ISCS 2013: Interdisciplinary Symposium on Complex Systems

In this paper, we give a brief overview of the geometry of the Mandelbrot set. We show how to distinguish each of the principal bulbs hanging off the main cardioid of this set by counting the spokes of the antennas attached to each bulb. We also use these antennas to attach a fraction to each such bulb, and this then indicates how these bulbs are arranged around the boundary of the main cardioid.

In their seminal works, Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type,

$$S=-\sum \nolimits _i p_i \log p_i$$

. In many physical systems one of these axioms may be violated. For non-ergodic systems the so called separation axiom (Shannon-Khinchin axiom 4) is not valid. We show that whenever this axiom is violated the entropy takes a more general form,

$$S_{c,d}\propto \sum _i ^W \Gamma (d+1, 1- c \log p_i)$$

, where

$$c$$

and

$$d$$

are scaling exponents and

$$\Gamma (a,b)$$

is the incomplete gamma function. These exponents

$$(c,d)$$

define equivalence classes for

all

!, interacting and non interacting, systems and unambiguously characterize any statistical system in its thermodynamic limit. The proof is possible because of two newly discovered scaling laws which any entropic form has to fulfill, if the first three Shannon-Khinchin axioms hold [1].

$$(c,d)$$

can be used to define equivalence classes of statistical systems. A series of known entropies can be classified in terms of these equivalence classes. We show that the corresponding distribution functions are special forms of Lambert-

$$\mathcal{W}$$

exponentials containing—as special cases—Boltzmann, stretched exponential, and Tsallis distributions (power-laws). We go on by showing how the dependence of phase space volume

$$W(N)$$

of a classical system on its size

$$N$$

, uniquely determines its extensive entropy, and in particular that the requirement of extensivity fixes the exponents

$$(c,d)$$

, [2]. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a

generalized

(non-additive) form. We showed that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit [2]. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional ‘surface’. We explicitly illustrated the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion [2]. In this contribution we largely follow the lines of thought presented in [1–3].

Insights and methods of complex systems science are transforming science and providing clarity about the impact of policies to address major societal problems. These conceptual and mathematical advances allow us to study interdependence, patterns, networks, multiscale behaviors, and “big data.” Here I focus on the application of these advances to real-world concerns. I discuss case studies from global socioeconomic systems and immune cell regulation. Our analysis of the global food crisis exposes the causes and consequences of rapidly increasing and volatile food prices. Food price spikes in 2007–2008 and 2010–2011 triggered food riots across the world and precipitated the Arab Spring. Our quantitative models of nonequilibrium markets show that the food price increases are due to (1) US biofuel quotas increasing the amount of corn to ethanol conversion and (2) deregulation of commodity trading enabling speculator trend-following to cause bubbles and crashes. Policy action by the US and the European Union could alleviate or even resolve these problems. Our analysis of cell regulation makes use of gene expression data to obtain whole-cell regulatory models describing the response of immune cells to dynamic perturbations. Moreover, we have shown that cell dynamics are controlled by attractor states with implications for understanding biological development and treating cancer. Our analyses demonstrate the opportunity for complex systems science to inform both social policy decisions and medical advances.

This chapter presents a method for visualization of the dynamics of evolutionary algorithms in the form of complex networks and is continuation of our previous research. The analogy between individuals of populations in an arbitrary evolutionary algorithm and vertices of a complex network is mentioned, as well as between edges in a complex network and communication between individuals in a population. Visualization of various attributes of network based on differential algorithm is presented here.

The brain equation is a solution to the “second survival problem.” The latter is called “positional adaptation.” It unlike Darwin’s first (“metabolic adaptation”) is history-independent. As such it is mathematically well posed. The equation applies to all life forms in the cosmos that live in a structured environment in which survival depends on position in space in a short-term fashion. An eusocial version does not exist. The equation solves, in conjunction with the necessarily attached VR machine, the famous NP-complete “decision-type travelling salesman problem” for finite times. The resulting autonomous optimizer with cognition is susceptible to a “function change” in the sense of Bob Rosen which so far is known empirically only from the human brain.

