Proceedings Series


Vol. 5 (2012), No. 1, pp. 1 – 190

Summer Solstice 2011 International Conference on Discrete Models of Complex Systems

Turku, Finland; June 6–10, 2011

Chaos, Synchronization and Control in Cellular Automata

abstract

We investigate the mechanism of pinching synchronization (complete synchronization for a fraction of system) for cellular automata, considered as prototypes of discrete systems with unpredictable behaviour (finite-distance chaoticity). The pinching synchronization threshold is related to this chaoticity. Some control problems may be reformulated as targeted synchronization. In these problems one aims at discovering a protocol that keeps the distance between two replicas below a certain threshold with the minimum effort, given some constraints. We have chosen to investigate the behaviour of two control schemes based on the local number of non-zero first-order derivatives, taking as reference the “blind” pinching synchronization protocol. We have shown that, differently from usual chaotic systems, one can exploit self-annihilation of defects to obtain synchronization with a weaker control.


Modelling a Simple Adaptive Cognitive Agent

abstract

Agent-based models approximate the behaviour of simple natural and man-made systems. Their performance is limited by the abstractions used to implement them, i.e. , finite state machines. “Cognitive Agents” perform “Cognitive Acts” (i.e. , Perceiving, Reasoning, Judging, Responding, and Learning) and are the closest to the behaviour of simple biological entities. We present a simple cognitive agent capable of evaluating if a strategy has been applied successfully and capable of applying this strategy again with small changes to a similar but new situation. We describe how a simple agent can be trained to learn how to safely cross a road with “one lane one directional highway” and later, when the situation changes, a road with “two lanes one directional highway” and “two lanes on a bi-directional highway”. Future research is outlined.


Structural Hamiltonian of the International Trade Network

abstract

It is common wisdom that no nation is an isolated economic island. All nations participate in the global economy and are linked together through trade and finance. Here, we analyze international trade network (ITN), being the network of import–export relationships between countries. We show that in each year over the analyzed period of 50 years (since 1950) the network is a typical representative of the ensemble of maximally random networks. Structural Hamiltonians characterizing binary and weighted versions of ITN are formulated and discussed. In particular, given binary representation of ITN (i.e. binary network of trade channels) we show that the network of partnership in trade is well described by the configuration model. We also show that in the weighted version of ITN, bilateral trade volumes (i.e. directed connections which represent trade/money flows between countries) are only characterized by the product of the trading countries’ GDPs, like in the famous gravity model of trade.


The Dependency Network in Free Operating System

abstract

Phenomena observed in many complex systems can be attributed to their network structure. In this paper we present an analysis of the dependency network of a large software project — Debian Operating System (GNU/Linux distribution) and show its properties, like power-law degree distribution, modularity and hierarchical organization.


Rotor-routing Algorithms Described by CA-w

abstract

The GCA-w model (Global Cellular Automata with write access) is an extension of the GCA (Global Cellular Automata) model, which is based on the cellular automata model (CA). Whereas the CA model uses static links to local neighbors, the GCA model uses dynamic links to potentially global neighbors. The GCA-w model is a further extension that allows modifying the neighbors’ states. Thereby neighbors can dynamically be activated or deactivated. Algorithms can be described more concisely and may execute more efficiently because redundant computations can be avoided. If the neighborhood of the GCA-w model is locally restricted, we will call the model “CA-w” (Cellular Automata with Write-access). Rotor-routing algorithms are good examples showing the usefulness of the CA-w model. The Propp-machine and the Chip-firing problem are first described by CA for comparison, and then by CA-w. It is shown that the CA-w descriptions are more concise, more “natural” compared to the CA descriptions, and more power saving because only the active cells have to be computed.


Structural Stochastic Multiresonance in the Ising Model on Two Coupled Scale-free Networks

abstract

The phenomenon of structural stochastic multiresonance is studied in the Ising model on a composite network consisting of two coupled scale-free subnetworks with, possibly, different critical temperatures for the ferromagnetic transition, driven by a weak, slowly oscillating magnetic field. Theoretical results obtained from the linear response theory in the mean-field approximation and numerical results from Monte Carlo simulations yield qualitatively similar results. The spectral power amplification, evaluated from the time-dependent order parameter, as a function of temperature exhibits two or, possibly, three maxima, depending on the exponent in the power-law tails of the degree distributions of the subnetworks and the fraction of inter-network edges. For small to moderate fraction of inter-network edges sharp maxima occur at temperatures close to the critical ones for the Ising model on the individual subnetworks. For densely coupled networks the spectral power amplification is determined mainly by the response of the spins on the subnetwork with higher critical temperature to the oscillating magnetic field.


Phase-sensitive Cellular Automata on Stochastic Network as a Model for Cardiac Pacemaker Rhythmicity

abstract

Oscillating cellular automata placed on two-dimensional stochastic lattice are proposed to model normal and abnormal cardiac pacemaker activity. In addition to Greenberg–Hasting approach, interactions which elongate the cellular period are proposed. Stationary states of the proposed system depend on density of intercellular connections, and thresholds for cell-to-cell interactions. The transition from expanding to collapsing wave patterns is observed at certain model parameters. A physiological meaning can be given to that transition, namely, as the arrhythmia phenomenon developing in the real heart due to abnormal high potassium concentration in the blood.


