arXiv subjects

Zoran Levnajić

Publications and source records attributed to Zoran Levnajić.

At least 19 recordsLinked to original sources

arXiv2026

Network model selection: A review of methods

Understanding the processes behind the evolution of complex networks is a key objective in network science. An effective framework for tackling this challenge is network model selection, which involves finding the model from a set of candidates that best explains a given network. This book is a systematic review of methods for this purpose. Each method is outlined in three parts: its core principle (used to organize methods into four categories), other relevant details including my own observations, and software availability. The book provides a comprehensive overview of the state-of-the-art in network model selection and concludes by exploring future directions. A unified, optimal method could identify the mechanisms that shape real-world networks more precisely than any current approach. This work represents the first step toward developing such an optimal method. It will be a valuable resource for students and researchers in network science.

physics.soc-ph↗

arXiv2023

Terrorist attacks sharpen the binary perception of "Us" vs. "Them"

Terrorist attacks not only harm citizens but also shift their attention, which has long-lasting impacts on public opinion and government policies. Yet measuring the changes in public attention beyond media coverage has been methodologically challenging. Here we approach this problem by starting from Wikipedia's répertoire of 5.8 million articles and a sample of 15 recent terrorist attacks. We deploy a complex exclusion procedure to identify topics and themes that consistently received a significant increase in attention due to these incidents. Examining their contents reveals a clear picture: terrorist attacks foster establishing a sharp boundary between "Us" (the target society) and "Them" (the terrorist as the enemy). In the midst of this, one seeks to construct identities of both sides. This triggers curiosity to learn more about "Them" and soul-search for a clearer understanding of "Us". This systematic analysis of public reactions to disruptive events could help mitigate their societal consequences.

physics.soc-ph↗

arXiv2020

Collective dynamics of phase-repulsive oscillators solves graph coloring problem

We show how to couple phase-oscillators on a graph so that collective dynamics "searches" for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring) into a functional optimization problem (finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system's evolution). Using a sample of graphs, we show that our method can serve as a viable alternative to the traditional combinatorial algorithms. Moreover, we show that, with the same computational cost, our method efficiently solves the harder problem of improper coloring of weighed graphs.

nlin.CD↗

arXiv2019

Humans make best use of social heuristics when confronting hard problems in large groups

We report the results of a game-theoretic experiment with human players who solve the problems of increasing complexity by cooperating in groups of increasing size. Our experimental environment is set up to make it complicated for players to use rational calculation for making the cooperative decisions. This environment is directly translated into a computer simulation, from which we extract the collaboration strategy that leads to the maximal attainable score. Based on this, we measure the error that players make when estimating the benefits of collaboration, and find that humans massively underestimate these benefits when facing easy problems or working alone or in small groups. In contrast, when confronting hard problems or collaborating in large groups, humans accurately judge the best level of collaboration and easily achieve the maximal score. Our findings are independent on groups' composition and players' personal traits. We interpret them as varying degrees of usefulness of social heuristics, which seems to depend on the size of the involved group and the complexity of the situation.

physics.soc-ph↗

arXiv2018

Synchronization in time-varying random networks with vanishing connectivity

A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly, an extremely low instantaneous connectivity. We show that, provided strong coupling and fast enough rewiring are considered, the network is able to reach partial synchronization even in the vanishing connectivity limit. We also provide an intuitive analytical argument, based on the comparison between the different characteristic timescales of our system in the low connectivity regime, which is able to predict the transition to synchronization threshold with satisfactory precision. In the formal fast switching limit, finally, we argue that the onset of collective synchronization is captured by the time-averaged connectivity network. Our results may be relevant to qualitatively describe the emergence of consensus in social communities with time-varying interactions and to study the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities.

nlin.CD↗

arXiv2015

Quantifying the consistency of scientific databases

Science is a social process with far-reaching impact on our modern society. In the recent years, for the first time we are able to scientifically study the science itself. This is enabled by massive amounts of data on scientific publications that is increasingly becoming available. The data is contained in several databases such as Web of Science or PubMed, maintained by various public and private entities. Unfortunately, these databases are not always consistent, which considerably hinders this study. Relying on the powerful framework of complex networks, we conduct a systematic analysis of the consistency among six major scientific databases. We found that identifying a single "best" database is far from easy. Nevertheless, our results indicate appreciable differences in mutual consistency of different databases, which we interpret as recipes for future bibliometric studies.

cs.DL↗

arXiv2014

Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. The range of method's applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschlé map and extended standard map.

nlin.CD↗

arXiv2013

Network topology reconstructed from derivative-variable correlations

A method of network reconstruction from the dynamical time series is introduced, relying on the concept of derivative-variable correlation. Using a tunable observable as a parameter, the reconstruction of any network with known interaction functions is formulated via simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model and observation errors.

physics.data-an↗

arXiv2013

Derivative-variable correlation reveals the structure of dynamical networks

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the network adjacency matrix. Our assumptions are the possession of time series describing the network dynamics, and the precise knowledge of the interaction functions. Our method involves a tunable parameter, allowing for the reconstruction precision to be optimized within the constraints of given dynamical data. The method is illustrated on a simple example, and the dependence of the reconstruction precision on the dynamical properties of time series is discussed. Our theory is in principle applicable to any weighted or directed network whose internal interaction functions are known.

