Ljupco Kocarev

Publications (48)44.37 Total impact

• Source

  Available from: ArXiv

  Article: Influence of the network topology on epidemic spreading.

  Daniel Smilkov, Ljupco Kocarev
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  ABSTRACT: The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network, such as the largest eigenvalue of a topology related matrix. However, little is known about the direct influence of the network topology on the microscopic level, such as the influence of the (neighboring) network on the probability of a particular node's infection. To answer this question, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible-infective-susceptible model for two cases of spreading processes: reactive and contact processes. The bounds are derived by considering the n-hop neighborhood of the node; the bounds are tighter as one uses a larger n-hop neighborhood to calculate them. Consequently, using local information for different neighborhood sizes, we assess the extent to which the topology influences the spreading process, thus providing also a strong macroscopic connection between the former and the latter. Our findings are complemented by numerical results for a real-world email network. A very good estimate for the infection density ρ is obtained using only two-hop neighborhoods, which account for 0.4% of the entire network topology on average.
  Physical Review E 01/2012; 85(1 Pt 2):016114. · 2.26 Impact Factor
• Source

  Available from: ArXiv

  Article: Identifying communities by influence dynamics in social networks.

  Angel Stanoev, Daniel Smilkov, Ljupco Kocarev
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  ABSTRACT: Communities are not static; they evolve, split and merge, appear and disappear, i.e., they are the product of dynamical processes that govern the evolution of a network. A good algorithm for community detection should not only quantify the topology of the network but incorporate the dynamical processes that take place on the network. We present an algorithm for community detection that combines network structure with processes that support the creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes the node's involvement in each community. This way, in addition to the overlapping communities, we can identify nodes that are good followers of their leader and also nodes with no clear community involvement that serve as proxies between several communities and that are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results, including other possible applications.
  Physical Review E 10/2011; 84(4 Pt 2):046102. · 2.26 Impact Factor
• Chapter: Chaos-Based Public-Key Cryptography

  Igor Mishkovski, Ljupco Kocarev
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  ABSTRACT: In this chapter we give an overview and the state of the art in the field of Chaos-based cryptography. The public key cryptosystems based on Chebyshev polynomials enjoy some nice chaotic properties, which makes them suitable for use in both encryption and digital signature. The cryptosystem can work either on real or integer numbers. The cryptosystem that works on real numbers is not secure and permits to recover the corresponding plaintext from a given ciphertext. In addition, it also allows forgeries if the cryptosystem is used for signing messages. On the other hand, ElGamal-like and RSA-like algorithms when using Chebyshev polynomials on integer numbers are secure as the aforementioned encryption algorithms. The chaos-based cryptography is discussed from a point of view which we believe is closer to the spirit of both cryptography and chaos theory than the way the subject has been treated recently by many researchers.
  07/2011: pages 27-65;
• Source

  Available from: ArXiv

  Article: Analytically solvable processes on networks.

  Daniel Smilkov, Ljupco Kocarev
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  ABSTRACT: We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics.
  Physical Review E 07/2011; 84(1 Pt 2):016104. · 2.26 Impact Factor
• Source

  Available from: ArXiv

  Article: Rich-club and page-club coefficients for directed graphs

  Daniel Smilkov, Ljupco Kocarev
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  ABSTRACT: Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and Email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that {}"elite" papers are cited by other {}"elite" papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that {}"elite" patents are cited by other {}"elite" patents. Finally, for e-mail communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.
  03/2011;
• Source

  Available from: 144.206.159.178

  Article: Exploring the possibilities to control the molecular switching properties and dynamics: A field-switchable rotor-stator molecular system.

