Macedonian Academy for science and Arts

Skopje, Macedonia

Macedonian Academy for science and Arts

Skopje, Macedonia
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Trpevski I.,Macedonian Academy for science and Arts | Trpevski D.,Macedonian Academy for science and Arts
Understanding Complex Systems | Year: 2013

We examine a method of estimating unknown parameters in models of chaotic dynamical systems by synchronizing the model with the time series measured as output of the system. The method drives the model's parameters by a set of proper parameter update rules to the true values of the parameters of the modeled system. The theory on how to construct this parameter update rules is given along with simple demonstrations with the Lorenz and Rössler systems. Both the scenario when the output represents the full system of the state, and the case when it is a scalar time series representing a function of the system variables are considered. We demonstrate how to apply the method for estimating the topology of a network of chaotic oscillators. Finally, we illustrate its application to estimating parameters of spatially extended systems that possess translational symmetry with a toy atmospheric model. © 2013 Springer-Verlag Berlin Heidelberg.


Stanoev A.,Macedonian Academy for science and Arts | Stanoev A.,Max Planck Institute of Molecular Physiology | Filiposka S.,Ss. Cyril and Methodius University of Skopje | In V.,Space and Naval Warfare Systems Center Pacific | And 3 more authors.
Ad Hoc Networks | Year: 2016

In order to obtain an efficient wireless sensor network localization, several enhancements based on the decentralized approach are proposed. These features can be used in the cases when multiple distance measurements are used as input, where each node iteratively updates its estimated position using a maximum likelihood estimation method based on the previously estimated positions of its neighbors. Three novel features are introduced. First, a backbone is constructed, that is, a subset of nodes that are intermediaries between multiple beacon nodes, which guides the localization process of the other (non-backbone) nodes. Second, the space is perturbed more often during the earlier time steps to avoid reaching poor local minima in some cases regarding the localization optimization function. Third, for better localization of the non-backbone (or peripheral) nodes and avoidance of the rigidity problem, 2-hop neighboring distances are approximated. The introduced features are incorporated in a range-based algorithm that is fully distributed, shows good performance, and is scalable to arbitrary network size. © 2016 Elsevier B.V.


Stanoev A.,Macedonian Academy for science and Arts | Smilkov D.,Macedonian Academy for science and Arts | Kocarev L.,Macedonian Academy for science and Arts | Kocarev L.,University of California at San Diego
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

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. © 2011 American Physical Society.


Smilkov D.,Macedonian Academy for science and Arts | Kocarev L.,Macedonian Academy for science and Arts | Kocarev L.,University of California at San Diego
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

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. © 2011 American Physical Society.


Trpevski D.,Macedonian Academy for science and Arts | Tang W.K.S.,City University of Hong Kong | Kocarev L.,Macedonian Academy for science and Arts | Kocarev L.,University of California at San Diego
ISCAS 2010 - 2010 IEEE International Symposium on Circuits and Systems: Nano-Bio Circuit Fabrics and Systems | Year: 2010

In this paper, a novel model for opinion dissemination over network is suggested so that market penetration activities can be described. The model assumes the existence of two different products, one of which is always considered first and the supporters' (or users') opinions are allowed to propagate among individuals of the population. This is to describe the dynamics of market penetration of a particular product, by gaining the market share of its competitor or attracting new users, even the competitor is with higher reputation. From the simulation results, it is found that the product with lower preference can still obtain a non-zero fraction of market share in many cases, when a small-world network is considered. Some level of clustering in the network facilitates the adoption of the product, while increasing randomness undermines its existence. The simulations also show the importance of the users' remembrance of a product and the communication effectiveness in related to market penetration. ©2010 IEEE.


Kocarev L.,Macedonian Academy for science and Arts | Zlatanov N.,Macedonian Academy for science and Arts | Trajanov D.,Macedonian Academy for science and Arts
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2010

The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks-the network of infrastructures and the EU power grid-identifying the most vulnerable nodes of these networks. © 2010 The Royal Society.


Smilkov D.,Massachusetts Institute of Technology | Smilkov D.,Macedonian Academy for science and Arts | Hidalgo C.A.,Massachusetts Institute of Technology | Kocarev L.,Macedonian Academy for science and Arts | And 2 more authors.
Scientific Reports | Year: 2014

The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that-for the SIS model-differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node's degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.


Trpevski D.,Macedonian Academy for science and Arts | Tang W.K.S.,City University of Hong Kong | Kocarev L.,Macedonian Academy for science and Arts | Kocarev L.,University of California at San Diego
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

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. © 2010 The American Physical Society.


Smilkov D.,Macedonian Academy for science and Arts | Kocarev L.,University of California at San Diego
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

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. © 2012 American Physical Society.


PubMed | Macedonian Academy for science and Arts
Type: Journal Article | Journal: Physical review. E, Statistical, nonlinear, and soft matter physics | Year: 2012

The influence of the networks 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 nodes 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 is obtained using only two-hop neighborhoods, which account for 0.4% of the entire network topology on average.

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