Understanding the dynamical behavior of many-particle systems both in and out of equilibrium is a central issue in both statistical mechanics and complex systems theory. One question involves “nature versus nurture”: given a system with a random initial state evolving through a well-defined stochastic dynamics, how much of the information contained in the state at future times depends on the initial condition (“nature”) and how much on the dynamical realization (“nurture”)? We discuss this question and present both old and new results for low-dimensional Ising spin systems.

Cellular automata and L-Systems are well-known formal models to describe the behaviour of biological processes. They are discrete dynamical systems, each of which can have complex and varied behaviour. Here, we study a class of substitutive systems incorporating properties of both cellular automata and L-systems, that exhibits self-reproducing behaviour. A one-dimensional array of cells is considered, each cell has a set of modes or states which are determined by a number from

$$\mathbb {Z}/\mathbf{{n}}\mathbb {Z}^*$$

(

$$n$$

prime). The behaviour of a cell depends on the states of its neighbours and obeys an additive rule. It has also a cell-division mode, which allows the line of cells to grow. The behaviour of such a model can be complex, but, using algebraic techniques, we prove that it can describe a reproducing system.

Globalization leads us towards dealing with very complex systems that consist of evolving, overlapping, and interacting “socio-technical fabrics”. An existing general systems control theory cannot cope with problems occurring in such systems. This chapter is, first of all, an attempt to present an entirely new approach to the adequacy of system model and reality, based on a causal correspondence between information and knowledge obtained from a reality and its model. Secondly, the chapter suggests two possible control loops: one is meant to improve the model and another is the way to attain a certain planned goal to be reached by our reality. Four doctrines are presented as the basic principles of general fuzzy systems control theory (GFSCT) aiming to deal with the real fuzzy systems operating and functioning in a multiple space-time coordinate system. The minimization of a certain potential V-function is considered as a universal principle for existence of each system in the real world. Moreover, decentralized stochastic control is proposed to improve our reality and guarantee its lifetime unlimited behavior with a proper degree of certainty and space-time stability.

In this chapter are described some properties of emergent phenomena and situations that appear in natural complex systems. There are introduced three classes of unexpected situations and two of them belong to emergent situations. For the detecting possibility of appearance of emergent situation is used the indication of violation of structural invariant of the complex system. Here is used only one type of structural invariant—matroid and matroid bases. A simple calculus for the emergent situation appearance computation is introduced. The application of the presented approach and computation method is demonstrated by three simple emergent situations: the change of the strategy in swarm colony, traffic jam and floods.

All complex systems presenting chaotic behaviour are non-linear ones and many problems of their analysis and modelling are caused by application of linear or pseudo-linear models which are not able to represent all aspects of signals generated by these systems. Experiments with some natural-based signal data like e.g. EEG ones concluded presence of typical composite periodic functions, like sin(sin(x)). These functions have specific behaviours which will be presented. Especially, they are non-stationar, have continuous spectrum and thus it is hard to apply usual tools like Fourier transform. To analyse these signals, evolutionary GPA-ES system was used.

Based on the information theory of mutifractal objects was developed the method for analysis of complex self-organized system, such as living cells. To demonstrate some of the features of the analysis we choose the simplest system—the Belousov–Zhabotinsky reaction (chemical clock). It is always composed of observed sequence of states stable for certain period of time and the experimenter has full control of mechanical constraints imposed on the system. We use the Renyi information entropy equation for calculation of information gain by which a point contributes to the total information in the image. In this way we create characteristic vector of the system state in phenomenological coordinates of phase space. We have also derived related variables, the point information gain entropy and point information gain entropy density. The later values are unique to structured information. The ultimate goal of the method is to determine the characteristics of a system which best characterize momentary multifractal properties of the system. The relation between the phenomenological phase space and the internal coordinates of the system remain unknown.

