-2015 using the A1B scenario, and the expected changes up to 2030 were presented. Spreading and relative abundance of Anopheles hyrcanus was positively correlated with the trend of the mean annual temperature. We anticipated a nearly twofold increase in the number of invaded sites up to 2030. The frequency of WNV detections in Culex pipiens was significantly correlated to overwintering temperature averages and seasonal relative humidity at the sampling sites. Regression model projects a twofold increase in the incidence of WNV positive Cx. pipiens for a rise of 0.5˚C in overwintering T October-April temperatures. The projected increase of 56% in the number of days with T max � 30˚C (Hot Days-HD) and UVR doses (up to 1.2%) corresponds to an increasing trend in melanoma incidence. Simulations of the Pannonian countries climate anticipate warmer and drier conditions with possible dominance of temperature and number of HD