physics.data-an↗

arXiv2012

Evolutionary design of non-frustrated networks of phase-repulsive oscillators

Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the links with probability proportional to their frustration, until the final network displaying a unique non-frustrated dynamical state is reached. Resulting networks are bipartite and with zero clustering. In addition, the designed non-frustrated anti-phase synchronised networks display a clear topological scale. This contrasts usually studied cases of networks with phase-attractive dynamics, whose performance towards full synchronisation is typically enhanced by the presence of a topological hierarchy.

cond-mat.stat-mech↗

arXiv2012

Dynamical networks reconstructed from time series

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method on a simple example, and discuss the dependence of the reconstruction precision on the properties of time series. Our method is applicable to any network, allowing for reconstruction precision to be maximized, and errors to be estimated.

physics.data-an↗

arXiv2011

Emergent multistability and frustration in phase-repulsive networks of oscillators

We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states. In opposition to widely studied phase-attractive case, the properties of final dynamical states in our model critically depend on the network topology. In particular, each network's total frustration value is intimately related to its topology. Moreover, phase-repulsive networks in general display multiple final frustration states, whose statistical and stability properties are uniquely identifying them.

cond-mat.stat-mech↗

arXiv2011

Network reconstruction from random phase-resetting

We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random phase-resets of the system dynamics. The desired details of network structure are then revealed by appropriately averaging over the ensemble. The method is applicable for a wide class of networks with arbitrary emergent dynamics, including full synchrony.

nlin.CD↗

arXiv2010

Phase resetting of collective rhythm in ensembles of oscillators

Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble evolution to derive the analytical phase resetting equations. We show the final phase reset value to be composed of two parts: an immediate phase reset directly caused by the perturbation, and the dynamical phase reset resulting from the relaxation of the perturbed system back to its dynamical equilibrium. Analytical, semi-analytical and numerical approximations of the final phase resetting curve are constructed. We support our findings with extensive numerical evidence involving identical and non-identical oscillators. The validity of our theory is discussed in the context of large ensembles approximating the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2010

Chaotic dephasing in a double-slit scattering experiment

We design a computational experiment in which a quantum particle tunnels into a billiard of variable shape and scatters out of it through a double-slit opening on the billiard's base. The interference patterns produced by the scattered probability currents for a range of energies are investigated in relation to the billiard's geometry which is connected to its classical integrability. Four billiards with hierarchical integrability levels are considered: integrable, pseudo-integrable, weak-mixing and strongly chaotic. In agreement with the earlier result by Casati and Prosen [1], we find the billiard's integrability to have a crucial influence on the properties of the interference patterns. In the integrable case most experiment outcomes are found to be consistent with the constructive interference occurring in the usual double-slit experiment. In contrast to this, non-integrable billiards typically display asymmetric interference patterns of smaller visibility characterized by weakly correlated wave function values at the two slits. Our findings indicate an intrinsic connection between the classical integrability and the quantum dephasing, responsible for the destruction of interference.

nlin.CD↗

arXiv2010

Ergodic Theory and Visualization I: Mesochronic Plots for Visualization of Ergodic Partition and Invariant Sets

We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation - based on time averages of observables - a Mesochronic Plot (from Greek: \textit{meso} - mean, \textit{chronos} - time}. The method is useful for identifying low-dimensional projections (e.g. two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the Mesochronic Scatter Plot (MSP). We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froéschle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional Extended standard map for which we study the conjecture on its ergodicity [3]. We extend the study in our next paper [4] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator.

nlin.CD↗

arXiv2010

Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli

The collective dynamics of coupled two-dimensional chaotic maps on complex networks is known to exhibit a rich variety of emergent properties which crucially depend on the underlying network topology. We investigate the collective motion of Chirikov standard maps interacting with time delay through directed links of Gene Regulatory Network of bacterium Escherichia Coli. Departures from strongly chaotic behavior of the isolated maps are studied in relation to different coupling forms and strengths. At smaller coupling intensities the network induces stable and coherent emergent dynamics. The unstable behavior appearing with increase of coupling strength remains confined within a connected sub-network. For the appropriate coupling, network exhibits statistically robust self-organized dynamics in a weakly chaotic regime.

cond-mat.stat-mech↗

arXiv2009

Modular Gene Dynamics and Network Theory at Mesoscopic Scale

Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example of system that can be described as a network of interacting genes. The behavior of a complex dynamical system is characterized by cooperativity of its units at various scales, leading to emergent dynamics which is related to the system's function. Among the key problems concerning complex systems is the issue of stability of their functioning, in relation to different internal and external interaction parameters. In this Thesis we study two-dimensional chaotic maps coupled through non-directed networks with different topologies. We use a non-symplectic coupling which involves a time delay in the interaction among the maps. We test the stability of network topologies through investigation of their collective motion, done by analyzing the departures from chaotic nature of the isolated units. The study is done on two network scales: (a) full-size networks (a computer generated scalefree tree and a tree with addition of cliques); (b) tree's characteristic sub-graph 4-star, as a tree's typical dynamical motif which captures its topology in smallest possible number of nodes and is suitable for time-delayed interaction. We study the dynamical relationship between these two network structures, examining the emergence of cooperativity on a large scale (trees) as a consequence of mesoscale dynamical patterns exhibited by the 4-star. (FULL ABSTRACT INSIDE THE TEXT)

cond-mat.stat-mech↗