C. Project description (max. 10 pages)

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1 C. Project description (max. 10 pages) C1. Scientific context and motivation. Synchronization of a large number of oscillators is a well-known form of collective behavior. The expression collective behavior [1] was first used by Robert Park, a sociologist from the University of Chicago, as an alternative of crowd behaviour. In time, the expression has become a collector concept that covers a large area of social, biological and physical phenomena. Wherever we deal with a system composed of a large number of interacting units, capable of an emergent behavior that is not predictable solely from the properties of one unit, we deal with a form of collective behavior. Physics dealt with collective behavior much earlier than the expression was even born. Systems with a big number of interacting components that together can produce emerging effects on a larger scale are familiar to physicists. Synchronization of oscillators [2] is the first ever studied collective behavior in physics. From the viewpoint of collective behavior science is interested in the emerging synchronization of a large number of coupled oscillators. In a broad sense any system exhibiting a quasi-periodic dynamics can be considered an oscillator. Such systems are very frequent in nature, and the most interesting ones are in living organism. Pacemaker cells in the heart or neurons that control rhythmic activities are able of synchronization. Synchronization of chirping crickets, flashing fireflies in south-east Asia, menstrual cycles of women living together or clapping of spectators are also well-known examples [3]. Synchronization in such systems might have a more complex mechanism than synchronization of simple physical pendulums. Biological and sociological systems usually do have a tendency to optimize their evolution, and probably synchronization is not their primary aim, it is just a byproduct of some complex optimization procedure. Models that aim to describe realistically such systems should take these differences into consideration and should consider a complex interdisciplinary approach stepping over the simple picture of interacting mechanical oscillators. The present research project intends to study both experimentally and theoretically aspects of spontaneously arising synchronization in various physical and biological systems. Classical systems exhibiting emergent synchronization. Emergent synchronization of real (non-identical) oscillators was a serious paradox in physics for a long period of time. Oscillators with similar frequencies can obviously synchronize when phase-minimizing coupling acts between them. In nature however it is practically impossible to find two "exactly" similar oscillators. Synchronization of oscillators with different frequencies in the absence of an external periodic driving is a phenomenon that is highly nontrivial. It is not obvious at all if the system will spontaneously find a common frequency and all elements will 11

2 abandon their natural rhythm and synchronize following this common frequency. A simple system that is able under certain conditions for spontaneous synchronization is the ensemble of coupled pendulum clocks or metronomes. Another physical system capable of spontaneous synchronization was found in the early 1920 by E. V. Appleton and B. Van der Pol. They have experimentally studied and described the synchronization of triode vibrations [4]. After discovering superconductivity, physicists realized, that also coupled Josephson junctions synchronize as pendulums do [4]. Exploring the rhythms of living organisms, rhythmical behavior of plants, animals or people, synchronization became an important issue for biologists and sociologists as well. Probably the most fascinating biological example is the emergent synchronization of flashing fireflies along the bank of the rivers in south-east Asia [5]. Similar phenomena were observed for other biological systems, animal and human behavior. Spontaneous synchronization of pacemaker cells in the heart, or neurons fires are examples on cell level [1,2]. In the human society a good example for emergent synchronization is the rhythmic applause. This intriguing phenomenon was described and studied by our group [6-8]. Another example is the synchronization of the menstrual cycles of women that lives for long time together or the steps of pedestrians walking together. Recently many new results were reported on complex systems capable of spontaneous synchronization: lighting activity in distant storm cells, the light of burning candles, or water flowing out from plastic bottles. Our group has also built a system of flashing electronic oscillators capable of highly nontrivial spontaneous synchronization [9-10]. Classical models for emergent synchronization Despite the fact, that Huygens discovered spontaneous synchronization in the 17th century, mathematical models appeared just after 1960, and were first elaborated by biologists. The models progressed rapidly due to the quick evolution of the computers, and studying methods borrowed from physics, and mathematics (for a review please consult [11]). Most of these models fall into two broad categories: those describing phase-coupled oscillators, and those that use pulse-coupling between the units. The classical phase-coupled model of synchronization was first introduced by Winfree and solved analytically by Kuramoto and Nishikawa [12]. These types of models are known as Kuramoto type models. In the simplest version of the model, each oscillator has an associated phase between 0 and 2 π. The oscillators evolve according to a set of coupled first order differential equations, with a coupling that minimizes the phase difference between them. In the thermodynamic limit, this model shows a second-order phase transition as a function of the coupling strength. There is a critical coupling below which the system does not synchronize. Above the critical coupling value the system exhibits partial synchronization, and the synchronization level increases in a monotonic manner with the coupling strength. The critical coupling is linearly proportional with the variance of the oscillators' frequencies. Pulse-coupled 12

