Koordinacija je organizacija različnih elementov kompleksnega sistema z namenom, da je njegovo kolektivno delovanje učinkovito. Kot takšna, koordinacija zajema širok spekter različnih procesov, vključujoč sodelovanje, sinhronizacijo, in tvorjene vzorcev. Sodelovanje je najpomembnejši izziv s katerim se sooča Darwinova teorija evolucije in le-to je bistveno za razumevanje glavnih evolucijskih prehodov, ki so vodili od enoceličnih organizmov do kompleksnih živalskih in človeških družb. Če preživijo le najmočnejši, zakaj naj bi nek organizem izvajal nesebično dejanje, ki koristi pa drugemu? Sinhronizacija in tvorjenje vzorcev, po drugi strani, pa sta med najbolj izstopajočimi in univerzalnimi pojavi v nelinearni znanosti kakor tudi v tekočih kristalih. Metode neravnovesne statistične fizike, še posebej kolektivno obnašanje delcev v interakciji blizu faznih prehodov, so se šele pred kratkim izkazale kot neprecenljive za razumevanje koordiniranih izidov v kompleksnih sistemih na večplastnih omrežjih.

Vodilni partner projekta

UM Fakulteta za naravoslovje in matematiko

Vodja projekta

Prof. dr. Matjaž Perc

Vodja projekta za UP FM

Prof. dr. Ajda Fošner

Partnerji projekta

• Institut »Jožef Stefan«,

• Združenje Pomurska akademsko znanstvena unija

Šifra programa

J1-2457

Trajanje projekta

1. 9. 2020 – 31. 08. 2023

Vsebina projekta

Metode neravnovesne statistične fizike so se šele pred kratkim izkazale kot neprecenljive za razumevanje koordiniranih izidov v kompleksnih sistemih na večplastnih omrežjih. Pomembno je, da več-točkovne interakcije, ki so vključene v tovrstne procese, povzročajo kritično obnašanje, ki po svoji kompleksnosti prekaša kar je doslej znanega o interakcijah v parih, ki jih tipično najdemo v sistemih fizike trdne snovi. Nepopolnost obstoječe teorije je nadalje še izrazitejša pri interakcijah med omrežji, ki povzročajo medsebojne soodvisnosti na večih nivojih, kar pa lahko sproži soodvisne napake in pospeši nenadne prehode k celo-sistemskim katastrofam. Naš namen je koristno uporabiti in razširiti koncept faznih prehodov in univerzalnosti tako, da bo postal primeren za opisovanje in razlago pojava koordinacije v večplastnih omrežjih. Razvili bomo široko uporabne teoretične osnove, ki bodo odprle nova obzorja na poti k razumevanju, predvidevanju in nadziranju bogate raznolikosti pomembnih pojavov, ki so odvisni od koordinacije. Vse od sodelovanja v človeški družbi do tvorjenja vzorcev v tekoče-kristalnih filmih do boljšega vrednotenja znanosti, obljuba dobrega teoretičnega razumevanja faznih prehodov, ki vodijo do koordinacije v večplastnih omrežjih bo imela široko stimulativne učinke v teoretični in statistični fiziki.

Ključne besede

Koordinacija, večplastna omrežja, fazni prehodi

Faze projekta in njihova realizacija

1. WP1: We would like to understand how local topological features of interaction networks influence the emergence of coordination through the decisions of individual agents as they create and sever connections towards other members in the multilayer structure. Here we cancontinue onwards from our existing research efforts that have identified key coevolutionary processes that might facilitate cooperation and synchronization, as notable examples of coordination. The obvious goal is to extend this theory towards multilayer networks, where certain players are members in two or more different yet interdependent network layers. 
2. WP2: Identification and classification of phase transitions in coevolutionary models where besides strategies also the interactions between the networks are subject to evolution. We wish to understand how the optimal interdependence for coordination between two networks emerges, and what are the properties that define an optimal interaction. We aim to establish percolation criteria and universality classes based on the observed outcomes. We also aim to clarify the possibilities related to the extension of this theory to “multiplexes of multilayer networks” where several multilayer networks interact.
3. WP3: Identification and classification of phase transitions in coevolutionary models where the interactions among networks influence the payoff matrix and the utility function of competing players. Here the goal is to understand thoroughly how the interactions between networks affect the fitness of individual players, and how the differences at the micro scale affect the macroscopic state of the system. The separation of times scales between different microscopic processes, like interaction and adoption, is expected to be a crucial element which influences the macroscopically observable interactions between different network layers. The fundamental question is how the coevolution of such an interdependence leads to the emergence of biased utilities, and which phase transitions are involved.
4. WP4: A generalization of work packages 2 and 3 towards mathematical models that are haracterized by multi-point interactions, as opposed to pairwise interactions. The focus will Public call for co-financing of research projects in 2020 be on the qualitative differences of phase transitions that emerge as a consequence of multipoint interactions.
5. WP5: Characterization of phase transitions and spatial patterns that govern the evolution of punishment in multilayer networks. Current research already highlights the incompleteness of the existing concept of phase transitions to account for all the fascinating results, and the reasonable expectation is that the interactions among network layers will only add further to the complexity. We shall also address in detail the difference between peer-based punishment efforts and institutional sanctioning, as well as the competition between the two in achieving coordination.
6. WP6: Although reward is, besides punishment, just another manifestation of reciprocity in the context of coordination in humans, the outcomes on an isolated network can be very different. A fundamental question is whether interactions among networks diminish or amplify these differences, and whether the existing classification of phase transitions suffices to explain all the paths towards coordination. Ultimately, we may seek to understand the impact of  correlated reward and punishment in different network layers, as well as the potentials of institutionalized reward for coordinated actions.
7. WP7: In addition to reward and punishment, we also want to clarify the consequences of more sophisticated strategies, like conditional coordination as well as other unexplored behavioral types that constitute social behavior in complex multilayer networks.
8. WP8: One of the fundamental discoveries on which we wish to elaborate on further is that specific interactions of agents do not simply yield characteristic spatial patterns, but also that the emerging spatial patterns in turn influence the stability of possible solutions. This research could be especially relevant for biological systems where several strategies (or species) compete for space, and where the competition is therefore driven by a highly complex food web, and where thus coordination is particularly difficult to achieve.
9. WP9: The high relevance of the analysis of spatial patterns is rooted in the fact that multipoint interactions among agents may result in counterintuitive and unexpected changes that affect the invasion velocity between propagating fronts, or even altogether revert the expected direction of invasion. Importantly, these changes cannot be deduced from pairwise comparisons of competing domains. Such efforts could be particularly useful in the absence of direct information about the microscopic interactions, as is for example the case in the majority of microbiological systems. In these cases, the evaluation of emerging patterns could help to identify and resolve the main microscopic processes that drive coordination. This mayfind application in liquid crystals research too, where the exotic phases often yield multipoint interactions.
10. WP10: Expanding the theory to related problems that go beyond coordination. Interacting networks are susceptible not only to the challenges of coordination, but also to the challenge of fairness, competition, and attack. The emergence of fairness is traditionally modeled with ultimatum bargaining. With methods of statistical physics, we aim to reveal hidden complexity in the pursuit of fair play in multilayer networks.
11. WP11: We intend to explore the impact of different types of heterogeneities of payoff elements on the emergence of coordination. Heterogeneous payoff elements could be the consequence of many different effects. For example, the heterogeneity of resource availability may be due to permanently unequal or time-varying external conditions. Furthermore, it is reasonable to assume that the payoff elements depend also on the actual status of individual players. These considerations give rise to different types of heterogeneities, which are likely to introduce different phase transitions to coordination in multilayer networks.

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