  Irina Petreska, Ljupco Pejov, Ljupco Kocarev
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  ABSTRACT: A bistable, dipolar stator-rotor molecular system-candidate for molecular electronics is investigated. We demonstrate that it is possible to control the intramolecular torsional states and dynamics in this system by applying an appropriate additional electric field (instead of biasing one), achieving fine tuning and modulation of the relevant properties. The electric field effects on the quantities responsible for torsional dynamics (potential energy surface, potential barrier height, quantum and classical transition probabilities, correlation time, HOMO-LUMO gap) are studied from first principles. Our results indicate that it is possible to artificially stabilize the metastable conformational state of the studied molecule. The importance of this is evident, as the current-voltage characteristics of the metastable state are clearly distinguishable from the current-voltage characteristics of the two stable states. We report for the first time exact calculations related to the possibilities to control the thermally induced stochastic switching, and reduce the noise in a practical application. Thus, we believe that the molecule studied in this paper could operate as a field-switchable molecular device under real conditions.
  The Journal of chemical physics 01/2011; 134(1):014708. · 3.09 Impact Factor
• Chapter: An Agglomerative Clustering Technique Based on a Global Similarity Metric

  Angel Stanoev, Igor Trpevski, Ljupco Kocarev
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  ABSTRACT: In this paper we address the problem of detecting communities or clusters in networks. An efficient hierarchical clustering algorithm based on a global similarity metric is introduced. The technique exploits several characteristic average values of the similarity function. Also an analytical result is provided for the average similarity of vertices on an Erdos-Renyi graph in the asymptotic limit of the graph size. Finaly the performance of the algorithm is evaluated over a set of computer-generated graphs. Our analysis shows that newly proposed algorithm is superior when compared to the popular algorithm of Girvan and Newman and has equal or lower running time. KeywordsSimilarity metrics–Clustering Algorithms–Community Detection–Complex Networks
  12/2010: pages 266-275;
• Article: Model for rumor spreading over networks.

  Daniel Trpevski, Wallace K S Tang, Ljupco Kocarev
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  ABSTRACT: An alternate model for rumor spreading over networks is suggested, in which two rumors (termed rumor 1 and rumor 2) with different probabilities of acceptance may propagate among nodes. The propagation is not symmetric in the sense that when deciding which rumor to adopt, nodes always consider rumor 1 first. The model is a natural generalization of the well-known epidemic SIS (susceptible-infective-susceptible) model and reduces to it when some of the parameters of this model are zero. We find that preferred rumor 1 is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the Watts-Strogatz small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it. For Erdos-Renyi networks, a low average degree allows the coexistence of the two types of rumors. In Barabasi-Albert networks generated with a low m , where m is the number of links when a new node is added, it is also possible for rumor 2 to spread over the network.
  Physical Review E 05/2010; 81(5 Pt 2):056102. · 2.26 Impact Factor
• Conference Proceeding: An opinion disseminating model for market penetration in social networks.

  Daniel Trpevski, Wallace Kit-Sang Tang, Ljupco Kocarev
  International Symposium on Circuits and Systems (ISCAS 2010), May 30 - June 2, 2010, Paris, France; 01/2010
• Source

  Available from: arxiv.org

  Article: Random walks on networks: cumulative distribution of cover time.

  Nikola Zlatanov, Ljupco Kocarev
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  ABSTRACT: We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n) , is also presented. The approximation is numerically tested only for graphs with n<or=1000 nodes.
  Physical Review E 10/2009; 80(4 Pt 1):041102. · 2.26 Impact Factor
• Article: Cryptanalysis of Chaotic Communication Schemes by Dynamical Minimization Algorithm.

  Ying Liu, Yu Mao, Wallace Kit-Sang Tang, Ljupco Kocarev
  I. J. Bifurcation and Chaos. 01/2009; 19:2429-2437.
• Article: Identification of biological neurons using adaptive observers.

  Yu Mao, Wallace Tang, Ying Liu, Ljupco Kocarev
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  ABSTRACT: This paper is to investigate the use of adaptive observers for the modeling of biological neurons and networks. Assuming that a neuron can be modeled as a continuous-time nonlinear system, it is possible to determine its unknown parameters using adaptive observer, based on the concept of adaptive synchronization. The same technique can be extended for the identification of an entire biological neural network. Some conventional observer designs are studied in this paper and satisfactory results are obtained, yet with some restrictions. To further extend the applicability of adaptive observers for the modeling process, a new design is suggested. It is based on a combination of linear feedback control approach and the dynamical minimization algorithm. The effectiveness of the designed adaptive observer is confirmed with simulations.
  Cognitive Processing 11/2008; 10 Suppl 1:S41-53. · 1.57 Impact Factor
• Article: Synchronization in Networks of Hindmarsh-Rose Neurons.