The relevance of classical invariants in the quantization and dynamics of quantum systems is discussed. Special attention is paid to the influence of periodic orbits (“

scars

”) and the associated homoclinic and heteroclinic orbits. As an illustration we present some results concerning the vibrational dynamics of the LiNC/LiCN isomerizing system.

Be stars are characterized by prominent emission lines in their spectrum. In the past research has attention been given to creation a feature extraction method for classification of Be stars with focusing on the automated classification of Be stars based on typical shapes of their emission lines. The aim was to design a reduced, specific set of features characterizing and discriminating the shapes of Be lines. In this chapter we discuss possibility to create in an evolutionary way the model of spectra of Be stars. We focus on the evolutionary synthesis of the mathematical models of Be stars based on typical shapes of their emission lines. Analytical programming powered by classical random as well as chaotic random-like number generator is used here. Experimental data are used from the archive of the Astronomical Institute of the Academy of Sciences of the Czech Republic. Interpretation and explanation of analysis is given and discussed in this chapter.

The knowledge of several transport properties is important especially when heat transfer has to be evaluated. However, not always the data such as thermal diffusivity is known or available for specific types of material. In this paper, a study was performed to describe the equations that lead to the calculus of thermal diffusivity, heat transfer and calculus of temperature in function of time of a sphere particle that is immersed in a well stirred fluid. The model obtained was tested by comparing the predicted thermal diffusivity value of an orange and the real value.

Dynamical traps as a new emergence mechanism related to the bounded capacity of human cognition is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. This is described in terms of some neighborhood of the equilibrium point, the region of dynamical traps, wherein each point is regarded as an equilibrium one by the operators. So when a system enters this region and while it is located in it, maybe for a long time, the operator control is suspended. A simple model of oscillator with dynamical traps and the characteristic features of its dynamics are discussed. Experiments on the balancing of a virtual pendulum were conducted to examine the basic features of human control over unstable systems that are expected to be affected by human fuzzy rationality. It is demonstrated that practically only the dimensions of the phase space region wherein a given pendulum trajectory is located depend on the subject age and skill as well as the pendulum parameters determining the difficulty of the balancing. In contrast, the forms of the distribution functions are the same for all the subjects. The data of the virtual experiments are compared to the results of numerical simulation of the oscillator with dynamical traps. The phase trajectories and the phase variable distributions are shown to be similar for the two systems. In addition a chain of oscillators with dynamical traps which mimics cooperative interaction of human operators is considered also. It is, actually, demonstrated that the human fuzzy rationality can cause complex cooperative dynamics in many-element ensembles.

This chapter describes model of the human cognitive functions, especially these ones which are important for the creative process. The broad context of this work is a development of the conceptual redesign method with computer support (called CRDP—Computer Redesign Process). This method is based on postmodern principles of the interpretation, on the respect to complexity of the creative process and at the impossibility of its direct control. Psychological approaches (e.g. the mind mapping [1] or creativity timing) are used in this interpretation method and its core is a creating of the interpretation map. The aim of this submission is to describe the emergent design processes for the purpose of their simulation and method’s HCI improving. The model is made in Unify Modelling Language. The fractal approach to the communication between user (designer) and software system (CRDP) was outlined.

Mathematical modeling of clinical systems is difficult as these usually comprise complex systems with many interacting components. We show how it is still possible to model these systems by making use of a dynamical systems point of view. By calculating bifurcation diagrams, one can discriminate between different models and clinical parameter regimes can be identified. The emphasis in this presentation will be in particular on models of atherosclerosis, but the suggested approach is applicabe to a much wider class of clinical models.

We propose a spatially extended deterministic model with time delay for the circadian oscillations in the fungal species

Neurospora crassa

. The temporal behavior of the system is governed by a two variable model based on the nonlinear interplay between the

FRQ

and

WCC

proteins which are products of transcription of

frequency

and

white collar

genes. We show numerically that the model accounts for various features observed in experiments. Spatio-temporal protein patterns excited in

Neurospora

in complete darkness are studied for different initial conditions. It is shown that basal activation of transcription factors has a strong effect on pattern formation.

