Electrical and Electronic Engineering - Research Publications

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Author: Ahmadizadeh, Saeed × End date: 2019 × Start date: 2017 × Type: Journal Article ×

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    Corrigendum to "On eigenvalues of Laplacian matrix for a class of directed signed graphs" (vol 523, pg 281, 2017)
    Ahmadizadeh, S ; Shames, I ; Martin, S ; Nesic, D (Elsevier, 2017-10-01)
    This note corrects an error in the results of Subsection 3.1 in authors' paper “On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs”, which appeared in Linear Algebra and its Applications 523 (2017), 281–306.
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    On eigenvalues of Laplacian matrix for a class of directed signed graphs
    Ahmadizadeh, S ; Shames, I ; Martin, S ; Nesic, D (ELSEVIER SCIENCE INC, 2017-06-15)
    The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. The Laplacian matrix naturally arises in a wide range of applications involving networks. First, a class of directed signed graphs is studied in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary and sufficient condition is proposed to attain the following objective for the perturbed graph: the real parts of the non-zero eigenvalues of its Laplacian matrix are positive. Under certain assumption on the unperturbed graph, it is established that the objective is achieved if and only if the magnitudes of the added negative weights are smaller than an easily computable upper bound. This upper bound is shown to depend on the topology of the unperturbed graph. It is also pointed out that the obtained condition can be applied in a recursive manner to deal with multiple edges with negative weights. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.
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    Bifurcation analysis of two coupled Jansen-Rit neural mass models
    Ahmadizadeh, S ; Karoly, PJ ; Nesic, D ; Grayden, DB ; Cook, MJ ; Soudry, D ; Freestone, DR ; Cymbalyuk, G (PUBLIC LIBRARY SCIENCE, 2018-03-27)
    We investigate how changes in network structure can lead to pathological oscillations similar to those observed in epileptic brain. Specifically, we conduct a bifurcation analysis of a network of two Jansen-Rit neural mass models, representing two cortical regions, to investigate different aspects of its behavior with respect to changes in the input and interconnection gains. The bifurcation diagrams, along with simulated EEG time series, exhibit diverse behaviors when varying the input, coupling strength, and network structure. We show that this simple network of neural mass models can generate various oscillatory activities, including delta wave activity, which has not been previously reported through analysis of a single Jansen-Rit neural mass model. Our analysis shows that spike-wave discharges can occur in a cortical region as a result of input changes in the other region, which may have important implications for epilepsy treatment. The bifurcation analysis is related to clinical data in two case studies.