3 oscillators are mainly used in integrate-and-fire type models [13]. These models are probably the simplest ones able to approximate the collective behavior of a neuron ensemble. Each oscillator has a phase and a state variable, linked by a monotonic function. The dynamics of an isolated oscillator is simple: the phase increases monotonically until it reaches a given value. At this point the oscillator emits a pulse (it fires) and resets its state and phase-variable. In an ensemble of interacting oscillators when one oscillator fires, the state variable of all those other oscillators that can detect the emitted pulse increases instantly by a fixed value. Accordingly, the phase of these oscillators increases too. Under the right conditions, a single pulse can trigger an avalanche of pulses in the system causing a high proportion of the units to fire at the same time. Synchronization in such systems can appear under very broad conditions. Mirollo, Strogatz and Bottani studied in detail theses systems [14,15]. Recently a different type of emergent synchronization mechanism was introduced and studied by our group [10,16]. The multi-mode oscillator model considers an ensemble of pulse-like oscillators governed by a simple optimization principle. The oscillators are stochastic elements capable of emitting pulses and detecting the pulse emitted by the others. They are called multi-mode oscillators because they have several operational modes, characterized by different oscillating periods. Shifting between these modes is induced by a simple optimization rule: the average output intensity is kept around a fixed G threshold. This simple dynamical rule realizes the coupling of the elements and leads to a complex collective behavior. Computer simulations indicate that for a given interval of the G parameter partial synchronization of the elements can occur. The appearance and disappearance of this synchronization as G is changed indicates a phasetransition type behavior. The observed synchronization is highly nontrivial, since in contrast with all simple synchronization models no phase-difference minimizing interactions are considered in this system, synchronization arises as a side effect of a simple optimization rule. C2. Objectives. The main objective of the present project is to continue the studies concerning emergent synchronization in complex systems. We plan: (1) an experimental study on some fascinating systems (detailed below) capable of emergent synchronization and theoretical modeling of them; (2) a detailed theoretical study on the classical spontaneous synchronization models, considering a complex interaction topology and finite signal (interaction) propagation speed; (3) a general discussion of emergent synchronization in complex systems. Experiments First we plan to study an ensemble of coupled metronomes, and investigate the conditions under which they spontaneously synchronize. We study also the transient dynamics leading to synchronization and the stable/meta-stable synchronized states. This study is a natural continuation 13