A new algorithm for calculating the dynamics of spatially-extended reaction-diffusion systems where the current state depends on the whole or partial previous evolution of the system is proposed. The algorithm is based on a finite difference method and involves an adaptive optimization of data storage by storing in a computer memory not all previous nodal data, but only some selected of them, called the base states. The intermediate states are restored by interpolation between the base states. The use of this technique allows the numerical calculations to be implemented on computer systems without large RAM memory. The algorithm efficiency is shown in three numerical examples.

This paper presents a novel approach for the problem of detecting and extracting the QRS complex of electrocardiogram signals for different kinds of arrhythmias. First, an autocorrelation function is used in order to obtain the period of an electrocardiagram signal and then the Hilbert transform is applied to obtain R-peaks and beats. Twenty three different records extracted from the MIT-BIH arrhythmia database were used to validate the proposed approach. In this testing has been observed a 99.9 % of accuracy in detecting the QRS complexity, being a positive result in comparison with other recent researches.

Electricity price is by its features like mean-reversion, high volatility rate and frequent occurrence of jumps different from other commodities. These differences are mainly caused by non-storability of the electricity, which need to balance supply and demand in real time. Due to these features, electricity price behavior seems somewhat chaotic. In this chapter we will introduce methods for investigating whether or not electricity spot prices can be described by usual time series, stochastic models. For this reason we will estimate the largest Lyapunov exponent and the 0–1 test for chaos. We will do a case study on the EPEX Phelix spot index.

We show that a number of realistic financial time series can be well mimicked by multiplicative multifractal cascade processes. The key observation is that the multi-scale behavior in financial progressions fits well the multifractal cascade scaling paradigm. Connections with Kolmogorov’s idea of multiplicative cascade of eddies in the well developed turbulence are briefly discussed. To put some flesh on a bare bones we compare volatility time series for S&P 500 stock index with a simulated multiplicative multifractal cascade processes. Qualitative agreement is surprisingly good. Salient issues, such as Codimension functions or Multifractal Diffusion analysis and its role in scaling identification are also discussed.

It is shown that catastrophic processes of the Earth occur at simultaneous action of several groups of factors that include external global space influences (the Sun and the Moon) and internal geological influences, which provide the condition in strong earthquake area. The chaotic space-time distribution of earthquakes tells us about this. On the basis of the analysis of events occurring during 110 years it is possible to assert that on an average quantity the number of earthquakes with magnitude

$$\mathrm{M}\ge 7$$

has not increased. From the other hand, time intervals when the time distribution of earthquakes has periodic character are found. The purpose of this work is to reveal time intervals, during of which there is predominant influence of the separate factor. In order to do this we use statistical methods. The problem is complex because the ensemble of factors is impacting. By assuming a simultaneous influence of several factors (the Sun, the Moon and geological conditions) we performed the statistical division of the time series consisting of >500 events (during 1973–2005) into groups, in which one can see the influence of separate factors. It has been shown that the geological factor and the cyclic character of the Moon influence play the main role in appearance of the seismic activity.

The simple three variable evolutionary model of boreal forest of Perm region has been proposed. The model is built as a complex system, where each population is represented by individual trees competing for solar light. Other factors taking into account are growth rate, seed dispersal and mortality. The parameter values used in the model were calibrated from the information available for Perm forests. This work has a fundamental aspect because a formation of dynamical macroscopic patterns in ecological systems attracts great interest of researchers. In addition, the proposed model can have many applications for more effective forest management.