A Lattice-gas Cellular Automaton Model for in Vitro Sprouting Angiogenesis

abstract

The mechanisms of sprout formation and branching during sprouting angiogenesis are only partially understood and mostly attributed to nonlocal signals mediated by the heterogeneous distribution of vascular endothelial growth factor (VEGF). Here, we show that purely local mechanisms can account for angiogenic network formation. In particular, we examine the effects of homogeneous stimulation by VEGF on local endothelial cell–cell interactions and on interactions between endothelial cells and the microenvironment. We adopt a cell-based mathematical modeling approach (lattice-gas cellular automaton) and fit our model to image data obtained from in vitro experiments tailored to homogeneous conditions. This approach reveals the basal effects of (homogeneous) VEGF stimulation, in particular increased movement coordination and cell–cell adhesion but no significant change in contact guidance and extracellular matrix remodeling.


Discrete and Continuous Models of Pedestrian Movement — a Comparison

abstract

In this work, we study both continuous models of evacuation based on differential equations and discrete models based on cellular automata. Our discrete model is a floor field model with additional rules of movement (i.e. random movement, a form of pressure and enforced blocking of pedestrians). The continuous model is a variant of the Langevin equation. By performing simulations of evacuation from rooms with similar geometries we try to compare both approaches and find their strengths and weaknesses. In order to do that, we study evacuation times, relative evacuation times and other variables. We find that evacuation times are comparable but the results highly depend on geometry.


Labour and Goods Market Dynamics Using an Abstract Microeconomical Model

abstract

This paper presents a multilayer cellular automata on a graph to model the exchanges of working hours against salary coupled with the exchanges of cash against goods, thus creating an artificial labour and goods markets. During the time evolution, the cooperation and the competition between the individuals create rich behaviours: the strongly connected components (SCC) of the whole market emerge, a steady state or chaotic state appears, poor and rich cells emerge. When reaching the steady state, we show also that the distribution of cash is, in average, proportional to the in-degree of the cells.


The Computational Advantage of Probabilistic Automata over Deterministic Automata in Hyperbolic Plane

abstract

In this paper, we address the question whether a probabilistic finite-state automaton (pfa) could recognize a language not recognizable by a deterministic finite-state automaton in polynomial time. We show that there is such a language in a hyperbolic plane and prove that a 5-way error-bounded pfa can recognize it in polynomial time of the number of nodes on the plane.


Entropy Measures of Heart Rate Variability for Short ECG Datasets in Patients with Congestive Heart Failure

abstract

We investigated the usefulness of entropy measures calculated for short ECG series in distinguishing healthy subjects from patients with congestive heart failure (CHF). Four entropy measures were tested: Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (FuzzyEn) and Permutation Entropy (PE), each computed for ECG series of \(1000\), \(500\), \(250\) and \(100\) RR intervals. We found that with a reduction of the data set length up to 250 RR intervals, values of ApEn, SampEn, FuzzyEn and PE can remain significantly different in patients with CHF compared to healthy individuals. SampEn and FuzzyEn differentiated considered groups even for data sets of 100 RR intervals.


On Reading Multifractal Spectra. Multifractal Age for Healthy Aging Humans by Analysis of Cardiac Interbeat Time Intervals

abstract

Structure-function-based multifractal analysis performed on a signal (as if it is a stochastic walk), and on its integrated counterpart (as if it is a noise) provides an insight into a generic structure of the data i.e. whether there appears a multiplicative organization among signal values. Tests of scaling properties in synthetic signals with known fractal properties, when scaling intervals correspond to the time scales important for the cardiac physiology, validate application of the methodology to cardiac interbeat time RR intervals. 24-hour Holter recordings of healthy people of different age are studied. The nocturnal signals of young people reveal the presence of the multiplicative structure. This structure is significantly weaker in diurnal signals and becomes less evident for elderly people. The above finding is used to develop a qualitative and quantitative way to estimate the advancement of the aging process in a healthy human is proposed.


Emergence of Sparsity and Motifs in Gene Regulatory Networks

abstract

We consider a simple model of gene regulatory dynamics derived from the statistical framework describing the binding of transcription factors to DNA. We show that the networks representing essential interactions in gene regulation have a minimal connectivity compatible with a given function. We discuss statistical properties using Monte Carlo sampling. We show that functional networks have a specific motifs statistics. In the case where the regulatory networks are to exhibit multistability, we find a high frequency of gene pairs that are mutually inhibitory and self-activating. In contrast, networks having periodic gene expression patterns (mimicking for instance the cell cycle) have a high frequency of bifan-like motifs involving four genes with at least one activating and one inhibitory interaction.


Autonomic Antagonism Underlies Heart Rate Complexity

abstract

We investigate multiscale properties of intermittency of heart rate variability (HRV) through non-Gaussianity and through two-point one-scale magnitude correlations in HRV of patients with congestive heart failure (CHF) — both survivors (CHF–SV) and non-survivors (CHF–NS) — and of patients with primary autonomic failure (PAF). We confirm the sympathetic origin of the non-Gaussianity index elucidating its random character. We further confirm intermittency of the high frequency, fine scale firing of the parasympathetic nervous system branch, responsible for the multifractal complexity. We obtain further confirmation of the antagonistic function of the autonomic regulation of HRV, this time in terms of intermittency — heteroscedastic clustering of variance. In this context, we identify autonomic antagonism as the source of the mid to low frequency, intermediate scale intermittency observed at higher levels in CHF patients with elevated sympathetic activation and suppressed in the PAF patients — the case of neurogenic SNS dysfunction.


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