  Paolo Checco, Marco Righero, Mario Biey, Ljupco Kocarev
  IEEE Trans. on Circuits and Systems. 01/2008; 55-II:1274-1278.
• Article: An Adaptive Observer Design for Auto-Synchronization of Lorenz System.

  Ying Liu, Wallace Kit-Sang Tang, Ljupco Kocarev
  I. J. Bifurcation and Chaos. 01/2008; 18:2415-2423.
• Source

  Available from: ippt.gov.pl

  Article: On some properties of the discrete Lyapunov exponent

  José M Amigó, Ljupco Kocarev, Janusz Szczepanski, C R Doering
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  ABSTRACT: One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting.
  Physics Letters A. 01/2008; 372:6265-6268.
• Source

  Available from: physik3.gwdg.de

  Chapter: Chaos synchronization

  Ulrich Parlitz, Lutz Junge, Ljupco Kocarev
  10/2007: pages 511-525;
• Source

  Available from: Marco Righero

  Article: Estimating topology of networks.

  Dongchuan Yu, Marco Righero, Ljupco Kocarev
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  ABSTRACT: We suggest a method for estimating the topology of a network based on the dynamical evolution supported on the network. Our method is robust and can be also applied when disturbances and/or modeling errors are presented. Several examples with networks of phase oscillators, pulse-coupled Hindmarch-Rose neurons, and Lorenz oscillators are provided to illustrate our approach.
  Physical Review Letters 12/2006; 97(18):188701. · 7.37 Impact Factor
• Source

  Available from: arxiv.org

  Article: Distribution of edge load in scale-free trees.

  Attila Fekete, Gábor Vattay, Ljupco Kocarev
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  ABSTRACT: Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and non-scale-free trees. We aim at the probability distribution of edge betweenness under the condition that a local property, the in-degree of the "younger" node of a randomly selected edge, is known. En route to the conditional distribution of edge betweenness the exact joint distribution of cluster size and in-degree, and its one-dimensional marginal distributions have been presented in the paper as well. From the derived probability distributions the expectation values of different quantities have been calculated. Our results provide an exact solution not only for infinite, but for finite networks as well.
  Physical Review E 05/2006; 73(4 Pt 2):046102. · 2.26 Impact Factor
• Chapter: Synchronization in Complex Networks

  Ljupco Kocarev, Gábor Vattay
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  ABSTRACT: The study of complex systems pervades all of science, from cell biology to ecology, from computer science to meteorology. A paradigm of a complex system is a network [1] where complexity may come from di.erent sources: topological structure, network evolution, connection and node diversity, and/or dynamical evolution. Examples of networks include food webs [2, 3], electrical power grids, cellular and metabolic networks, the World-Wide Web [4], the Internet backbone [5], neural networks, and co-authorship and citation networks of scientists. These networks consist of nodes which are interconnected by a mesh of links. The macroscopic behavior of a network is determined by both the dynamical rules governing the nodes and the flow occurring along the links.
  01/2006: pages 309-328;
• Source

  Available from: nuaa.edu.cn

  Article: Synchronization in power-law networks.

  Ljupco Kocarev, Paolo Amato
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  ABSTRACT: We consider realistic power-law graphs, for which the power-law holds only for a certain range of degrees. We show that synchronizability of such networks depends on the expected average and expected maximum degree. In particular, we find that networks with realistic power-law graphs are less synchronizable than classical random networks. Finally, we consider hybrid graphs, which consist of two parts: a global graph and a local graph. We show that hybrid networks, for which the number of global edges is proportional to the number of total edges, almost surely synchronize.
  Chaos An Interdisciplinary Journal of Nonlinear Science 07/2005; 15(2):24101. · 2.08 Impact Factor