Many real-world networks lend themselves to the use of graphs for analysing and modeling their structure. This approach has proved to be very useful for a wide variety of networks stemming from very different fields. Yet, only few papers focused their attention on legal networks. This paper intends precisely to remedy this situation by analysing a major legal network by means of complex system methods. The network under investigation is the network composed by decisions taken by the International Criminal Court since its creation. We first model the network by a simple directed graph in which nodes are the decisions and links represent citations between decisions. Our analysis shows that standard properties shared by common real networks are also present in this network. Then we turn to studying the network by means of bipartite graphs that involve both decisions and articles of law. We show that this two-level structure presents several non trivial properties and we show evidences of the relevance of the bipartite representation to explain properties observed in the graph of citations.

In this chapter we present the application of control theoretical concepts to stochastic dynamical systems which are based on the current knowledge of genetic networks. We showcase the application of reinforcement learning algorithm inferring an optimized control strategy for a genetic switch reversal. The approach does not require precise knowledge of gene network mathematical equations and is therefore also applicable to experimentally obtained time traces.

The density classification problem aims to find automata able to correctly classify the density of the initial configuration. This problem is highly challenging as the desired computation requires global coordination while Cellular Automata (CAs) rules rely on the local interaction of simple components. Instead of using the standard CA topology of regular lattice, the current chapter focuses on network topologies that can be used in connection with a simple fixed rule in CA computation. The state of a cell evolves according to the majority of its neighbors in the network. In this chapter, we propose a hill-climbing approach to find good network topologies for the density classification problem starting from initial small-world networks. The network solution space is searched in a random hill-climbing manner based on a simple mutation operator changing the network each iteration. Experiments emphasize the identification of network topologies with a good performance for CA computation. The best identified networks are further studied under a dynamic framework to test their robustness against failures and changes that might occur in the network. Results confirm a good sustained performance of networks identified using hill-climbing search.

We show with two simple examples, one—an autocorrelated random walk, the other—an accelerated random walk, that two processes that are fundamentally different on a microscopical level, so different in fact that the two processes implement different types of entropic concepts, still can be indistinguishable from a probabilistic point of view, i.e. all finite moments of the two processes may coincide. The immediate consequence of this observation is that entropy primarily is a property associated with the structure of phase-space rather than a consequence of specific observable distribution functions.

This paper deals with complex network constructing with using evolutionary algorithm SOMA AllToOne version. The main goal is to visualize complex networks developing and analyse their properties, especially in-degrees and their realiances on fitness value evolution. Thank this analysis we can make an analysis of the populations evolutions during the evolutionary algorithm.

The aim of this work is to present a new algorithm for the evaluation of sentiment in Czech language texts. The algorithm is based on a new dictionary and uses n-gram searching. For the creation of the dictionary, it was important to use language specific phrases and exceptions, which can completely change the final evaluation of a sentiment. The solution also includes automatic search for a new subjects (aspects) of evaluation and also searching for new words determining sentiment. A similar algorithm can also be applied to other languages. The work emphasizes the transformation of the acquired data into valuable information. Our experiment is realized in the experimental adaptive web system in e-learning content domain and in eShop domain. The success and benefits of the algorithm are also discussed in this text.

Ecosystems are open, self-organizing systems and energy of different quantity and quality provides the stimulus for organization, enabling different processes to progress at different rates. Here, information acts internally within the system to constrain its behavior, which can also flow into the system from outside, thereby prompting the self-organizing processes. The interplay of environmental conditions, energy, matter, and information defines the context and constraints for the set of processes and structures that may emerge during self-organization. Using the KoFlux tower-based measurements of energy, water and CO 2 flux time series in 2008 in a temperate forest in Korea, we have evaluated statistical measures of characterizing the organization of the information flow in ecohydrological process networks in a forest ecosystem. Here, process network is a network of feedback loops and direction of flow of matter, energy and information between the different variables. The goal of this study is to understand how ecosystem organization changes in time, and identify and characterize network-scale emergent properties by quantifying the varying ecosystem states. Ecosystem integrity is preserved when its self-organizing processes are preserved. The inherent challenges associated with the time series data and the potential use of this conceptual approach and statistical tools are discussed for sustainable ecosystem management.

