Spectral Perturbation and Reconstructability of Complex Networks

In recent years, many network perturbation techniques, such as topological perturbations and service perturbations, were employed to study and improve the robustness of complex networks. However, there is no general way to evaluate the network robustness. In this paper, we propose a new global measure for a network, the reconstructability coefficient {\theta}, defined as the maximum number of eigenvalues that can be removed, subject to the condition that the adjacency matrix can be reconstructed exactly. Our main finding is that a linear scaling law, E[{\theta}]=aN, seems universal, in that it holds for all networks that we have studied.Comment: 9 pages, 10 figure

Effective graph resistance

AbstractThis paper studies an interesting graph measure that we call the effective graph resistance. The notion of effective graph resistance is derived from the field of electric circuit analysis where it is defined as the accumulated effective resistance between all pairs of vertices. The objective of the paper is twofold. First, we survey known formulae of the effective graph resistance and derive other representations as well. The derivation of new expressions is based on the analysis of the associated random walk on the graph and applies tools from Markov chain theory. This approach results in a new method to approximate the effective graph resistance. A second objective of this paper concerns the optimisation of the effective graph resistance for graphs with given number of vertices and diameter, and for optimal edge addition. A set of analytical results is described, as well as results obtained by exhaustive search. One of the foremost applications of the effective graph resistance we have in mind, is the analysis of robustness-related problems. However, with our discussion of this informative graph measure we hope to open up a wealth of possibilities of applying the effective graph resistance to all kinds of networks problems

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Integrating cross-frequency and within band functional networks in resting-state MEG: A multi-layer network approach

Neuronal oscillations exist across a broad frequency spectrum, and are thought to provide a mechanism of interaction between spatially separated brain regions. Since ongoing mental activity necessitates the simultaneous formation of multiple networks, it seems likely that the brain employs interactions within multiple frequency bands, as well as cross-frequency coupling, to support such networks. Here, we propose a multi-layer network framework that elucidates this pan-spectral picture of network interactions. Our network consists of multiple layers (frequency-band specific networks) that influence each other via inter-layer (cross-frequency) coupling. Applying this model to MEG resting-state data and using envelope correlations as connectivity metric, we demonstrate strong dependency between within layer structure and inter-layer coupling, indicating that networks obtained in different frequency bands do not act as independent entities. More specifically, our results suggest that frequency band specific networks are characterised by a common structure seen across all layers, superimposed by layer specific connectivity, and inter-layer coupling is most strongly associated with this common mode. Finally, using a biophysical model, we demonstrate that there are two regimes of multi-layer network behaviour; one in which different layers are independent and a second in which they operate highly dependent. Results suggest that the healthy human brain operates at the transition point between these regimes, allowing for integration and segregation between layers. Overall, our observations show that a complete picture of global brain network connectivity requires integration of connectivity patterns across the full frequency spectrum

Insights in a restricted temporary pacemaker strategy in a lean transcatheter aortic valve implantation program

OBJECTIVES: To study the safety and feasibility of a restrictive temporary‐RV‐pacemaker use and to evaluate the need for temporary pacemaker insertion for failed left ventricular (LV) pacing ability (no ventricular capture) or occurrence of high‐degree AV‐blocks mandating continuous pacing. BACKGROUND: Ventricular pacing remains an essential part of contemporary transcatheter aortic valve implantation (TAVI). A temporary‐right‐ventricle (RV)‐pacemaker lead is the standard approach for transient pacing during TAVI but requires central venous access. METHODS: An observational registry including 672 patients who underwent TAVI between June 2018 and December 2020. Patients received pacing on the wire when necessary, unless there was a high‐anticipated risk for conduction disturbances post‐TAVI, based on the baseline‐ECG. The follow‐up period was 30 days. RESULTS: A temporary‐RV‐pacemaker lead (RVP‐cohort) was inserted in 45 patients, pacing on the wire (LVP‐cohort) in 488 patients, and no pacing (NoP‐cohort) in 139 patients. A bailout temporary pacemaker was implanted in 14 patients (10.1%) in the NoP‐cohort and in 24 patients (4.9%) in the LVP‐cohort. One patient in the LVP‐cohort needed an RV‐pacemaker for incomplete ventricular capture. Procedure time was significantly longer in the RVP‐cohort (68 min [IQR 52–88.] vs. 55 min [IQR 44–72] in NoP‐cohort and 55 min [IQR 43–71] in the LVP‐cohort [p < 0.005]). Procedural high‐degree AV‐block occurred most often in the RVP‐cohort (45% vs. 14% in the LVP and 16% in the NoP‐cohort [p ≤ 0.001]). Need for new PPI occurred in 47% in the RVP‐cohort, versus 20% in the NoP‐cohort and 11% in the LVP‐cohort (p ≤ 0.001). CONCLUSION: A restricted RV‐pacemaker strategy is safe and shortens procedure time. The majority of TAVI‐procedures do not require a temporary‐RV‐pacemaker

Architectural aspects of QoS-aware personal networks

Personal Networks (PN) are future communication systems that combine wireless and infracuture based networks to provide users a variety of services anywhere and anytime. PNs introduce new design challenges due to the heterogeneity of the involved technologies, the need for self-organization, the dynamics of the system composition, the application-driven nature, the co-operation with infrastructure-based networks, and the security hazards. This paper discusses the challenges of security and QoS provisioning in designing self-organized personal networks and combines them all into an integrated architectural framework