Browsing by Author "Atay, Fatihcan M."
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Item Open Access Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes(Hacettepe University, 2020) Gölgeli, M.; Atay, Fatihcan M.Infectious diseases are a serious problem for public health and spark the interest in interdisciplinary studies. In this paper, we present two mathematical models describing a possible scenario for infectious diseases. The first model considers the dynamics of the disease among adults and emphasizes the role of carriers in the SIR model and the second model assumes that the disease is transmitted to children by adults. We state the equilibria for each model and study the local stability of the equilibria. Furthermore, we perform simulations using a parameter set that explains the spread of a specific infectious disease (meningococcal disease) and interpret the possible cases of transmission via simulations.Item Open Access Bifurcation analysis of the dynamics of interacting subnetworks of a spiking network(Nature Publishing Group, 2019-08) Lagzi, F.; Atay, Fatihcan M.; Rotter, S.We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or diferent nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two diferent network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the efect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.Item Open Access Cheeger constants, structural balance, and spectral clustering analysis for signed graphs(Elsevier, 2020-01-01) Atay, Fatihcan M.; Liu, S.We introduce a family of multi-way Cheeger-type constants{hσk,k=1,2,...,n}on asigned graphΓ=(G,σ) such thathσk=0 if and only ifΓhaskbalanced connectedcomponents. These constants are switching invariant and bring together in a unifiedviewpoint a number of important graph-theoretical concepts, including the classicalCheeger constant, those measures of bipartiteness introduced by Desai-Rao, Trevisan,Bauer–Jost, respectively, on unsigned graphs, and the frustration index (originally calledthelineindexofbalancebyHarary)onsignedgraphs.Wefurtherunifythe(higher-orderor improved) Cheeger and dual Cheeger inequalities for unsigned graphs as well as theunderlying algorithmic proof techniques by establishing their corresponding versionson signed graphs. In particular, we develop a spectral clustering method for findingkalmost-balanced subgraphs, each defining a sparse cut. The proper metric for sucha clustering is the metric on a real projective space. We also prove estimates of theextremal eigenvalues of signed Laplace matrix in terms of number of signed triangles(3-cycles).Item Open Access Correction to: Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy(Springer, 2021-06-14) Bulut, H.; Gölgeli, M.; Atay, Fatihcan M.Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARS-CoV-2 pandemic, individuals follow these measures with varying degrees of meticulousness, as the perceptions regarding the impending danger and the efficacy of the measures are not uniform within a population. In this paper, a compartmental mathematical model is presented that takes into account the importance of personal cautiousness (as evidenced, for example, by personal hygiene habits and carefully following the rules) during the COVID-19 pandemic. Two countries, Turkey and Italy, are studied in detail, as they share certain social commonalities by their Mediterranean cultural codes. A mathematical analysis of the model is performed to find the equilibria and their local stability, focusing on the transmission parameters and investigating the sensitivity with respect to the parameters. Focusing on the (assumed) viral exposure rate, possible scenarios for the spread of COVID-19 are examined by varying the viral exposure of incautious people to the environment. The presented results emphasize and quantify the importance of personal cautiousness in the spread of the disease.Item Open Access A delayed consensus algorithm in networks of anticipatory agents(IEEE, 2016) Atay, Fatihcan M.; Irofti, D.We introduce and analyze a delayed consensus algorithm as a model for interacting agents using anticipation of their neighbors' states to improve convergence to consensus. We derive a necessary and sufficient condition for the system to reach consensus. Furthermore, we explicitly calculate the dominant characteristic root of the consensus problem as a measure of the speed of convergence. The results show that the anticipatory algorithm can improve the speed of consensus, especially in networks with poor connectivity. Hence, anticipation can improve performance in networks if the delay parameter is chosen judiciously, otherwise the system might diverge as agents try to anticipate too aggressively into the future.Item Open Access Deriving pairwise transfer entropy from network structure and motifs(Royal Society Publishing, 2020) Novelli, L.; Atay, Fatihcan M.; Jost, J.; Lizier, J. T.Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.Item Open Access Preface(Springer Science and Business Media Deutschland GmbH, 2020) Atay, Fatihcan M.; Kurasov, P. B.; Mugnolo, D.; Atay, F. M.; Kurasov, P. B.; Mugnolo, D.Item Open Access Robustness and delay margin analysis of a gene regulatory network model(Elsevier, 2022-10-10) Öztürk, Dilan; Özbay, Hitay; Atay, Fatihcan M.In the past, a special type of nonlinear delay differential system structure was proposed for gene regulatory networks. For this cyclic dynamical system, stability analysis was done using various tools from systems theory. This paper investigates robust stability of an extended gene regulatory network model with time delayed negative feedback. Specifically, the delay margin analysis is done for this system under multiplicative uncertainty. The effect of uncertainty on the delay margin is determined. It is also shown that for particular higher order extensions of the model it is possible to improve the delay margin.Item Open Access Stability of phase difference trajectories of networks of kuramoto oscillators with time-varying couplings and intrinsic frequencies(Society for Industrial and Applied Mathematics Publications, 2018) Lu, W.; Atay, Fatihcan M.We study dynamics of phase differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In the case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable if there exists T > 0 such that the aggregation of the time-varying graphs across any time interval of length T has a spanning tree. We also consider the situation that the coupling coefficients may be negative and provide sufficient conditions for the asymptotic stability of the PD dynamics. Due to time variations, the PDs are asymptotic to time-varying patterns rather than constant values. Hence, the PD dynamics can be regarded as a generalization of the well-known phase-locking phenomena. We explicitly investigate several particular cases of time-varying graph structures, including asymptotically periodic PDs due to periodic coupling coefficients and intrinsic frequencies, small perturbations, and fast-switching near constant coupling and frequencies, which lead to PD dynamics close to a phase-locked one. Numerical examples are provided to illustrate the theoretical results.Item Open Access Synchronization in networks of anticipatory agents(IEEE - Institute of Electrical and Electronics Engineers, 2023-07-17) Dönmez, Bengi; Atay, Fatihcan M.We consider a coupled Kuramoto system composed of agents that anticipate the future states of their neighbors based on past data and try to align their states accordingly. We show that this anticipatory behavior results in multiple synchronized solutions at different collective frequencies and different stability characteristics. We derive an exact condition for the stability of the synchronized states. We show that the system can exhibit multistability, converging to different synchronized solutions depending on the initial conditions.