The successful surface activation and joint promotion of lightweight aircraft grade carbon composites using atmospheric pressure plasma jets has the to improve the economics of the aircraft industry. To achieve these economic savings the technological challenge of plasma processing of thermally sensitive composites must be met in an industrial manufacturing environment. This chapter describes an acoustic plasma control strategy that is based upon the complex acoustic dynamics of the plasma-composite interaction.

This paper reviews some of the major approaches to the evolution of altruism and cooperation, addressing the question of how fitness reducing behaviors could evolve and become fixed in a population. An often overlooked important point is that human psychology must be taken into account, in particular the way that personal identity is tied to adherence to social and cultural norms and approved behaviors resulting in an identification of personal biological survival with a social group and the markers of that group.

Three characteristic scales of a biological system are distinguished in the chapter: microscopic (gene’s size), mesoscopic (cell’s size) and macroscopic (organism’s size). For each case the approach to modeling of the circadian rhythms is discussed on the base of a time-delay model. The stochastic description has been used at the gene’s scale. The deterministic description within the spatially extended model has been suggested on the mesoscopic scale. Macroscopic effects have been analyzed within the discrete model describing the collective behaviour of large amount of cells. The effect of collective rhythms synchronization for each case has been studied. The problem of cross-linking of the results obtained at different scales is discussed.

In this chapter, previously proposed utilization of discrete Lozi map based chaos pseudo-random number generator to enhance the performance of PSO algorithm is investigated with the detailed focus on the chaotic system dynamics. The elaborated tuning of chaotic system accessible parameters based experiment is presented here together with the investigation on the impact to the performance of PSO algorithm.

This work represents the brief introduction into the issue of development of complex cost function for evolutionary optimization of control of discrete chaotic systems. This work introduces briefly the evolutionary approach representing tuning of parameters for an existing control method. The main part of this work is focused on the process of development of the proper cost function design used within the evolutionary process. As an example of discrete chaotic system, two-dimensional Hénon map was used.

Geodynamic processes are acting in the Earth’s interior and they cause earthquakes of various intensity. Earthquakes occur randomly and they are often in clusters. Sometimes it happens that before strong earthquakes there is a seismic quiescence that is characterized by the absence of significant seismic events. This may indicate that Earth’s geological system prepares itself for a catastrophe. Complexity theory describes regularities of the behavior of dynamical systems before the occurrence of a disaster. The main part of this chapter is formulating a problem to investigate the behavior of a geophysical parameter, namely seismic velocity before the occurrence of the strong earthquake. Considering that velocity is a random variable, we apply the distribution function to estimate the dynamic state of the strong earthquakes complex system.

The Tjörnes Fracture Zone (TFZ) is an active seismic zone in Northeast Iceland. It plays a key role to understand the geodynamic movement and location of tectonic plates. However the seismic experiment can not be performed close to earthquake sources, because sources are mainly located in the Greenland Sea. The unusual geological structure of TFZ and the limited conditions of an experiment lead to significant deviations between real observations and the values that are calculated in accordance with theoretical models. Consequently, there is a loss of adequacy and stability of tomography systems. Outcomes of the method, which takes into account this problem, are analyzed in the present chapter. Values and locations of P-wave velocity anomalies are comparing with those, which previously obtained from studies in geochemistry field and with GPS data.

A distinctive features of the Ahtyirskiy fault (Krasnodar, Russia) are its long length and the unusual geological structure. The fault demarcates the boundary between highlands and flat landform. To study the fault displacement we have applied two methods. The first structural–geo-morphological method reconstructs orientation of the compression/expansion axis in a horizontal plane and thus determines the direction of a horizontal displacement along the fault. In this study the method has been modified by analyzing of individual segments of the Ahtyirskiy fault. Another method is the microseismic sounding that determines a distribution of surface wave characteristics in a vertical plane. We conclude that the displacement along the fault has average direction, which we call the upthrust right-shift. However there are segments that are deformed in a special manner and displacements along them can not be explained via theoretical models. Mainly the fault plane falls to the south direction while its individual parts fall to the north.