Predicting Dynamics on Networks Hardly Depends on the Topology

Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an unknown network, based on past observations of the dynamics. For a general class of governing equations, we propose a prediction algorithm which infers the network as an intermediate step. Inferring the network is impossible in practice, due to a dramatically ill-conditioned linear system. Surprisingly, a highly accurate prediction of the dynamics is possible nonetheless: Even though the inferred network has no topological similarity with the true network, both networks result in practically the same future dynamics

Communication and Collaboration Between Home and School With Digital Media: Current State of Research and Research Agenda

BMBF und KMK fordern in aktuellen Strategiepapieren zur «Bildung in der digitalen Welt» eine Erweiterung der Kommunikation und Kooperation auf allen Ebenen der Schulgemeinschaft. Der Digitalisierung wird in diesem Zusammenhang das Potenzial zugeschrieben, den Informationsfluss und die Zusammenarbeit zwischen Lehrkräften und Eltern verbessern und eine stärkere Mitbestimmung am schulischen Leben fördern zu können. Der Beitrag diskutiert, inwiefern sich für diese Optimierungsunterstellung Hinweise in der Forschung finden lassen. Es zeigt sich, dass die Forschung in diesem Bereich noch am Anfang steht. Wichtige Fragen zur Rolle digitaler Medien in den Kommunikations- und Kooperationsprozessen zwischen Eltern und Schule, zur aktuellen Verbreitung und Verwendung digitaler Technologien und zu den dadurch bewirkten Veränderungen der Zusammenarbeit zwischen Elternhaus und Schule können derzeit nicht umfassend beantwortet werden. Im vorliegenden Beitrag werden deshalb zum einen wichtige Merkmale und Rahmenbedingungen einer gelingenden Zusammenarbeit herausgearbeitet und erste Forschungsergebnisse zu den Besonderheiten und Veränderungen einer digital unterstützten Kommunikation und Kooperation zusammengefasst. Zum anderen werden aktuelle Forschungsdesiderate beschrieben und eine Forschungsagenda für diesen zentralen Bereich von Schule entworfen.In current strategy papers on the issues and challenges of education in a digital world education policy makers call for an expansion of communication and cooperation at all levels of the school community (KMK 2016). In this context, digital technologies are seen as having the potential to improve the flow of information and collaboration between teachers and parents, and to promote greater participation in school life. In this article, we discuss how evidence in recent research supports the postulated «optimization assumption» and identify current research desiderata in this field. However, research in this area is still in its beginning stages. Important questions about the role of digital media for communication and cooperation processes between parents and school, about the current use and dissemination of digital technologies, and about the resulting changes in home-school cooperation are not comprehensively addressed in present research. Therefore, in this article, we identify important characteristics and conditions for successful home-school cooperation and – in using this as a framework – summarize existing research results on digitally supported communication and cooperation between parents and school. We then describe current research desiderata and draft a research agenda for future research in this field

Transition from time-variant to static networks: timescale separation in NIMFA SIS epidemics

We extend the N-intertwined mean-field approximation (NIMFA) for the Susceptible-Infectious-Susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analysed under the assumption that the process and network evolution happen on different timescales. This approximation is called timescale separation. We investigate timescale separation between disease spreading and topology updates of the network. We introduce the transition times $\mathrm{\underline{T}}(r)$ and $\mathrm{\overline{T}}(r)$ as the boundaries between the intermediate regime and the annealed (fast changing network) and quenched (static network) regimes, respectively. By analysing the convergence of static NIMFA processes, we analytically derive upper and lower bounds for $\mathrm{\overline{T}}(r)$. Our results provide insights/bounds on the time of convergence to the steady state of the static NIMFA SIS process. We show that, under our assumptions, the upper transition time $\mathrm{\overline{T}}(r)$ is almost entirely determined by the basic reproduction number $R_0$ of the network. The value of the upper transition time $\mathrm{\overline{T}}(r)$ around the epidemic threshold is large, which agrees with the current understanding that some real-world epidemics cannot be approximated with the aforementioned timescale separation.Comment: 30 pages, 13 figure

Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequency-specific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequency-specific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated in-silico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical resting-state MEG data obtained from healthy subjects and reconstructed two-layered networks consisting of either alpha-to-beta or theta-to-gamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by one-to-one interactions for both alpha-to-beta band and theta-to-gamma band networks. For theta-gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the one-to-one connections. Our work is an stepping stone towards the identification of interdependencies across frequency-specific networks. Our results lay the ground for the use of the promising multilayer framework in this field with more-informed and justified interlayer connections

Backtracking-based dynamic programming for resolving transmit ambiguities in WSN localization

Abstract The complexity of agent localization increases significantly when unique identification of the agents is not possible. Corresponding application cases include multiple-source localization, in which the agents do not have identification sequences at all, and scenarios in which it is infeasible to send sufficiently long identification sequences, e.g., for highly resource-limited agents. The complexity increase is due to the need to solve an additional optimization problem to resolve the indifferentiability of the agents and thus to enable their localization. In this work, we present a thorough analysis of this problem and propose a maximum a posteriori (MAP)-optimal algorithm based on graph decompositions and expression trees. The proposed algorithm efficiently exploits the fixed-parameter tractability of the underlying graph-theoretical problem and employs dynamic programming and backtracking. We show that the proposed algorithm is able to reduce the run time by up to 88.3% compared with a corresponding MAP-optimal integer linear programming formulation