4 and generalization of recent studies realized on two coupled metronomes [17,18]. The specific experimental setup we have in mind is sketched in Figure 1. On a freely rotating disk we place different number (N) of mechanical metronomes. Each metronome will be equipped with an optical sensor able to detect its phase. The sensors are coupled through a proper interface to a computer and the phase of all metronomes are constantly recorded. The metronomes are started with roughly the same natural frequencies (mean value ν with a natural standard deviation Δ ν ) and random phases. They are then placed on the perimeter of the rotating disk. The free rotation of the disk acts as a global interaction mechanism among the ticking metronomes and under some specific conditions this coupling will synchronize them. The free rotation of the disk will have a possibility to be finely tuned (controlling either the friction in the rotation axes by screws, or making a magnetic breaking) and through this the strength of coupling will be finely controlled. The relevant parameters of the system are the ν average frequency, the Δ ν standard deviation of the natural frequencies, the number of metronomes (N=1,2,3...8) and the controlled friction on the disks axe. Experiments will study the obtained synchronization patterns and the level of synchronization as a function of theses parameters. We are also interested in the transient dynamics leading to synchronization, i.e in the mechanism the system achieves its stable or meta-stable synchronization pattern. The system will be also modeled theoretically using a globally coupled Kuramoto type model with a finite number of rotators. The system of coupled differential equations of the Kuramoto model will be numerically integrated. Fig. 1 Experimental setup for studying synchronization of metronomes The second experiment we have planned considers synchronization of an ensemble of burning candles placed in various spatial topologies. When one places several candles close to each other they will burn with one single flame, and the height and intensity of the common flame becomes unstable, presenting time-like oscillations due to the lack of oxygen around the burning point. Recently it has been shown experimentally that two such groups of candles will synchronize their flame oscillations [19]. This puzzling phenomenon has momentarily a theoretical explanation based on the Stefan-Boltzmann radiation law. Our aim is to continue these experiments using one 14

5 and two-dimensional array of candles and to observe whether an ensemble of such candle-groups presents synchronization. Experiments will be done using both a high-speed camera to observe in detail the oscillations and to detect fast oscillations, and a thermal camera for visualizing the temperature profile in the system. We plan to test the theoretical description given in [19] and to elaborate a description for the candle array. The third experiment we have planed considers synchronization of the contractions of HL-1 heart tumor cells of a mouse. These cells [20] represent a good biological model for normal pacemaker cells and are much easier to be used than the real pacemaker cells of the heart. The proposed experiment is a cell-biology study and cannot be realized in our laboratory. It will be realized in collaboration with Dr. Zoltan Balint from the Ludwig Boltzmann Institute for Lung Vascular Research in Graz, Austria. The data analyses and theoretical modeling will be realized in Cluj. The HL-1 cells have the advantage to be grown easily in compact colonies and can couple optimally for signal transmission. They are able for spontaneous contractions and cell division, and can be kept in life for long periods in vitro conditions. C.S. Peskin created a proper model [21] for the activity of such cells, a model that motivated the elaboration of the integrate and fire type oscillator models. Due to their rhythmic dynamic activity and coupling an ensemble of HL-1 cells can show fascinating collective behavior. The propagation time of the signal responsible for the coupling for a reasonable long chain of HL-1 cells (several thousand) is comparable with their average contraction rhythm. As a result of this in extended systems a totally synchronized contraction cannot be achieved. Instead of a clear synchronized phase one will observe the propagation of synchronized domains. Such waves are constantly present in our heart, understanding their dynamics and modeling them is of primary interest. Fig 2. Sync waves in a population of HL-1 cells. Experimental setup Using a Cell Observer microscope, our aim is to visualize and to study the formation and dynamics of such travelling waves of synchronized domains. In order to visualize these cells they are painted with calcium sensible fluorescent paint, and we detect in the microscope the calcium level fluctuations during the cell contraction. The experimental setup proposed for the HL-1 cells is sketched in Figure 2. The rhythmic dynamics in the system will be modeled by using an Integrate 15

