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1.
Stochastic resonance on excitable small-world networks via a pacemaker
Matjaž Perc, 2007, original scientific article

Abstract: We show that the correlation between the frequency of subthreshold pacemaker activity and the response of an excitable array is resonantly dependent on the intensity of additive spatiotemporal noise. Thereby, the effect of the underlying network, defining the interactions among excitable units, largely depends on the coupling strength. Only for intermediate coupling strengths is the small world property able to enhance the stochastic resonance, whereas for smaller and larger couplings the impact of the transition from diffusive to random networks is less profound. Thus, the optimal interplay between a localized source of weak rhythmic activity and the response of the whole array demands a delicate balance between the strength of excitation transfer and the effectiveness of the network structure to support it.
Keywords: stochastic resonance, small-world networks, cardiology, neurophysiology, nonlinear dynamical systems, spatiotemporal phenomena
Published: 31.05.2012; Views: 1073; Downloads: 60
URL Link to full text

2.
Encyclopedia of complexity and systems science
dictionary, encyclopaedia, lexicon, manual, atlas, map

Abstract: Encyclopedia of Complexity and Systems Science provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of near-term problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another. This unique work will extend the influence of complexity and system science to a much wider audience than has been possible to date.
Keywords: cellular automata, complex networks, computational nanoscience, ecological complexity, ergodic theory, fractals, game theory, granular computing, graph theory, intelligent systems, perturbation theory, quantum information science, system dynamics, traffic management, chaos, climate modelling, complex systems, dynamical sistems, fuzzy theory systems, nonlinear systems, soft computing, stochastic processes, synergetics, self-organization, systems biology, systems science
Published: 01.06.2012; Views: 1545; Downloads: 77
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3.
Establishing the stochastic nature of intracellular calcium oscillations from experimental data
Matjaž Perc, Anne K. Green, C. Jane Dixon, Marko Marhl, 2008, original scientific article

Abstract: Calcium has been established as a key messenger in both intra- and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, time-independent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics.
Keywords: dynamic systems, stochastic processes, cellular signaling, calcium oscillations, time series analyses, noise, temporal correlation
Published: 07.06.2012; Views: 1051; Downloads: 76
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4.
Stochastic resonance in soft matter systems : combined effects of static and dynamic disorder
Matjaž Perc, Marko Gosak, Samo Kralj, 2008, original scientific article

Abstract: We study the impact of static and dynamic disorder on the phenomenon of stochastic resonance (SR) in a representative soft matter system. Due to their extreme susceptibility to weak perturbations, soft matter systems appear to be excellent candidates for the observation of SR. Indeed, we derive generic SR equations from a polymer-stabilized ferroelectric liquid crystal (LC) cell, which is a typical soft matter representative constituting one of the basic components in several electro-optic applications. We generalize these equations further in order to study an even broader class of qualitatively different systems, especially disclosing the influence of different types of static disorder and interaction ranges amongst LC molecules on the SR response. We determine the required conditions for the observation of SR in the examined system, and moreover, reveal that a random field type static disorder yields qualitatively different responses with respect to random dilution, random bond and spin glass universality classes. In particular, while the latter three decrease the level of dynamic disorder (Gaussian noise) warranting the optimal response, the former evokes exactly the opposite effect, hence increasing the optimal noise level that is needed to resonantly fine-tune the system's response in accordance with the weak deterministic electric field. These observations are shown to be independent of the system size and range of interactions, thus implying their general validity and potentially wide applicability also within other similar settings. We argue that soft matter systems might be particularly adequate as a base for different SR-based sensitive detectors and thus potent candidates for additional theoretical as well as experimental research in the presently outlined direction.
Keywords: dynamic systems, stochastic processes, stochastic resonance, nonlinear dynamical systems, soft-matter systems, static disorder, dynamic disorder
Published: 07.06.2012; Views: 1104; Downloads: 52
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5.
Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game
Matjaž Perc, 2007, original scientific article

Abstract: We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner's dilemma game. We find that Gaussian-distributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed.
Keywords: stochastic systems, spatial resonance, stochastic payoff variations, nonlinear systems, noise, spatial dynamics, mathematical models, prisoner's dilemma
Published: 07.06.2012; Views: 1167; Downloads: 60
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6.
Periodic calcium waves in coupled cells induced by internal noise
Matjaž Perc, Marko Gosak, Marko Marhl, 2007, original scientific article

Abstract: We show that internal stochasticity, originating from finite cell sizes and related small numbers of reactant ions participating in the dynamics, is able to extract a characteristic spatial frequency of calcium waves in the medium of diffusively coupled cells. Internal noise is thereby the only agent acting on the system. As the spatial periodicity is best pronounced at an intermediate level of stochasticity the reported phenomenon is thus a novel observation of internal noise spatial coherence resonance in biochemical tissue-like media. In addition, results shed light on the stochastic versus deterministic nature of dynamics at the cellular and tissue level.
Keywords: noise, spatiotemporal noise, intensity, spatial resonance, chemical media, stochastic systems
Published: 07.06.2012; Views: 982; Downloads: 52
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7.
Noise-guided evolution within cyclical interactions
Matjaž Perc, Attila Szolnoki, 2007, original scientific article

Abstract: We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by Gaussian noise. Conditions are identified that warrant the largest impact of noise on the evolutionary process, and the results of Monte Carlo simulations are qualitatively reproduced by a four-point cluster dynamical mean-field approximation. The observed noise-guided evolution is deeply routed in short-range spatial correlations, which is supported by simulations on other host lattice topologies. Our findings are conceptually related to the coherence resonance phenomenon in dynamical systems via the mechanism of threshold duality. We also show that the introduced concept of noise-guided evolution via the exploitation of threshold duality is not limited to predator-prey cyclical interactions, but may apply to models of evolutionary game theory as well, thus indicating its applicability in several different fields of research.
Keywords: dynamic systems, stochastic processes, cyclical interactions, evolutionary rules, flow simulations, Monte Carlo simulations
Published: 07.06.2012; Views: 1190; Downloads: 240
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