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A streamflow time series encompasses a large amount of hidden information and reliable prediction of its behavior in the future remains a challenge. It seems that the use of information measures can significantly contribute to determining the time horizon of rivers and improving predictability. Using the Kolmogorov complexity (KC) and its derivatives (KC spectrum and its highest value), and Lyapunov exponent (LE), it has previously been shown that the degree of streamflow predictability depends on human activities, environmental factors, and natural characteristics. This paper applied the KC and LE measures to investigate the randomness and chaotic behavior of monthly streamflow of 1879 rivers from the United States for a period from 1950 to 2015 and evaluated their time horizons via the Lyapunov and Kolmogorov time (LT and KT, respectively)., Comment: 27 pages, 10 figures

From the perspective of the physics of complex systems (1) we deal with the current state of modern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context; (2) considering the strength of the Goedel Incompleteness Theorems we point out the following open questions in physics: (i) the limits of the precision of certainty, (ii) the limits of making decisions on information and (iii) the limitations of reasoning that sometimes affect progress, (3) since further advances will necessarily require synergy between physics and seemingly distinct fields - mathematics, information science, chemistry, biology, medicine, psychology, and art. We illustrate this relation by providing examples based on our research. Point (1) is discussed in Ch1 while Ch2-Ch5 encompasses the point (2) and point (3) is covered in Ch6-Ch10.

From the perspective of the physics of complex systems (1) we deal with the current state of mod-ern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context; (2) considering the strength of the Goedel s Incompleteness Theorems we point out the following open questions in physics: (i) the limits of the precision of certainty, (ii) the limits of making decisions on information and (iii) the limitations of reasoning that sometimes affect progress, (3) since further advances will necessarily require synergy between physics and seemingly distinct fields - mathematics, information science, chemistry, biology, medicine, psychology, and art. We illustrate this relation by providing examples based on our research. Point (1) is discussed in Ch1 while Ch2-Ch5 encompasses the point (2) and point (3) is covered in Ch6-Ch10.

Analysis of daily streamflow variability in space and time is important for water resources planning, development, and management. The natural variability of streamflow is being complicated by anthropogenic influences and climate change, which may introduce additional complexity into the phenomenological records. To address this question for daily discharge data recorded during the period 1989-2016 at twelve gauging stations on Brazos River in Texas (USA), we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures to assess complexity, and Lyapunov time (LT) to assess predictability. We find that all daily discharge series exhibit long memory with an increasing downflow tendency, while the randomness of the series at individual sites cannot be definitively concluded. All Kolmogorov complexity measures have relatively small values with the exception of the USGS (United States Geological Survey) 08088610 station at Graford, Texas, which exhibits the highest values of these complexity measures. This finding may be attributed to the elevated effect of human activities at Graford, and proportionally lesser effect at other stations. In addition, complexity tends to decrease downflow, meaning that larger catchments are generally less influenced by anthropogenic activity. The correction on randomness of Lyapunov time (quantifying predictability) is found to be inversely proportional to the Kolmogorov complexity, which strengthens our conclusion regarding the effect of anthropogenic activities, considering that KC and LT are distinct measures, based on rather different techniques.

We examine the threshold of the influence of the tunneling nanotubes (TNTs) on the cell-to-cell communication integrity. A deterministic model is introduced with the Michaelis-Menten dynamics and the intercellular exchange of substance. The influence of TNTs are considered as a functional perturbation of the main communication and treated as the matrix nearness problems. We analyze communication integrity in terms of the \emph{pseudospectra} of the exchange, to find the \emph{distance to instability}. The threshold of TNTs influence is computed for Newman-Gastner and Erd\H{o}s-R\'enyi gap junction (GJ) networks., Comment: 6 pages, 4 figures

We have considered the complexity and asymptotic stability in the process of biochemical substance exchange in a coupled ring of cells. We have used coupled maps to model this process. It includes the coupling parameter, cell affinity and environmental factor as master parameters of the model. We have introduced: (i) the Kolmogorov complexity spectrum and (ii) the Kolmogorov complexity spectrum highest value to analyze the dynamics of two cell model. The asymptotic stability of this dynamical system using an eigenvalue-based method has been considered. Using these complexity measures we have noticed an 'island' of low complexity in the space of the master parameters for the weak coupling. We have explored how stability of the equilibrium of the biochemical substance exchange in a multi-cell system (N=100) is influenced by the changes in the master parameters of the model for the weak and strong coupling. We have found that in highly chaotic conditions there exists space of master parameters for which the process of biochemical substance exchange in a coupled ring of cells is stable., Comment: 17 pages, 8 figures; This paper has been submitted to Chaos, Solitons and Fractals

Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's Theorem and Rosen's definition of complexity and predictability is discussed. It is pointed out to occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form. A coupled system of equations, often used in climate models is analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this systems. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, is analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameters, the logistic parameter and the parameter of exchange, was studied calculating the Lyapunov exponent under simulations with the closed contour of N=100 environmental interfaces. Finally, we have explored possible differences in complexities of two global and two regional climate models using their output time series by applying the algorithm for calculating the Kolmogorov complexity., Comment: 21 pages, 6 figures, 1 table; This paper has been submitted to Advances in Meteorology

We consider an environmental interface regarding as a complex system, in which difference equations for calculating the environmental interface temperature and deeper soil layer temperature are represented by the coupled maps. First equation has its background in the energy balance equation while the second one in the prognostic equation for deeper soil layer temperature, commonly used in land surface parameterization schemes. Nonlinear dynamical consideration of this coupled system includes: (i) examination of period one fixed point and (ii) bifurcation analysis. Focusing part of analysis is calculation of the Lyapunov exponent for a specific range of values of system parameters and discussion about domain of stability for this coupled system. Finally, we calculate Kolmogorov complexity of time series generated from the coupled system., Comment: 12 pages, 6 figures; This paper has been publish in Modern Physics Letters B, Volume No.27, Issue No. 26

We have suggested a complexity measure based method for studying the dependence of measured 222Rn concentration time series on indoor air temperature and humidity. This method is based on the Kolmogorov complexity (KL). We have introduced (i) the sequence of the KL, (ii) the Kolmogorov complexity highest value in the sequence (KLM) and (iii) the KL of the product of time series. The noticed loss of the KLM complexity of 222Rn concentration time series can be attributed to the indoor air humidity that keeps the radon daughters in air., Comment: 20 pages, 4 figures; This paper has been submitted to Applied Radiation and Isotopes

We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the physical as well as other complexities. To get better insights into the complexity of complex systems and time series analysis we have introduced the 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 on different time series originating from: the model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and economy (stock prices dynamics). Results which are obtained offer deeper insights into complexity of the system dynamics behavior and time series analysis when the proposed complexity measures are applied., Comment: 22 pages, 13 figures, 1 table; This paper has been submitted to Physica A on Oct, 4th 2013

We have used the Kolmogorov complexity and sample entropy measures to estimate the complexity of the UV-B radiation time series in the Vojvodina region (Serbia) for the period 1990-2007. We defined the Kolmogorov complexity spectrum and have introduced the Kolmogorov complexity spectrum highest value (KLM). We have established the UV-B radiation time series on the basis of their daily sum (dose) for seven representative places in this region using (i) measured data, (ii) data calculated via a derived empirical formula and (iii) data obtained by a parametric UV radiation model. We have calculated the Kolmogorov complexity (KL) based on the Lempel-Ziv Algorithm (LZA), KLM and Sample Entropy (SE) values for each time series. We have divided the period 1990-2007 into two sub-intervals: (a) 1990-1998 and (b)1999-2007 and calculated the KL, KLM and SE values for the various time series in these sub-intervals. It is found that during the period 1999-2007, there is a decrease in the KL, KLM and SE, comparing to the period 1990-1998. This complexity loss may be attributed to (i) the increased human intervention in the post civil war period causing increase of the air pollution and (ii) the increased cloudiness due to climate changes., Comment: 10 pages, 1 figure, 1 table. arXiv admin note: substantial text overlap with arXiv:1301.2039; This paper has been accepted in Modern Physics Letters B on Aug 14, 2013

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 1926-1990. 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 sub-intervals: (a) 1926-1945, (b)1946-1965 and (c)1966-1990, and calculated the KLL, KLU, SE and PE values for the various time series in these sub-intervals. 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 Second World War, on these rivers because of their use for water consumption and (ii) climate change in recent time., Comment: 13 pages, 4 figures, 1 table; This paper has been accepted in Physica A on Sept 25, 2013

Exchange of biochemical substances is essential way in establishing communication between bacterial cells. It is noticeable that all phases of the process are heavily influenced by perturbations of either internal or external parameters. Therefore, instead to develop an accurate quantitative model of substances exchange between bacterial cells, we are interested in formalization of the basic shape of the process, and creating the appropriate strategy that allows further investigation of synchronization. Using a form of coupled difference logistic equations we investigated synchronization of substances exchange between abstract cells and its sensitivity to fluctuations of environmental parameters using methods of nonlinear dynamics., Comment: 23 pages, 5 figures

Communication between cells is realized by exchange of biochemical substances. Due to internal organization of living systems and variability of external parameters, the exchange is heavily influenced by perturbations of various parameters at almost all stages of the process. Since communication is one of essential processes for functioning of living systems it is of interest to investigate conditions for its stability. Using previously developed simplified model of bacterial communication in a form of coupled difference logistic equations we investigate stability of exchange of signaling molecules under variability of internal and external parameters., Comment: 11 pages, 3 figures