6 and Fire type oscillator chain [13] with a finite pulse propagation velocity. Our primary aim is to detect and describe the travelling and synchronized domains and to control them. Theoretical modeling Besides the already mentioned theoretical modeling exercises we also plan a detailed and general computational study on the classical models of synchronization (Kuramoto, Integrate and Fire, Multimode stochastic oscillators models) for the case when the propagation speed of the interaction is finite. In extended systems, the finite propagation speed will add an extra degree of complexity and applicability for the models. The oscillators will be spread spatially following different topologies and the interaction strength will be considered in different manner: short-range, nearestneighbor interactions or distance dependent long-range interactions will be considered. Synchronization and dynamics of such systems is a complex issue, rich phase-diagrams as a function of the model parameters are thus expected. For studying different models, different computational methods will be used. For the Kuramoto type models simple numerical integration methods are proper, while for the Integrate and Fire or the Multimode Oscillator systems molecular dynamics type simulations are used. Due to the fact that multi-mode oscillators have also a stochastic regime, in such cases basic Monte Carlo methods are also necessary. General (philosophical) aspects The concept and theories of emergence prove to have an increased relevance in nowadays multidisciplinary approaches regarding the analysis of complex systems behavior, as well as the general research methodology reframed by introducing new concepts, perspectives and instruments (see, for ex.,[22-25]). This is why emergence becomes a key-concept for the understanding of complex systems in their dynamics and fluidity. At the same time, the term may be successfully applied in both natural sciences and humanities, allowing general broader conceptualizations meant to bridge different research fields which may thus communicate and offer answer to more complex situations. The second term to be philosophically interpreted is synchronization. The project mainly refers to synchronization as pointing to the specific way and process of emergent cooccurrence, and secondly to describing and defining the new emergent relation usually referred to, in the philosophical discourse, by the term synchronicity (first developed by Carl Gustav Jung [26]). In consequence, the project brings into attention the tight connection between synchronization as a process and the emergence phenomena. C3. Method and approach The project has both a theoretical and an experimental part. The research team is formed in such manner that both lines are covered with adequate specialists. Concerning the construction of the necessary interfaces and setting up the experiments, the group has a proven experience. Professor 16

7 Neda and Dr. Tunyagi together with the PhD student Sz. Boda, built already similar devices and solved the automatic data acquisition when they created and studied systems of flashing electronic fireflies [9,10]. The experiment concerning the system of HL-1 cells (growing of the cells, visualization of the cell contraction by the calcium sensible fluorescent paint) will be realized using the expertise of our collaborator Dr. Zoltan Balint from the Ludwig Boltzmann Institute for Lung Vascular Research in Graz, Austria, who will help us in growing the cells and marking them. Our team will realize the experiments and data acquisition. Collected data will be analyzed at our modern computer cluster in Cluj. For theoretical modeling, most of the group members has a proven experience, and will participate in it according to the proposed work plan from below. The involvement of group members in the projects and their expertise is give in the following table : Name Scientific title Expertise Involvement month % of /man fullposition Z. Neda Professor, PhD statistical physics, modeling and computer 9 27 simulations, complex systems, sync Zs. Sarkozi Ass.Prof., PhD experimental techniques, sync problems 7 21 F. Jarai-Szabo Ass.Prof., PhD computer simulations, complex systems 5 15 Z. Lazar Ass.Prof., PhD computer simulation, numerical methods 3 9 M. Axinciuc Ass.Prof., PhD emergence, philosophic aspects 5 15 A. Tunyagi PhD electronics, interfaces, data collection 3 9 M. E-Ravasz PhD computer simulation in statistical physics 7 21 Sz. Boda PhD student computer simulations and electronics 6 18 The research will be done according to the following work-plan: Activities Periods Involved persons Realizing the experimental setup for Z. Neda, A. Tunyagi, Sz. Boda synchronization of metronomes Measurements on the metronome system (2012) Zs. Sarkozi Sz. Boda Modeling and computer simulations on the metronome system (2012) Z. Neda, F. Jarai-Szabo Zs. Lazar, M. Ercsey-Ravasz Publication, and dissemination of the results on metronomes, collaborations Z. Neda F. Jarai-Szabo Zs. Sarkozi 17

8 Realizing the experimental setup for the candle flame synchronization system (2012) Measurements on the candle flame synchronization system (2012) Modeling and computer simulations on the candle flame synchronization system (2012) Publication, collaborations, interpretation and dissemination of the results on candles Experiments on the HL-1 cell system Data analyses for the results obtained on the HL-1 system (2013) Modeling and computer simulations the HL-1 cell system Publication, collaborations, interpretation and dissemination of the results on HL-1 (2014) cells Modeling and computer simulations on synchronization models with timedelayed interactions Publication, collaborations and dissemination of the results on sync with (2014) time-delay Elaborating a unified and generalized view on emergent synchronization Publication, and dissemination of the results on general aspects of sync (2014) Z. Neda, A. Tunyagi Sz. Boda Zs. Sarkozi, Sz. Boda Z. Neda, F. Jarai-Szabo Sz. Boda Z. Neda, Zs. Sarkozi F. Jarai-Szabo, A Tunyagi Z. Neda, F. Jarai-Szabo Zs. Sarkozi Z. Neda, Zs. Sarkozi Sz. Boda Z. Neda Zs. Lazar, M. Ercsey-Ravasz Z. Neda, Zs. Sarkozi F. Jarai-Szabo, Sz. Boda Z. Neda, M. Ercsey-Ravasz F. Jarai-Szabo, Zs. Lazar Z. Neda, M. Ercsey-Ravasz F. Jarai-Szabo, A. Tunyagi M. Axinciuc, Z. Neda M. Axinciuc, Z. Neda C4. Impact, relevance, applications. Spontaneous synchronization is the most known form of emergent collective behavior. Studying it with well-controlled model systems will definitely bring new fundamental understanding to this fascinating field. The present study targets not only phenomena related to physics. Our aim is to construct model systems and basic theoretical models that are suitable for describing biological and social synchronization as well. In such cases the intelligence of the elements brings new and extra 18

9 degree of complexity in the system. Approaching these systems by classical models of statistical physics may work or may not work. The really interesting cases are when the classical synchronization models fail, and the intelligence of elements seems decisive in understanding the complex collective behavior in the system. Our previous studies on rhythmic applause and multimode stochastic oscillators published in Nature [6], Phys. Rev. Lett. [16] or Phys. Rev. E [7], proved that the scientific community is keenly interested in such approach and problems. Our hope is that the present research will have a similar impact on the scientific community as the previous works did. The problem targeting synchronization of HL-1 cells has direct applications in understanding the dynamics of pace-maker cells in the heart and consequently in understanding and controlling cardiac dysrhythmia (or arrhytmia). As shown in our previous works, the emergent synchronization of muli-mode stochastic oscillators can be used to engineer oscillators with a perfect periodicity from highly non-perfect units [7]. Studying classic synchronization models with time-delayed coupling will also bring an extra degree of reality for the models and will naturally lead to several other possible practical applications. The project implies a twofold contribution, being innovative on the level of the approached subject matter (i.e., the proposed experiment and its interpretation), as well as on the methodological level (indicating toward the development of concepts, tools and instruments relevant not only within the field of Physics, but also in other different contexts and research areas). C5. Resources and budget. For most of the experiments adequate lab and infrastructure is available at the host institution (BBU). The high-speed camera and the thermal camera are already purchased from previous research grants. Other necessary equipments and materials (metronomes, rotating disk, candles, electronic parts for interfaces and data acquisition) will be purchased from the present proposal. For the experiments concerning the system of HL-1 cells (growing of the cells, visualization of the cell contraction by the calcium sensible fluorescent paint) the necessary apparatus is available at the Ludwig Boltzmann Institute for Lung Vascular Research in Graz, Austria. There, with the help of Dr. Zoltan Balint our team will realize the experiments and data acquisition. Travels for collaborations are thus necessary during the present project. Computer simulations will be done on the powerful parallel cluster with 88 Xeon processors of the group at the UBB. Also sever workstations are available in the research group. Some new laptop computers will be purchased, these are necessary for daily office use. Travels for conferences and publication charges in journals are also needed. New books will be bought and subscriptions for basic journals like Nature and Nature Physics will be renewed. 19